yields of produced particles

I want to research papers contain tables, as in the accompanying publications .

(yields of produced particles) (STAR 26, Page 26, TABLE VIII) , (PHENIX 30, Page 30 , TABLE II) , (PHENIX 16 Page 16 , TABLE VIII).

I want seven publications contain tables (Pi, K ,P,intPi,intK,intP)(dN/dy), but do not want to duplicate tables.

You can find papers PHENIX, ALCE, CMS, STARand ATLAS collaborations.

arXiv:nucl-ex/0307022v1 28 Jul 2003 Identified Charged Particle Spectra and Yields in Au+Au Collisions at √ sNN = 200 GeV S.S. Adler, 5 S. Afanasiev,17 C. Aidala, 5 N.N. Ajitanand,43 Y. Akiba,20, 38 J. Alexander,43 R. Amirikas,12 L. Aphecetche,45 S.H. Aronson, 5 R. Averbeck,44 T.C. Awes,35 R. Azmoun,44 V. Babintsev,15 A. Baldisseri,10 K.N. Barish, 6 P.D. Barnes,27 B. Bassalleck,33 S. Bathe,30 S. Batsouli, 9 V. Baublis,37 A. Bazilevsky,39, 15 S. Belikov,16, 15 Y. Berdnikov,40 S. Bhagavatula,16 J.G. Boissevain,27 H. Borel,10 S. Borenstein,25 M.L. Brooks,27 D.S. Brown,34 N. Bruner,33 D. Bucher,30 H. Buesching,30 V. Bumazhnov,15 G. Bunce,5, 39 J.M. Burward-Hoy,26, 44 S. Butsyk,44 X. Camard,45 J.-S. Chai,18 P. Chand, 4 W.C. Chang, 2 S. Chernichenko,15 C.Y. Chi, 9 J. Chiba,20 M. Chiu, 9 I.J. Choi,52 J. Choi,19 R.K. Choudhury, 4 T. Chujo, 5 V. Cianciolo,35 Y. Cobigo,10 B.A. Cole, 9 P. Constantin,16 D.G. d’Enterria,45 G. David, 5 H. Delagrange,45 A. Denisov,15 A. Deshpande,39 E.J. Desmond, 5 O. Dietzsch,41 O. Drapier,25 A. Drees,44 R. du Rietz,29 A. Durum,15 D. Dutta, 4 Y.V. Efremenko,35 K. El Chenawi,49 A. Enokizono,14 H. En’yo,38, 39 S. Esumi,48 L. Ewell, 5 D.E. Fields,33, 39 F. Fleuret,25 S.L. Fokin,23 B.D. Fox,39 Z. Fraenkel,51 J.E. Frantz, 9 A. Franz, 5 A.D. Frawley,12 S.-Y. Fung, 6 S. Garpman,29, ∗ T.K. Ghosh,49 A. Glenn,46 G. Gogiberidze,46 M. Gonin,25 J. Gosset,10 Y. Goto,39 R. Granier de Cassagnac,25 N. Grau,16 S.V. Greene,49 M. Grosse Perdekamp,39 W. Guryn, 5 H.- ˚A. Gustafsson,29 T. Hachiya,14 J.S. Haggerty, 5 H. Hamagaki, 8 A.G. Hansen,27 E.P. Hartouni,26 M. Harvey, 5 R. Hayano, 8 X. He,13 M. Heffner,26 T.K. Hemmick,44 J.M. Heuser,44 M. Hibino,50 J.C. Hill,16 W. Holzmann,43 K. Homma,14 B. Hong,22 A. Hoover,34 T. Ichihara,38, 39 V.V. Ikonnikov,23 K. Imai,24, 38 D. Isenhower, 1 M. Ishihara,38 M. Issah,43 A. Isupov,17 B.V. Jacak,44 W.Y. Jang,22 Y. Jeong,19 J. Jia,44 O. Jinnouchi,38 B.M. Johnson, 5 S.C. Johnson,26 K.S. Joo,31 D. Jouan,36 S. Kametani,8, 50 N. Kamihara,47, 38 J.H. Kang,52 S.S. Kapoor, 4 K. Katou,50 S. Kelly, 9 B. Khachaturov,51 A. Khanzadeev,37 J. Kikuchi,50 D.H. Kim,31 D.J. Kim,52 D.W. Kim,19 E. Kim,42 G.-B. Kim,25 H.J. Kim,52 E. Kistenev, 5 A. Kiyomichi,48 K. Kiyoyama,32 C. Klein-Boesing,30 H. Kobayashi,38, 39 L. Kochenda,37 V. Kochetkov,15 D. Koehler,33 T. Kohama,14 M. Kopytine,44 D. Kotchetkov, 6 A. Kozlov,51 P.J. Kroon, 5 C.H. Kuberg,1, 27 K. Kurita,39 Y. Kuroki,48 M.J. Kweon,22 Y. Kwon,52 G.S. Kyle,34 R. Lacey,43 V. Ladygin,17 J.G. Lajoie,16 A. Lebedev,16, 23 S. Leckey,44 D.M. Lee,27 S. Lee,19 M.J. Leitch,27 X.H. Li, 6 H. Lim,42 A. Litvinenko,17 M.X. Liu,27 Y. Liu,36 C.F. Maguire,49 Y.I. Makdisi, 5 A. Malakhov,17 V.I. Manko,23 Y. Mao,7, 38 G. Martinez,45 M.D. Marx,44 H. Masui,48 F. Matathias,44 T. Matsumoto,8, 50 P.L. McGaughey,27 E. Melnikov,15 F. Messer,44 Y. Miake,48 J. Milan,43 T.E. Miller,49 A. Milov,44, 51 S. Mioduszewski, 5 R.E. Mischke,27 G.C. Mishra,13 J.T. Mitchell, 5 A.K. Mohanty, 4 D.P. Morrison, 5 J.M. Moss,27 F. M¨uhlbacher,44 D. Mukhopadhyay,51 M. Muniruzzaman, 6 J. Murata,38, 39 S. Nagamiya,20 J.L. Nagle, 9 T. Nakamura,14 B.K. Nandi, 6 M. Nara,48 J. Newby,46 P. Nilsson,29 A.S. Nyanin,23 J. Nystrand,29 E. O’Brien, 5 C.A. Ogilvie,16 H. Ohnishi,5, 38 I.D. Ojha,49, 3 K. Okada,38 M. Ono,48 V. Onuchin,15 A. Oskarsson,29 I. Otterlund,29 K. Oyama, 8 K. Ozawa, 8 D. Pal,51 A.P.T. Palounek,27 V.S. Pantuev,44 V. Papavassiliou,34 J. Park,42 A. Parmar,33 S.F. Pate,34 T. Peitzmann,30 J.-C. Peng,27 V. Peresedov,17 C. Pinkenburg, 5 R.P. Pisani, 5 F. Plasil,35 M.L. Purschke, 5 A.K. Purwar,44 J. Rak,16 I. Ravinovich,51 K.F. Read,35, 46 M. Reuter,44 K. Reygers,30 V. Riabov,37, 40 Y. Riabov,37 G. Roche,28 A. Romana,25 M. Rosati,16 P. Rosnet,28 S.S. Ryu,52 M.E. Sadler, 1 N. Saito,38, 39 T. Sakaguchi,8, 50 M. Sakai,32 S. Sakai,48 V. Samsonov,37 L. Sanfratello,33 R. Santo,30 H.D. Sato,24, 38 S. Sato,5, 48 S. Sawada,20 Y. Schutz,45 V. Semenov,15 R. Seto, 6 M.R. Shaw,1, 27 T.K. Shea, 5 T.-A. Shibata,47, 38 K. Shigaki,14, 20 T. Shiina,27 C.L. Silva,41 D. Silvermyr,27, 29 K.S. Sim,22 C.P. Singh, 3 V. Singh, 3 M. Sivertz, 5 A. Soldatov,15 R.A. Soltz,26 W.E. Sondheim,27 S.P. Sorensen,46 I.V. Sourikova, 5 F. Staley,10 P.W. Stankus,35 E. Stenlund,29 M. Stepanov,34 A. Ster,21 S.P. Stoll, 5 T. Sugitate,14 J.P. Sullivan,27 E.M. Takagui,41 A. Taketani,38, 39 M. Tamai,50 K.H. Tanaka,20 Y. Tanaka,32 K. Tanida,38 M.J. Tannenbaum, 5 P. Tarj´an,11 J.D. Tepe,1, 27 T.L. Thomas,33 J. Tojo,24, 38 H. Torii,24, 38 R.S. Towell, 1 I. Tserruya,51 H. Tsuruoka,48 S.K. Tuli, 3 H. Tydesj¨o,29 N. Tyurin,15 H.W. van Hecke,27 J. Velkovska,5, 44 M. Velkovsky,44 L. Villatte,46 A.A. Vinogradov,23 M.A. Volkov,23 E. Vznuzdaev,37 X.R. Wang,13 Y. Watanabe,38, 39 S.N. White, 5 F.K. Wohn,16 C.L. Woody, 5 W. Xie, 6 Y. Yang, 7 A. Yanovich,15 S. Yokkaichi,38, 39 G.R. Young,35 I.E. Yushmanov,23 W.A. Zajc,9, † C. Zhang, 9 S. Zhou,7, 51 and L. Zolin17 (PHENIX Collaboration) 1Abilene Christian University, Abilene, TX 79699, USA 2 Institute of Physics, Academia Sinica, Taipei 11529, Taiwa n 3Department of Physics, Banaras Hindu University, Varanasi 221005, India 4Bhabha Atomic Research Centre, Bombay 400 085, India 5Brookhaven National Laboratory, Upton, NY 11973-5000, USA 6University of California – Riverside, Riverside, CA 92521, USA 2 7China Institute of Atomic Energy (CIAE), Beijing, People’s Republic of China 8Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan 9Columbia University, New York, NY 10027 and Nevis Laboratories, Irvington, NY 10533, USA 10Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France 11Debrecen University, H-4010 Debrecen, Egyetem t´er 1, Hungary 12Florida State University, Tallahassee, FL 32306, USA 13Georgia State University, Atlanta, GA 30303, USA 14Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan 15Institute for High Energy Physics (IHEP), Protvino, Russia 16Iowa State University, Ames, IA 50011, USA 17Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia 18KAERI, Cyclotron Application Laboratory, Seoul, South Korea 19Kangnung National University, Kangnung 210-702, South Korea 20KEK, High Energy Accelerator Research Organization, Tsukuba-shi, Ibaraki-ken 305-0801, Japan 21KFKI Research Institute for Particle and Nuclear Physics (RMKI), H-1525 Budapest 114, POBox 49, Hungary 22Korea University, Seoul, 136-701, Korea 23Russian Research Center “Kurchatov Institute”, Moscow, Russia 24Kyoto University, Kyoto 606, Japan 25Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France 26Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 27Los Alamos National Laboratory, Los Alamos, NM 87545, USA 28LPC, Universit´e Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France 29Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden 30Institut fuer Kernphysik, University of Muenster, D-48149 Muenster, Germany 31Myongji University, Yongin, Kyonggido 449-728, Korea 32Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan 33University of New Mexico, Albuquerque, NM, USA 34New Mexico State University, Las Cruces, NM 88003, USA 35Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 36IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France 37PNPI, Petersburg Nuclear Physics Institute, Gatchina, Russia 38RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, JAPAN 39RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, USA 40St. Petersburg State Technical University, St. Petersburg, Russia 41Universidade de S˜ao Paulo, Instituto de F´ısica, Caixa Postal 66318, S˜ao Paulo CEP05315-970, Brazil 42System Electronics Laboratory, Seoul National University, Seoul, South Korea 43Chemistry Department, Stony Brook University, SUNY, Stony Brook, NY 11794-3400, USA 44Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794, USA 45SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Universit´e de Nantes) BP 20722 – 44307, Nantes, Franc
e 46University of Tennessee, Knoxville, TN 37996, USA 47Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan 48Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan 49Vanderbilt University, Nashville, TN 37235, USA 50Waseda University, Advanced Research Institute for Science and Engineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan 51Weizmann Institute, Rehovot 76100, Israel 52Yonsei University, IPAP, Seoul 120-749, Korea (Dated: February 5, 2008) The centrality dependence of transverse momentum distributions and yields for π ±, K±, p and p in Au+Au collisions at √ sNN = 200 GeV at mid-rapidity are measured by the PHENIX experiment at RHIC. We observe a clear particle mass dependence of the shapes of transverse momentum spectra in central collisions below ∼ 2 GeV/c in pT . Both mean transverse momenta and particle yields per participant pair increase from peripheral to mid-central and saturate at the most central collisions for all particle species. We also measure particle ratios of π −/π+, K−/K+, p/p, K/π, p/π and p/π as a function of pT and collision centrality. The ratios of equal mass particle yields are independent of pT and centrality within the experimental uncertainties. In central collisions at intermediate transverse momenta ∼ 1.5 – 4.5 GeV/c, proton and anti-proton yields constitute a significant fraction of the charged hadron production and show a scaling behavior different from that of pions. PACS numbers: 25.75.Dw ∗Deceased †PHENIX Spokesperson:zajc@nevis.columbia.edu 3 I. INTRODUCTION The motivation for ultra-relativistic heavy-ion experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is the study of nuclear matter at extremely high temperature and energy density with the hope of creating and detecting deconfined matter consisting of quarks and gluons – the quark gluon plasma (QGP). Lattice QCD calculations [1] predict that the transition to a deconfined state occurs at a critical temperature Tc ≈ 170 MeV and an energy density ǫ ≈ 2 GeV/fm3 . Based on the Bjorken estimation [2] and the measurement of transverse energy (ET ) in Au+Au collisions at √ sNN = 130 GeV [3] and 200 GeV, the spatial energy density in central Au+Au collisions at RHIC is believed to be high enough to create such deconfined matter in a laboratory [3]. The hot and dense matter produced in relativistic heavy ion collisions may evolve through the following scenario: pre-equilibrium, thermal (or chemical) equilibrium of partons, possible formation of QGP or a QGP-hadron gas mixed state, a gas of hot interacting hadrons, and finally, a freeze-out state when the produced hadrons no longer strongly interact with each other. Since produced hadrons carry information about the collision dynamics and the entire space-time evolution of the system from the initial to the final stage of collisions, a precise measure of the transverse momentum (pT ) distributions and yields of identified hadrons as a function of collision geometry is essential for the understanding of the dynamics and properties of the created matter. In the low pT region (< 2 GeV/c), hydrodynamic models [4, 5] that include radial flow successfully describe the measured pT distributions in Au+Au collisions at √ sNN = 130 GeV [6, 7, 8]. The pT spectra of identified charged hadrons below pT ≈ 2 GeV/c in central collisions have been well reproduced by two simple parameters: transverse flow velocity βT and freeze-out temperature Tf o [8] under the assumption of thermalization with longitudinal and transverse flow [4]. The particle production in this pT region is considered to be dominated by secondary interactions among produced hadrons and participating nucleons in the reaction zone. Another model which successfully describes the particle abundances at low pT is the statistical thermal model [9]. Particle ratios have been shown to be well reproduced by two parameters: a baryon chemical potential µB and a chemical freeze-out temperature Tch. It is found that there is an overall good agreement between measured particle ratios at √ sNN = 130 GeV Au+Au and the thermal model calculations [10, 11]. On the other hand, at high pT (≥ 4 GeV/c) the dominant particle production mechanism is the hard scattering described by perturbative Quantum Chromodynamics (pQCD), which produces particles from the fragmentation of energetic partons. One of the most interesting observations at RHIC is that the yield of high pT neutral pions and non-identified charged hadrons in central Au+Au collisions at RHIC are below the expectation of the scaling with the number of nucleon-nucleon binary collisions, Ncoll [12, 13, 14]. This effect could be a consequence of the energy loss suffered by partons moving through deconfined matter [15, 16]. It has also been observed that the yield of neutral pions is more strongly suppressed than that for non-identified charged hadrons [12] in central Au+Au collisions at RHIC. Another interesting feature is that the proton and antiproton yields in central events are comparable to that of pions at pT ≈ 2 GeV/c [6], differing from the expectation of pQCD. These observations suggest that a detailed study of particle composition at intermediate pT (≈ 2 – 4 GeV/c) is very important to understand hadron production and collision dynamics at RHIC. The PHENIX experiment [17] has a unique hadron identification capability in a broad momentum range. Pions and kaons are identified up to 3 GeV/c and 2 GeV/c in pT , respectively, and protons and anti-protons can be identified up to 4.5 GeV/c by using a high resolution time-of-flight detector [18]. Neutral pions are reconstructed via π 0 → γγ up to pT ≈ 10 GeV/c through an invariant mass analysis of γ pairs detected in an electromagnetic calorimeter (EMCal) [19] with wide azimuthal coverage. During the measurements of Au+Au collisions at √ sNN = 200 GeV in year 2001 at RHIC, the PHENIX experiment accumulated enough events to address the above issues at intermediate pT as well as the particle production at low pT with precise centrality dependences. In this paper, we present the centrality dependence of pT spectra, hpT i, yields, and ratios for π ±, K±, p and p in Au+Au collisions at √ sNN = 200 GeV at mid-rapidity measured by the PHENIX experiment. We also present results on the scaling behavior of charged hadrons compared with results of π 0 measurements [14], which have been published separately. The paper is organized as follows. Section II describes the PHENIX detector used in this analysis. In Section III the analysis details including event selection, track selection, particle identification, and corrections applied to the data are described. The systematic errors on the measurements are also discussed in this section. For the experimental results, centrality dependence of pT spectra for identified charged particles are presented in Section IV A, and transverse mass spectra are given in Section IV B. Particle yields and mean transverse momenta as a function of centrality are presented in Section IV C. In Section IV D the systematic study of particle ratios as a function pT and centrality are presented. Section IV E studies the scaling behavior of identified charged hadrons. A summary is given in Section V. 4 II. PHENIX DETECTOR The PHENIX experiment is composed of two central arms, two forward muon arms, and three global detectors. The east and west central arms are placed at zero rapidity and designed to detect electrons, photons and charged hadrons. The north and south forward muon arms have full azimuthal coverage and are designed to detect muons. The global detectors measure the start time, vertex, and multiplicity of the interactions. The following sections describe the parts of the detector that are used in the present analysis. A detailed description of the complete detector can be found elsewhere [17, 18, 19, 20, 21, 22]. A. Global Detectors In order to characterize the centrality of Au+Au collisions, zero-degree calorimeters (ZDC) [21] and beambeam counters (BBC) [20] are employed. The zero-de
gree calorimeters are small hadronic calorimeters which measure the energy carried by spectator neutrons. They are placed 18 m up- and downstream of the interaction point along the beam line. Each ZDC consists of three modules. Each module has a depth of 2 hadronic interaction lengths and is read out by a single photo-multiplier tube (PMT). Both time and amplitude are digitized for each PMT along with the analog sum of the three PMT signals for each ZDC. Two sets of beam-beam counters are placed 1.44 m from the nominal interaction point along the beam line (one on each side). Each counter consists of 64 Cerenkov ˇ telescopes, arranged radially around the beam line. The BBC measures the number of charged particles in the pseudo-rapidity region 3.0 < |η| < 3.9. The correlation between BBC charge sum and ZDC total energy is used for centrality determination. The BBC also provides a collision vertex position and start time information for time-of-flight measurement. B. Central Arm Detectors Charged particles are tracked using the central arm spectrometers [22]. The spectrometer on the east side of the PHENIX detector (east arm) contains the following subsystems used in this analysis: drift chamber (DC), pad chamber (PC) and time-of-flight (TOF). The drift chambers are the closest tracking detectors to the beam line – at a radial distance of 2.2 m. They measure charged particle trajectories in the azimuthal direction to determine the transverse momentum of each particle. By combining the polar angle information from the first layer of the PC with the transverse momentum, the total momentum p is determined. The momentum resolution is δp/p ≃ 0.7% ⊕ 1.0% × p (GeV/c), where the first term is due to the multiple scattering before the DC and the second term is the angular resolution of the DC. The momentum scale is known to 0.7%, from the reconstructed proton mass using the TOF. The pad chambers are multi-wire proportional chambers that form three separate layers of the central tracking system. The first pad chamber layer (PC1) is located at the radial outer edge of each drift chamber at a distance of 2.49 m, while the third layer (PC3) is 4.98 m from the interaction point. The second layer (PC2) is located at a radial distance of 4.19 m in the west arm only. PC1 and the DC, along with the vertex position measured by the BBC, are used in the global track reconstruction to determine the polar angle of each charged track. The time-of-flight detector serves as the primary particle identification device for charged hadrons by measuring the stop time. The start time is given by the BBC. The TOF wall is located at a radial distance of 5.06 m from the interaction point in the east central arm. This contains 960 scintillator slats oriented along the azimuthal direction. It is designed to cover |η| < 0.35 and ∆φ = 45o in azimuthal angle. The intrinsic timing resolution is σ ≃ 115 ps, which allows for a 3σ π/K separation up to pT ≃ 2.5 GeV/c, and 3σ K/p separation up to pT ≃ 4 GeV/c. III. DATA ANALYSIS In this section, we describe the event and track selection, charged particle identification and various corrections, including geometrical acceptance, particle decay, multiple scattering and absorption effects, detector occupancy corrections and weak decay contributions from Λ and Λ to proton and anti-proton spectra. The estimations of systematic uncertainties on the measurements are addressed at the end of this section. A. Event Selection For the present analysis, we use the PHENIX minimum bias trigger events, which are determined by a coincidence between north and south BBC signals. We also require a collision vertex within ± 30 cm from the center of the spectrometer. The collision vertex resolution determined by the BBC is about 6 mm in Au+Au collisions in minimum bias events [20]. The PHENIX minimum bias trigger events include 92.2 +2.5 −3.0% of the 6.9 barn Au+Au total inelastic cross section [14]. Figure 1 shows the correlation between the BBC charge sum and ZDC total energy for Au+Au at √ sNN = 200 GeV. The lines on the plot indicate the centrality definition in the analysis. For the centrality determination, these events are subdivided into 11 bins using the BBC and ZDC correlation: 0–5%, 5–10%, 10–15%, 15–20%, 20–30%, …, 70–80% and 80–92%. Due to the statistical limitations in the peripheral events, we also use the 60–92% centrality bin as the 5 FIG. 1: BBC versus ZDC analog response. The lines represent the centrality cut boundaries. TABLE I: The average nuclear overlap function (hTAuAui), the number of nucleon-nucleon binary collisions (hNcolli), and the number of participant nucleons (hNparti) obtained from a Glauber Monte Carlo [8, 14] correlated with the BBC and ZDC response for Au+Au at √ sNN = 200 GeV as a function of centrality. Centrality is expressed as percentiles of σAuAu = 6.9 barn with 0% representing the most central collisions. The last line refers to minimum bias collisions. Centrality hTAuAui (mb−1 ) hNcolli hNparti 0- 5% 25.37 ± 1.77 1065.4 ± 105.3 351.4 ± 2.9 0-10% 22.75 ± 1.56 955.4 ± 93.6 325.2 ± 3.3 5-10% 20.13 ± 1.36 845.4 ± 82.1 299.0 ± 3.8 10-15% 16.01 ± 1.15 672.4 ± 66.8 253.9 ± 4.3 10-20% 14.35 ± 1.00 602.6 ± 59.3 234.6 ± 4.7 15-20% 12.68 ± 0.86 532.7 ± 52.1 215.3 ± 5.3 20-30% 8.90 ± 0.72 373.8 ± 39.6 166.6 ± 5.4 30-40% 5.23 ± 0.44 219.8 ± 22.6 114.2 ± 4.4 40-50% 2.86 ± 0.28 120.3 ± 13.7 74.4 ± 3.8 50-60% 1.45 ± 0.23 61.0 ± 9.9 45.5 ± 3.3 60-70% 0.68 ± 0.18 28.5 ± 7.6 25.7 ± 3.8 60-80% 0.49 ± 0.14 20.4 ± 5.9 19.5 ± 3.3 60-92% 0.35 ± 0.10 14.5 ± 4.0 14.5 ± 2.5 70-80% 0.30 ± 0.10 12.4 ± 4.2 13.4 ± 3.0 70-92% 0.20 ± 0.06 8.3 ± 2.4 9.5 ± 1.9 80-92% 0.12 ± 0.03 4.9 ± 1.2 6.3 ± 1.2 min. bias 6.14 ± 0.45 257.8 ± 25.4 109.1 ± 4.1 most peripheral bin. After event selection, we analyze 2.02×107 minimum bias events, which represents ∼ 140 times more events than used in our published Au+Au data at 130 GeV [6, 8]. Based on a Glauber model calculation [8, 14] we use two global quantities to characterize the event centrality: the average number of participants hNparti and the average number of collisions hNcolli associated with each centrality bin (Table I). FIG. 2: Mass squared versus momentum multiplied by charge distribution in Au+Au collisions at √ sNN = 200 GeV. The lines indicate the PID cut boundaries for pions, kaons, and protons (anti-protons) from left to right, respectively. B. Track Selection Charged particle tracks are reconstructed by the DC based on a combinatorial Hough transform [25] – which gives the angle of the track in the main bend plane. The main bend plane is perpendicular to the beam axis (azimuthal direction). PC1 is used to measure the position of the hit in the longitudinal direction (along the beam axis). When combined with the location of the collision vertex along the beam axis (from the BBC), the PC1 hit gives the polar angle of the track. Only tracks with valid information from both the DC and PC1 are used in the analysis. In order to associate a track with a hit on the TOF, the track is projected to its expected hit location on the TOF. Tracks are required to have a hit on the TOF within ±2σ of the expected hit location in both the azimuthal and beam directions. Finally, a cut on the energy loss in the TOF scintillator is applied to each track. This β-dependent energy loss cut is based on a parameterization of the Bethe-Bloch formula, i.e. dE/dx ≈ β −5/3 , where β = L/(c · tTOF), L is the pathlength of the track trajectory from the collision vertex to the hit position of the TOF wall, tTOF is the time-of- flight, and c is the speed of light. The flight path-length is calculated from a fit to the reconstructed track trajectory. The background due to random association of DC/PC1 tracks with TOF hits is reduced to a negligible level when the mass cut used for particle identification is applied (described in the next section). 6 C. Particle Identification The charged particle identification (PID) is performed by using the combination of three measurements: timeof-flight from the
BBC and TOF, momentum from the DC, and flight path-length from the collision vertex point to the hit position on the TOF wall. The square of the mass is derived from the following formula, m2 = p 2 c 2 htTOF L/c 2 − 1 i , (1) where p is the momentum, tTOF is the time-of-flight, L is a flight path-length, and c is the speed of light. The charged particle identification is performed using cuts in m2 and momentum space. In Figure 2, a plot of m2 versus momentum multiplied by charge is shown together with applied PID cuts as solid curves. We use 2σ standard deviation PID cuts in m2 and momentum space for each particle species. The PID cut is based on a parameterization of the measured m2 width as a function of momentum, σ 2 m2 = σ 2 α K2 1 (4m4 p 2 ) + σ 2 ms K2 1 h 4m4 1 + m2 p 2 i + σ 2 t c 2 L2 4p 2 m2 + p 2 , (2) where σα is the angular resolution, σms is the multiple scattering term, σt is the overall time-of-flight resolution, m is the centroid of m2 distribution for each particle species, and K1 is a magnetic field integral constant term of 87.0 mrad·GeV. The parameters for PID are, σα = 0.835 mrad, σms = 0.86 mrad·GeV and σt = 120 ps. Through improvements in alignment and calibrations, the momentum resolution is improved over the 130 GeV data [8]. The centrality dependence of the width and the mean position of the m2 distribution has also been checked. There is no clear difference seen between central and peripheral collisions. For pion identifi- cation above 2 GeV/c, we apply an asymmetric PID cut to reduce kaon contamination of the pions. As shown by the lines in Figure 2, the overlap region which is within the 2σ cuts for both pions and kaons is excluded. For kaons, the upper momentum cut-off is 2 GeV/c since the pion contamination level for kaons is ≈ 10% at that momentum. The upper momentum cut-off on the pions is pT = 3 GeV/c – where the kaon contamination reaches ≈ 10%. The contamination of protons by kaons reaches about 5% at 4 GeV/c. Electron (positron) and decay muon background at very low pT (< 0.3 GeV/c) are well separated from the pion mass-squared peak. The contamination background on each particle species is not subtracted in the analysis. For protons, the upper momentum cut-off is set at 4.5 GeV/c due to statistical limitations and background at high pT . An additional cut on m2 for protons and anti-protons, m2 > 0.6 (GeV/c2 ) 2 , is mult ε 0.6 0.7 0.8 0.9 1 Positive + π + K p Npart 0 50 100 150 200 250 300 350 mult ε 0.6 0.7 0.8 0.9 1 Negative – π – K p  FIG. 3: Track reconstruction efficiency (ǫmult) as a function of centrality. The error bars on the plot represent the systematic errors. introduced to reduce background. The lower momentum cut-offs are 0.2 GeV/c for pions, 0.4 GeV/c for kaons, and 0.6 GeV/c for p and p. This cut-off value for p and p is larger than those for pions and kaons due to the large energy loss effect. D. Acceptance, Decay and Multiple Scattering Corrections In order to correct for 1) the geometrical acceptance, 2) in-flight decay for pions and kaons, 3) the effect of multiple scattering, and 4) nuclear interactions with materials in the detector (including anti-proton absorption), we use PISA (PHENIX Integrated Simulation Application), a GEANT [26] based Monte Carlo (MC) simulation program of the PHENIX detector. The single particle tracks are passed from GEANT through the PHENIX event reconstruction software [25]. In this simulation, the BBC, TOF, and DC detector responses are tuned to match the real data. For example, dead areas of DC and TOF are included, and momentum and time-of-flight resolution are tuned. The track association to TOF in both azimuth (φ) and along the beam axis (z) as a function of momentum and the PID cut boundaries are parameterized to match the real data. A fiducial cut is applied to choose identical active areas on the TOF in both the simulation and data. We generate 1×107 single particle events for each particle species (π ±, K±, p and p) with low pT enhanced (< 2 GeV/c) + flat pT distributions for 7 high pT (2 – 4 GeV/c for pions and kaons, 2 – 8 GeV/c for p and p) 1 . The efficiencies are determined in each pT bin by dividing the reconstructed output by the generated input as expressed as follows: ǫacc(j, pT ) = # of reconstructed MC tracks # of generated MC tracks , (3) where j is the particle species. The resulting correction factors (1/ǫacc) are applied to the data in each pT bin and for each individual particle species. E. Detector Occupancy Correction Due to the high multiplicity environment in heavy ion collisions, which causes high occupancy and multiple hits on a detector cell such as scintillator slats of the TOF, it is expected that the track reconstruction efficiency in central events is lower than that in peripheral events. The typical occupancy at TOF is less than 10% in the most central Au+Au collisions. To correct for this effect, we merge single particle simulated events with real events and calculate the track reconstruction efficiency for each simulated track as follows: ǫmult(i, j) = # of reconstructed embedded tracks # of embedded tracks , (4) where i is the centrality bins and j is the particle species. This study has been performed for each particle species and each centrality bin. The track reconstruction efficiencies are factorized (into independent terms depending on centrality and pT ) for pT > 0.4 GeV/c, since there is no pT dependence in the efficiencies above that pT . Figure 3 shows the dependence of track reconstruction efficiency for π ±, K±, p and p as a function of centrality expressed as Npart. The efficiency in the most central 0–5% events is about 80% for protons (p), 83% for kaons and 85% for pions. Slower particles are more likely lost due to high occupancy in the TOF because the system responds to the earliest hit. For the most peripheral 80–92% events, the efficiency for detector occupancy effect is ≈ 99% for all particle species. The factors are applied to the spectra for each particle species and centrality bin. Systematic uncertainties on detector occupancy corrections (1/ǫmult) are less than 3%. 1 Due to the good momentum resolution at the high pT region, the momentum smearing effect for a steeply falling spectrum is <1% at pT = 5 GeV/c. The flat pT distribution up to 5 GeV/c can be used to obtain the correction factors. [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ) T (p feed δ 0 0.1 0.2 0.3 0.4 0.5 0.6 p p  FIG. 4: The fractional contribution of protons (p) from Λ (Λ) decays in all measured protons (p), δfeed(pT ), as a function of pT . The solid (dashed) lines represent the systematic errors for protons (p). The error bars are statistical errors. F. Weak Decay Correction Protons and anti-protons from weak decays (e.g. from Λ and Λ) can be reconstructed as tracks in the PHENIX spectrometer. The proton and anti-proton spectra are corrected to remove the feed-down contribution from weak decays using a HIJING [27] simulation. HIJING output has been tuned to reproduce the measured particle ratios of Λ/p and Λ/p along with their pT dependencies in √ sNN = 130 GeV Au+Au collisions [28] which include contribution from Ξ and Σ0 . Corrections for feeddown from Σ± are not applied, as these yields were not measured. About 2×106 central HIJING events (impact parameter b = 0 − 3 fm) covering the TOF acceptance have been generated and processed through the PHENIX reconstruction software. To calculate the feed-down corrections, the p/p and Λ/Λ yield ratios were assumed to be independent of pT and centrality. The systematic error due to the feed-down correction is estimated at 6% by varying the Λ/p and Λ/p ratios within the systematic errors of the √ sNN =130 GeV Au+Au measurement [28] (±24%) and assuming mT -scaling at high pT . This uncertainty could be larger if the Λ/p and Λ/p ratios change significantly with pT and beam energy. The fractional contribution to the p (p) yield from Λ(Λ), δfeed(pT ), is shown in Figure 4. The solid (dashed) lines represent the systematic errors for protons (p). The obtained factor is about 4
0% below 1 GeV/c and 30% at 4 GeV/c. We multiply the proton and anti-proton spectra by the factor, Cfeed, for all centrality bins as a function of pT : Cfeed(j, pT ) = 1 − δfeed(j, pT ), (5) where j = p, p. 8 ] 2 2/ GeV dy [c T N / dp 2 ) d T p π (1/2 10 -3 10 -2 10 -1 1 10 10 2 10 3 + π + K p Positive (0 – 5% central) – π – K p  Negative (0 – 5% central) [GeV/c] pT 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ] 2 2/ GeV dy [c T N / dp 2 ) d T p π (1/2 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1 10 Positive (60 – 92% peripheral) [GeV/c] pT 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Negative (60 – 92% peripheral) FIG. 5: Transverse momentum distributions for pions, kaons, protons and anti-protons in Au+Au collisions at √ sNN = 200 GeV. The top two figures show pT spectra for the most central 0–5% collisions. The bottom two are for the most peripheral 60–92% collisions. The error bars are statistical only. The Λ (Λ) feed-down corrections for protons (anti-protons) have been applied. G. Invariant Yield Applying the data cuts and corrections discussed above, the final invariant yield for each particle species and centrality bin are derived using the following equation. 1 2πpT d 2N dpT dy = 1 2πpT · 1 Nevt(i) · Cij (pT )· Nj (i, pT ) ∆pT ∆y , (6) where y is rapidity, Nevt(i) is the number of events in each centrality bin i, Cij (pT ) is the total correction factor and Nj (i, pT ) is the number of counts in each centrality bin i, particle species j, and pT . The total correction factor is composed of: Cij (pT ) = 1 ǫacc(j, pT ) · 1 ǫmult(i, j) · Cfeed(j, pT ). (7) H. Systematic Uncertainties To estimate systematic uncertainties on the pT distribution and particle ratios, various sets of pT spectra and particle ratios were made by changing the cut parameters including the fiducial cut, PID cut, and track association windows slightly from what was used in the analysis. For each of these spectra and ratios using modified cuts, the same changes in the cuts were made in the Monte Carlo analysis. The absolutely normalized spectra with different cut conditions are divided by the spectra with the baseline cut conditions, resulting in uncertainties associated with each cut condition as a function of pT . The various uncertainties are added in quadrature. Three different centrality bins (minimum bias, central 0–5%, and peripheral 60–92%) are used to study the centrality dependence of systematic errors. The same procedure has been applied for the following particle ratios: π −/π+, 9 [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 ] 2 dy [(c / GeV) T N /dp 2 ) d T p π 1/(2 10 -5 10 -4 10 -3 10 -2 10 -1 1 10 10 2 10 3 10 4 10 5 + π [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 – π Centrality 0- 5%(x20) 5-10%(x10) 10-15%(x5) 15-20%(x2.5) 20-30%(x1.5) 30-40%(x1.0) 40-50%(x1.0) 50-60%(x1.0) 60-70%(x1.0) 70-80%(x1.0) 80-92%(x1.0) 60-92%(x0.1) FIG. 6: Centrality dependence of the pT distribution for π + (left) and π − (right) in Au+Au collisions at √ sNN = 200 GeV. The different symbols correspond to different centrality bins. The error bars are statistical only. For clarity, the data points are scaled vertically as quoted in the figure. K−/K+, p/p, K/π, p/π+, and p/π−. Table II shows the systematic errors of the pT spectra for central collisions. The systematic uncertainty on the absolute value of momentum (momentum scale) are estimated as 3% in the measured pT range by comparing the known proton mass to the value measured as protons in real data. It is found that the total systematic error on the pT spectra is 8–14% in both central and peripheral collisions. For the particle ratios, the typical systematic error is about 6% for all particle species. The dominant source of uncertainties on the central-to-peripheral ratio scaled by Ncoll (RCP ) are the systematic errors on the nuclear overlap function, TAuAu (see Table III). The systematic errors on dN/dy and hpT i are discussed in Section IV C together with the procedure for the determination of these quantities. IV. RESULTS In this section, the pT and transverse mass spectra and yields of identified charged hadrons as a function of centrality are shown. Also a systematic study of particle ratios in Au+Au collisions at √ sNN = 200 GeV at midrapidity is presented. A. Transverse Momentum Distributions Figure 5 shows the pT distributions for pions, kaons, protons, and anti-protons. The top two plots are for the most central 0–5% collisions, and the bottom two are for the most peripheral 60–92% collisions. The spectra for positive particles are presented on the left, and those for negative particles on the right. For pT < 1.5 GeV/c in central events, the data show a clear mass dependence in the shapes of the spectra. The p and p spectra have a shoulder-arm shape, the pion spectra have a concave shape, and the kaons fall exponentially. On the other hand, in the peripheral events, the mass dependences of the pT spectra are less pronounced and the pT spectra are more nearly parallel to each other. Another notable observation is that at pT above ≈ 2.0 GeV/c in central events, the p and p yields become comparable to the pion yields, which is also observed in 130 GeV Au+Au collisions [6]. This observation shows that a significant fraction of the total particle yield at pT ≈ 2.0 – 4.5 GeV/c in Au+Au central collisions consists of p and p. 10 [GeV/c] T p 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ] 2 dy [(c / GeV) T N /dp 2 ) d T p π 1/(2 10 -4 10 -3 10 -2 10 -1 1 10 10 2 10 3 10 4 10 5 + K [GeV/c] T p 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 – K Centrality 0- 5%(x20) 5-10%(x10) 10-15%(x5) 15-20%(x2.5) 20-30%(x1.5) 30-40%(x1.0) 40-50%(x1.0) 50-60%(x1.0) 60-70%(x1.0) 70-80%(x1.0) 80-92%(x1.0) 60-92%(x0.1) FIG. 7: Centrality dependence of the pT distribution for K+ (left) and K− (right) in Au+Au collisions at √ sNN = 200 GeV. The different symbols correspond to different centrality bins. The error bars are statistical only. For clarity, the data points are scaled vertically as quoted in the figure. These high statistics Au+Au data at √ sNN = 200 GeV allow us to perform a detailed study of the centrality dependence of the pT spectra. In this analysis, we use the eleven centrality bins described in Section III A as well as the combined peripheral bin (60–92%) for each particle species. Figure 6 shows the centrality dependence of the pT spectrum for π + (left) and π − (right). For clarity, the data points are scaled vertically as quoted in the figures. The error bars are statistical only. The pion spectra show an approximately power-law shape for all centrality bins. The spectra become steeper (fall faster with increasing pT ) for more peripheral collisions. Figure 7 shows similar plots for kaons. The data can be well approximated by an exponential function in pT for all centralities. Finally, the centrality dependence of the pT spectra for protons (left) and anti-protons (right) is shown in Figure 8. As in Figure 5, both p and p spectra show a strong centrality dependence below 1.5 GeV/c, i.e. they develop a shoulder at low pT and the spectra flatten (fall more slowly with increasing pT ) with increasing collision centrality. Up to pT = 1.5 ∼ 2 GeV/c, it has been found that hydrodynamic models can reproduce the data well for π ±, K±, p and p spectra at 130 GeV [8], and also the preliminary data at 200 GeV in Au+Au collisions (e.g. [5, 29]). These models assume thermal equilibrium and that the created particles are affected by a common transverse flow velocity βT and freeze-out (stop interacting) at a temperature Tf o with a fixed initial condition governed by the equation of state (EOS) of matter. There are several types of hydrodynamic calculations, e.g., (1) a conventional hydrodynamic fit to the experimental data with two free parameters, βT and Tf o [30], (2) a combination of hydrodynamics and a hadronic cascade model [5], (3) transverse and longitudinal flow with simultaneous chemical and thermal freeze-outs within the statistical thermal model [31], (4) requiring the early thermalization with a QGP type EOS [32]. Despite the differences between the hydrodynamic models, all models are
in qualitative agreement with the identified single particle spectra in central collisions at low pT as seen in reference [8]. However, they fail to reproduce the peripheral spectra above pT ≃ 1 GeV/c and their applicability in the high pT region (> 2 GeV/c) is limited. Comparison with the detailed centrality dependence of hadron spectra presented here would shed light on further understanding of the EOS, chemical properties in the model, and the freezeout conditions at RHIC. 11 [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ] 2 dy [(c / GeV) T N /dp 2 ) d T p π 1/(2 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1 10 10 2 10 3 p [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 p  Centrality 0- 5%(x20) 5-10%(x10) 10-15%(x5) 15-20%(x2.5) 20-30%(x1.5) 30-40%(x1.0) 40-50%(x1.0) 50-60%(x1.0) 60-70%(x1.0) 70-80%(x1.0) 80-92%(x1.0) 60-92%(x0.1) FIG. 8: Centrality dependence of the pT distribution for protons (left) and anti-protons (right) in Au+Au collisions at √ sNN = 200 GeV. The different symbols correspond to different centrality bins. The error bars are statistical only. Feed-down corrections for Λ (Λ) decaying into proton (p) have been applied. For clarity, the data points are scaled vertically as quoted in the figure. TABLE II: Systematic errors on the pT spectra for central events. All errors are given in percent. π + π − K+ K− p p pT range (GeV/c) 0.2 – 3.0 0.2 – 3.0 0.4 – 2.0 0.4 – 2.0 0.6 – 3.0 3.0 – 4.5 0.6 – 3.0 3.0 – 4.5 Cuts 6.2 6.2 11.2 9.5 6.6 11.6 6.6 11.6 Momentum scale 3 3 3 3 3 3 3 3 Occupancy correction 2 2 3 3 3 3 3 3 Feed-down correction – – – – 6.0 6.0 6.0 6.0 Total 7.2 7.2 12.0 10.4 9.9 13.7 9.9 9.9 TABLE III: Systematic errors on Central-to-Peripheral ratio (RCP ). All errors are given in percent. Source (π + + π −)/2 (K+ + K−)/2 (p + p)/2 Occupancy correction (central) 2 3 3 Occupancy correction (peripheral) 2 3 3 hTAuAui (0–10%) 6.9 6.9 6.9 hTAuAui (60–92%) 28.6 28.6 28.6 Total 29.5 29.7 29.7 12 10 -4 10 -3 10 -2 10 -1 1 10 10 2 + π + K p Positive (0 – 5% central) – π – K p  Negative (0 – 5% central) ] 2 4/ GeV dy [c T 2N / dm ) d T m π (1/2 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1 10 10 2 Positive (40 – 50% mid-central) Negative (40 – 50% mid-central) ] 2 mT – m0 [GeV/c 0 0.5 1 1.5 2 2.5 3 3.5 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1 10 Positive (60 – 92% peripheral) ] 2 mT – m0 [GeV/c 0 0.5 1 1.5 2 2.5 3 3.5 Negative (60 – 92% peripheral) FIG. 9: Transverse mass distributions for π ±, K±, protons and anti-protons for central 0–5% (top panels), mid-central 40–50% (middle panels) and peripheral 60–92% (bottom panels) in Au+Au collisions at √ sNN = 200 GeV. The lines on each spectra are the fitted results using mT exponential function. The fit ranges are 0.2 – 1.0 GeV/c 2 for pions and 0.1 – 1.0 GeV/c 2 for kaons, protons, and anti-protons in mT − m0. The error bars are statistical errors only. 13 ] 2 Mass [GeV/c 0 0.2 0.4 0.6 0.8 1 Inverse Slope T [GeV/c] 0.1 0.2 0.3 0.4 0.5 0.6 + π + K p Central (0-5%) Mid-central (40-50%) Peripheral (60-92%) ] 2 Mass [GeV/c 0 0.2 0.4 0.6 0.8 1 – π – K p FIG. 10: Mass and centrality dependence of inverse slope parameters T in mT spectra for positive (left) and negative (right) particles in Au+Au collisions at √ sNN = 200 GeV. The fit ranges are 0.2 – 1.0 GeV/c 2 for pions and 0.1 – 1.0 GeV/c 2 for kaons, protons, and anti-protons in mT − m0. The dotted lines represent a linear fit of the results from each centrality bin as a function of mass using Eq. 9. B. Transverse Mass Distributions In order to quantify the observed particle mass dependence of the pT spectra shape and their centrality dependence, the transverse mass spectra for identified charged hadrons are presented here. From former studies at lower beam energies, it is known that the invariant differential cross sections in p + p, p + A, and A+ A collisions generally show a shape of an exponential in mT − m0, where m0 is particle mass, and mT = p p 2 T + m2 0 is transverse mass. For an mT spectrum with an exponential shape, one can parameterize it as follows: d 2N 2πmT dmT dy = 1 2πT (T + m0) · A · exp (− mT − m0 T ), (8) where T is referred to as the inverse slope parameter, and A is a normalization parameter which contains information on dN/dy. In Figure 9, mT distributions for π ±, K±, p and p for central 0–5% (top panels), midcentral 40–50% (middle panels) and peripheral 60–92% (bottom panels) collisions are shown. The spectra for positive particles are on the left and for negative particles are on the right. The solid lines overlaid on each spectra are the fit results using Eq. 8. The error bars are statistical only. As seen in Figure 9, all the mT spectra display an exponential shape in the low mT region. However, at higher mT , the spectra become less steep, which corresponds to a power-law behavior in pT . Thus, the inverse slope parameter in Eq. 8 depends on the fitting range. In this analysis, the fits cover the range 0.2 – 1.0 GeV/c 2 for pions and 0.1 – 1.0 GeV/c 2 for kaons, protons, and anti-protons in mT − m0. The low mT region (mT − m0 < 0.2 GeV/c 2 ) for pions is excluded from the fit to eliminate the contributions from resonance decays. The inverse slope parameters for each particle species in the three centrality bins are summarized in Figure 10 and in Table IV. The inverse slope parameters increase with increasing particle mass in all centrality bins. This increase for central collisions is more rapid for heavier particles. Such a behavior was derived, under certain conditions, by E. Schnedermann et al. [33] for central collisions and by T. Cs¨org˝o et al. [34] for non-central heavy ion collisions: T = T0 + mhuti 2 . (9) Here T0 is a freeze-out temperature and huti is a measure of the strength of the (average radial) transverse flow. The dotted lines in Figure 10 represent a linear fit of the results from each centrality bin as a function of mass using Eq. 9. The fit parameters for positive and negative particles are shown in Table IV. It indicates, that the linear extrapolation of the slope parameter T (m) to zero mass has the same intercept parameters T0 in all the centrality classes, indicating that the freeze-out temperature is approximately independent of the centrality. On the other hand, huti, the strength of the average transverse flow is increasing with increasing centrality, supporting the hydrodynamic picture. Motivated by the idea of a Color Glass Condensate, the authors of reference [35] argued that the mT spectra (not mT − m0) of identified hadrons at RHIC energy follow a generalized scaling law for all centrality classes when the proton (kaon) spectrum is multiplied by a factor of 0.5 (2.0). The 200 GeV Au+Au pion and kaon spectra seem to follow this mT scaling, but proton and anti-proton spectra are below it by a factor of ∼ 2 for all centralities. Since p and p spectra presented here are corrected for weak decays from Λ and Λ, the model also needs to study the feed-down effect to conclude that a universal mT scaling law is seen at RHIC. C. Mean Transverse Momentum and Particle Yields versus Npart By integrating a measured pT spectrum over pT , one can determine the mean transverse momentum, hpT i, and particle yield per unit rapidity, dN/dy, for each particle species. The procedure to determine the mean pT and dN/dy is described below: (1) Determine dN/dy and hpT i by integrating over the measured pT range from the data. (2) Fit several appropriate functional forms (detailed below) to the pT spectra. Note that all of the fits are reasonable approximations to the data. Integrate from zero to the first data point and from the last data point to infinity. (3) Sum the data yield and the two functional yield pieces together to get dN/dy and hpT i in each functional form. (4) Take the average between the upper and lower bounds from the different functional forms to 14 TABLE IV: (Top) Inverse slope parameters for π, K, p and p for the 0–5%, 40–50% and 60–92% centrality bins, in units of MeV/c 2 . The errors are statistical only. (Bottom) The ext
racted fit parameters of the freeze-out temperature (T0) in units of MeV/c 2 and the measure of the strength of the average radial transverse flow (huti) using Eq. 9. The fit results shown here are for positive and negative particles, as denoted in the superscripts, and for three different centrality bins. Particle 0–5% 40–50% 60–92% π + 210.2 ± 0.8 201.9 ± 0.8 187.8 ± 0.7 π − 211.9 ± 0.7 203.0 ± 0.7 189.2 ± 0.7 K+ 290.2 ± 2.2 260.6 ± 2.4 233.9 ± 2.6 K− 293.8 ± 2.2 265.1 ± 2.3 237.4 ± 2.6 p 414.8 ± 7.5 326.3 ± 5.9 260.7 ± 5.4 p 437.9 ± 8.5 330.5 ± 6.4 262.1 ± 5.9 Fit parameter 0–5% 40–50% 60–92% T (+) 0 177.0 ± 1.2 179.5 ± 1.2 173.1 ± 1.2 T (−) 0 177.3 ± 1.2 179.6 ± 1.2 173.7 ± 1.1 huti (+) 0.48 ± 0.07 0.40 ± 0.07 0.32 ± 0.07 huti (−) 0.49 ± 0.07 0.41 ± 0.07 0.33 ± 0.07 Npart 0 50 100 150 200 250 300 350 > [GeV/c] T

[GeV/c] T

2 GeV/c. For comparison, the corresponding ratios for pT > 2 GeV/c observed in p + p collisions at lower energies [47], and in gluon jets produced in e + +e − collisions [48], are also shown. Within the uncertainties those ratios are compatible with the peripheral Au+Au results. In hard-scattering processes described by pQCD, the p/π and p/π ratios at high pT are determined by the fragmentation of energetic partons, independent of the initial colliding system, which is seen as agreement between p + p and e + + e − collisions. Thus, the clear increase in the p/π (p/π) ratios at high pT from p + p and peripheral to the mid-central and to the central Au+Au collisions requires ingredients other than pQCD. The first observation of the enhancement of protons and anti-protons compared to pions in the intermediate pT region was in the 130 GeV Au+Au data [6]. The data inspired several new theoretical interpretations and models. Hydrodynamics calculations [32] predict that the p/π ratio at high pT exceeds unity for central collisions. The expected p/π ratio in the thermal model at fixed and sufficiently large pT is determined by 2e −µB/Tch 17 [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 + π / – π 0 0.2 0.4 0.6 0.8 1 1.2 1.4 (central 0-5%) + /π – (a) π [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 (peripheral 60-92%) + /π – (b) π [GeV/c] T p 0 0.5 1 1.5 2 + – / K K 0 0.2 0.4 0.6 0.8 1 1.2 1.4 (central 0-5%) + /K- (c) K [GeV/c] T p 0 0.5 1 1.5 2 (peripheral 60-92%) + /K- (d) K FIG. 14: Particle ratios of (a) π −/π+ for central 0–5%, (b) π −/π+ for peripheral 60–92%, (c) K−/K+ for central 0–5%, and (d) K−/K+ for peripheral 60–92% in Au+Au collisions at √ sNN = 200 GeV. The error bars indicate the statistical errors and shaded boxes around unity on each panel indicate the systematic errors. [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 p / p 0.2 0.4 0.6 0.8 1 1.2 Central 0-5% [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Peripheral 60-92% FIG. 15: Ratio of p/p as a function of pT for central 0–5% (left) and peripheral 60–92% (right) in Au+Au collisions at √ sNN = 200 GeV. The error bars indicate the statistical errors and shaded boxes around unity on each panel indicate the systematic errors. ≈ 1.7 using Tch = 177 MeV and µB = 29 MeV [10] for 200 GeV Au+Au central collisions. Due to the strong radial flow effect at RHIC at relativistic transverse momenta (pT ≫ m), all hadron spectra have a similar shape. The hydrodynamic model thus explains the excess of p/π in central collisions at intermediate pT . However, the hydrodynamic model [49] predicts no or very little dependence on the centrality, which clearly disagrees with the present data. This model predicts, within 10%, the same pT dependence of p/π (p/π) for all centrality bins. Recently two new models have been proposed to explain the experimental results on the pT dependence of [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 p / p 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Au+Au at 200 GeV (Minimum Bias) /dy=750) g Baryon Junction + Quench (dN pQCD calculation FIG. 16: p/p ratios as a function of pT for minimum bias events in Au+Au at √ sNN = 200 GeV. The error bars indicate the statistical errors and shaded box on the right indicates the systematic errors. Two theoretical calculations are shown: baryon junction model (solid line) and pQCD calculation (dashed line) taken from reference [46]. [GeV/c] T p 0 0.5 1 1.5 2 Ratio 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Central (0-5%) Peripheral (60-92%) + / π + K [GeV/c] T p 0 0.5 1 1.5 2 – / π – K FIG. 17: K/π ratios as a function of pT for central 0–5% and peripheral 60–92% in Au+Au collisions at √ sNN = 200 GeV. The left is for K+/π+ and the right is for K−/π−. The error bars indicate the statistical errors. p/π and p/π ratios. One model is the parton recombination and fragmentation model [45] and the other model is the baryon junction model [50]. Both models explain qualitatively the observed feature of p/π enhancement in central collisions, and their centrality dependencies. Furthermore, both theoretical models predict that this baryon enhancement is limited to pT < 5 – 6 GeV/c. This will be discussed in Section IV E in detail. 2. Particle Ratio versus Npart Figure 19 shows the centrality dependence of particle ratios for π −/π+, K−/K+ and p/p. The ratios presented 18 Ratio 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 p / π [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Ratio 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 p / π  Au+Au 0-10% Au+Au 20-30% Au+Au 60-92% p+p, s = 53 GeV , gluon jet (DELPHI) – e + e FIG. 18: Proton/pion (top) and anti-proton/pion (bottom) ratios for central 0–10%, mid-central 20–30% and peripheral 60–92% in Au+Au collisions at √ sNN = 200 GeV. Open (filled) points are for charged (neutral) pions. The data at √ s = 53 GeV p + p collisions [47] are also shown. The solid line is the (p+p)/(π + +π −) ratio measured in gluon jets [48]. here are derived from the integrated yields over pT (i.e. dN/dy). The shaded boxes on each data point indicate the systematic errors. Within uncertainties, the ratios are all independent of Npart over the measured range. Figure 20 shows a comparison of the PHENIX particle ratios with those from PHOBOS [44], BRAHMS [43], and STAR (preliminary) [51] in Au+Au central collisions at √ sNN = 200 GeV at mid-rapidity. The PHENIX antiparticle to particle ratios are consistent with other experimental results within the systematic uncertainties. Figure 21 shows the centrality dependence of K/π and p/π ratios. Both K+/π+ and K−/π− ratios increase rapidly for peripheral collisions (Npart < 100), and then saturate or rise slowly from the mid-central to the most central collisions. The p/π+ and p/π− ratios increase for peripheral collisions (Npart < 50) and saturate from mid-central to central collisions – similar to the centrality dependence of K/π ratio (but possibly flatter). Within the framework of the statistical thermal model [9] in a grand canonical ensemble with baryon number, strangeness and charge conservation [10], particle ratios measured at √ sNN =130 GeV at mid-rapidity part N 0 50 100 150 200 250 300 350 Ratio 0 0.2 0.4 0.6 0.8 1 1.2 + / π – π + / K – K p / p  FIG. 19: Centrality dependence of particle ratios for π −/π+, K−/K+, and p/p in Au+Au collisions at √ sNN = 200 GeV. The error bars indicate the statistical errors. The shaded boxes on each data point are the systematic errors. Ratio 10 -1 1 + / π – π + / K – K p / p + / π + K – / π – K + p / π – p / π = 200 GeV (central) NN Au+Au s PHENIX PHOBOS BRAHMS STAR (Preliminary) thermal model FIG. 20: Comparison of PHENIX particle ratios with those of PHOBOS [44], BRAHMS [43], and STAR (preliminary) [51] results in Au+Au central collisions at √ sNN = 200 GeV at mid-rapidity. The thermal model prediction [10] for 200 GeV Au+Au central collisions are also shown as dotted lines. The error bars on data indicate the systematic errors. have been analyzed with the extracted chemical freezeout temperature Tch = 174±7 MeV and baryon chemical potential µB = 46±5 MeV. A set of chemical parameters at √ sNN =200 GeV in Au+Au were also predicted by using a phenomenological parameterization of the energy dependence of µB. The predictions were µB = 29 ± 8 MeV and Tch = 177 ± 7 MeV at √ sNN =200 GeV. The comparison between the PHENIX data at 200 GeV for 0–5% central and the thermal model prediction is shown in Table IX and Figure 20. There is a good agreement 19 Npart 0 50 100 150 200 250 300 350 Ratio 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 + / π + (a) K Npart 0 50 100 150 200 250 300 350 – / π – (b) K Npart 0 50 100 150 200 250 300 350 Ratio 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 + (c) p / π Npart 0 50 100 150 200 250 300 350 – (d) p / π  FIG. 21: Centrality dependence of particle ratios for (a) K+/π+, (b) K−/π−, (c) p/π+, and (d) p/π− in Au+Au collisions at √ sNN = 200 GeV. The error bars indicate the statistical errors. The shaded boxes on each data point are the systematic errors. TABLE IX: Comparison
between the data for the 0– 5% central collisions and the thermal model prediction at √ sNN = 200 GeV with Tch = 177 MeV and µB = 29 MeV [10]. Particles Ratio ± stat. ± sys. Thermal Model π −/π+ 0.984 ± 0.004 ± 0.057 1.004 K−/K+ 0.933 ± 0.007 ± 0.054 0.932 p/p 0.731 ± 0.011 ± 0.062 p/p (inclusive) 0.747 ± 0.007 ± 0.046 0.752 K+/π+ 0.171 ± 0.001 ± 0.010 K−/π− 0.162 ± 0.001 ± 0.010 0.147 p/π+ 0.064 ± 0.001 ± 0.003 p/π+ (inclusive) 0.099 ± 0.001 ± 0.006 p/π− 0.047 ± 0.001 ± 0.002 p/π− (inclusive) 0.075 ± 0.001 ± 0.004 0.089 between data and the model. The thermal model calculation was performed by assuming a 50% reconstruction efficiency of all weakly decaying baryons in reference [10]. However, our results have been corrected to remove these contributions. Therefore, Table IX includes p/p and p/π− ratios with and without Λ (Λ) feed-down corrections to the proton and anti-proton spectra. The ratios without the Λ (Λ) feed-down correction are labeled “inclusive”. The small µB is qualitatively consistent with our measurement of the number of net protons (≈ 5) in central Au+Au collisions at √ sNN = 200 GeV at midrapidity. E. Binary Collision Scaling of pT Spectra One of the most striking features in Au+Au collisions at RHIC is that π 0 and non-identified hadron yields at pT > 2 GeV/c in central collisions are suppressed with respect to the number of nucleon-nucleon binary collisions (Ncoll) scaled by p + p and peripheral Au+Au results [12, 13, 14]. Moreover, the suppression of π 0 is stronger than than that for non-identified charged hadrons [12], and the yields of protons and antiprotons in central collisions are comparable to that of pions around pT =2 GeV/c [6]. The enhancement of the p/π (p/π) ratio in central collisions at intermediate pT (2.0 – 4.5 GeV/c), which was presented in the previous section, is consistent with the above observations. These results show the significant contributions of proton and anti-proton yields to the total particle composition at this intermediate pT region. We present here the Ncoll scaling behavior for charged pions, kaons, and protons (anti-protons) in order to quantify the particle composition at intermediate pT . Figure 22 shows the pT spectra scaled by the averaged number of binary collisions, hNcolli, for (π + + π −)/2, (K+ +K−)/2, and (p+p)/2 in three centrality bins: central 0–10%, mid-central 40–50% and peripheral 60–92%. For (p + p)/2 in the range of pT = 1.5 – 4.5 GeV/c, it is clearly seen that the spectra are on top of each other. This indicates that proton and anti-proton production at high pT scales with the number of binary collisions. On the other hand, at pT below 1.5 GeV/c, different shapes for different centrality bins are observed, which indicates a strong contribution from radial flow. The scaling behavior of the kaons seems to be similar to protons, but this is not conclusive due to our PID limitations. For pions, the Ncoll scaled yield in central events is suppressed compared to that for peripheral events at pT > 2 GeV/c, which is consistent with the results in the π 0 spectra [12, 14]. Figure 23 shows the central (0–10%) to peripheral (60– 92%) ratio for Ncoll scaled pT spectra (RCP: the nuclear modification factor) of (p + p)/2, kaons, charged pions, and π 0 . In this paper we define RCP as: RCP = Yield0−10%/hNcoll 0−10%i Yield60−92%/hNcoll 60−92%i . (10) The peripheral 60–92% Au+Au spectrum is used as an approximation of the yields in p + p collisions, based on the experimental fact that the peripheral spectra scale with Ncoll by using the yields in p + p collisions measured by PHENIX [14, 24]. Thus the meaning of the RCP is expected to be the same as RAA used in our previous publications [12, 13, 14]. The lines in Figure 23 indicate the expectations of Npart (dotted) and Ncoll (dashed) scaling. The shaded bars at the end of each line represent the systematic error associated with the determination of these quantities for central and peripheral events. The 20 [GeV/c] T p 0 0.5 1 1.5 2 2.5 3 ] 2 dy [(c / GeV) T 2N /dp ) d T p π > 1/(2 coll 1/ 1/(2 coll 1/ 1/(2 coll 1/∼ 1.5 GeV/c, consistent with Ncoll scaling. The data for kaons also show the Ncoll scaling behavior around 1.5 – 2.0 GeV/c, but the behavior is weaker than for protons. As with neutral pions [14], charged pions are also suppressed at 2 – 3 GeV/c with respect to peripheral Au+Au collisions. Motivated by the observation that the (p+p)/2 spectra scale with Ncoll above pT =1.5 GeV/c, the ratio of the integrated yield between central and peripheral events (scaled by the corresponding Ncoll) above pT =1.5 GeV/c are shown in Figure 24 as a function of Npart. The pT ranges for the integration are, 1.5 – 4.5 GeV/c for (p + p)/2, 1.5 – 2.0 GeV/c for kaons, and 1.5 – 3.0 GeV/c for charged pions. The data points are normalized to the most peripheral data point. The shaded boxes in the figure indicate the systematic errors, which include the normalization errors on the pT spectra, the errors on the detector occupancy corrections, and the uncertainties of the hTAuAui determination for the numerator only. Only at the most peripheral data point, the uncertainty on the denominator hT 60−92% AuAu i is also added. The figure shows that (p + p)/2 scales with Ncoll for all centrality bins, while the data for charged pions show a decrease with Npart. The kaon data points are between the charged pions and the (p + p)/2 spectra. The standard picture of hadron production at high momentum is the fragmentation of energetic partons. While the observed suppression of the π 0 yield at high pT in central collisions may be attributed to the energy loss of partons during their propagation through the hot and dense matter created in the collisions, i.e. jet quench- [GeV/c] T p 0 1 2 3 4 5 6 7 CP R 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 (p + p) / 2  ) / 2 – + K + (K ) / 2 – + π + (π 0 π FIG. 23: Central (0–10%) to peripheral (60–92%) ratios of binary-collision-scaled pT spectra, RCP , as a function of pT for (p + p)/2, charged kaons, charged pions, and π 0 [14] in Au+Au collisions at √ sNN = 200 GeV. The lines indicate the expectations of Npart (dotted) and Ncoll (dashed) scaling, the shaded bars represent the systematic errors on these quantities. ing [15, 16], it is a theoretical challenge to explain the absence of suppression for baryons up to 4.5 GeV/c for all centralities along with the enhancement of the p/π ratio at pT = 2 – 4 GeV/c for central collisions. It has been recently proposed that such observations can be explained by the dominance of parton recombination at intermediate pT , rather than by fragmentation [45]. The competition between recombination and 21 Npart 0 50 100 150 200 250 300 350 > 1.5 GeV/c) T (p CP R 0 0.2 0.4 0.6 0.8 1 1.2 1.4 (p + p) / 2  ) / 2 – + K + (K ) / 2 – + π + (π FIG. 24: Centrality dependence of integrated RCP above 1.5 GeV/c normalized to the most peripheral 60–92% value. The data shows RCP for (p+p)/2, charged kaons, and charged pions in Au+Au collisions at √ sNN = 200 GeV. The error bars are statistical only. The shaded boxes represent the systematic errors (see text for details). fragmentation of partons may explain the observed features. The model predicts that the effect is limited to pT < 5 GeV/c, beyond which fragmentation becomes the dominant production mechanism for all particle species. Another possible explanation is the baryon junction model [50]. It invokes a topological gluon configuration with jet quenching. With pion production above 2 GeV/c suppressed by jet quenching, gluon junctions produce copious baryons at intermediate pT , thus lead to the enhancement of baryons in this pT region. The model reproduces the baryon-to-meson ratio and its centrality dependence qualitatively [52]. Both theoretical models predict that baryon enhancement is limited to pT < 5 – 6 GeV/c, which is unfortunately beyond our current PID capability. However, it is possible to test the two predictions indirectly by using the non-identified charged hadrons to ne
utral pion ratio (h/π0 ) as a measure of the baryon content at high pT , as published in [23]. The results support the limited behavior of baryon enhancement up to 5 GeV/c in pT . Similar trends are observed in Λ, K0 S and K± measurements by the STAR collaboration [53]. On the other hand, it is also possible that nuclear effects, such as the “Cronin effect” [54, 55], attributed to initial state multiple scattering (pT -broadening) [56], contribute to the observed species dependence. At center-of-mass energies up to √ s = 38.8 GeV, a nuclear enhancement beyond Ncoll scaling has been observed for π, K, p and their anti-particles in p + A collisions. The effect is stronger for protons and anti-protons than for pions which leads to an enhancement of the p/π and p/π ratios compared to p + p collisions. In proton-tungsten reactions, the increase is a factor of ∼ 2 in the range 3 < pT < 6 GeV. For pions, theoretical calculations at RHIC energies [57] predict a reduced strength of the Cronin effect compared to lower energies, although no prediction exists for protons. New data from d+Au collisions at √ sNN = 200 GeV will help to clarify this issue. V. SUMMARY AND CONCLUSION In summary, we present the centrality dependence of identified charged hadron spectra and yields for π ±, K±, p and p in Au+Au collisions at √ sNN = 200 GeV at mid-rapidity. In central events, the low pT region (≤ 2.0 GeV/c) of the pT spectra show a clear particle mass dependence in their shapes, namely, p and p spectra have a shoulder-arm shape while the pion spectra have a concave shape. The spectra can be well fit with an exponential function in mT at the region below 1.0 GeV/c 2 in mT − m0. The resulting inverse slope parameters show clear particle mass and centrality dependences, that increase with particle mass and centrality. These observations are consistent with the hydrodynamic radial flow picture. Moreover, at around pT =2.0 GeV/c in central events, the p and p yields are comparable to the pion yields. Here, baryons comprise a significant fraction of the hadron yield in this intermediate pT range. The hpT i and dN/dy per participant pair increase from peripheral to mid-central collisions and saturate for the most central collisions for all particle species. The net proton number in Au+Au central collisions at √ sNN = 200 GeV is ∼ 5 at mid-rapidity. The particle ratios of π −/π+, K−/K+, p/p, K/π, p/π and p/π as a function of pT and centrality have been measured. Particle ratios in central Au+Au collisions are well reproduced by the statistical thermal model with a baryon chemical potential of µB = 29 MeV and a chemical freeze-out temperature of Tch = 177 MeV. Regardless of the particle species and centrality, it is found that ratios for equal mass particles are constant as a function of pT , within the systematic uncertainties in the measured pT range. On the other hand, both K/π and p/π (p/π) ratios increase as a function of pT . This increase with pT is stronger for central than for peripheral events. The p/π and p/π ratios in central events both increase with pT up to 3 GeV/c and approach unity at pT ≈ 2 GeV/c. However, in peripheral collisions these ratios saturate at the value of 0.3 – 0.4 around pT = 1.5 GeV/c. The observed centrality dependence of p/π and p/p ratios in intermediate pT region is not explained by the hydrodynamic model alone, but both the parton recombination model and the baryon junction model qualitatively agree with data. The scaling behavior of identified charged hadrons is compared with results for neutral pions. In the Ncoll scaled pT spectra for (p + p)/2, the spectra scale with Ncoll from pT =1.5 – 4.5 GeV/c. The central-toperipheral ratio, RCP , approaches unity for (p + p)/2 from pT = 1.5 up to 4.5 GeV/c. Meanwhile, charged and 22 neutral pions are suppressed. The ratio of integrated RCP from pT =1.5 to 4.5 GeV/c exhibits an Ncoll scaling behavior for all centrality bins in the (p + p)/2 data, which is in contrast to the stronger pion suppression, that increases with centrality. APPENDIX A: TABLE OF INVARIANT YIELDS The invariant yields for π ±, K±, p and p in Au+Au collisions at √ sNN = 200 GeV at mid-rapidity are tabulated in Tables X – XXIX. The data presented here are for the the minimum bias events and each centrality bin (0–5%, 5–10%, 10–15%, 15–20%, 20–30%, …, 70–80%, 80–92%, and 60–92%). Errors are statistical only. Acknowledgments We thank the staff of the Collider-Accelerator and Physics Departments at Brookhaven National Laboratory and the staff of the other PHENIX participating institutions for their vital contributions. We acknowledge support from the Department of Energy, Office of Science, Nuclear Physics Division, the National Science Foundation, Abilene Christian University Research Council, Research Foundation of SUNY, and Dean of the College of Arts and Sciences, Vanderbilt University (U.S.A), Ministry of Education, Culture, Sports, Science, and Technology and the Japan Society for the Promotion of Science (Japan), Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico and Funda¸c˜ao de Amparo `a Pesquisa do Estado de S˜ao Paulo (Brazil), Natural Science Foundation of China (People’s Republic of China), Centre National de la Recherche Scientifique, Commissariat `a l’Energie Atomique, Institut National de ´ Physique Nucl´eaire et de Physique des Particules, and Institut National de Physique Nucl´eaire et de Physique des Particules, (France), Bundesministerium fuer Bildung und Forschung, Deutscher Akademischer Austausch Dienst, and Alexander von Humboldt Stiftung (Germany), Hungarian National Science Fund, OTKA (Hungary), Department of Atomic Energy and Department of Science and Technology (India), Israel Science Foundation (Israel), Korea Research Foundation and Center for High Energy Physics (Korea), Russian Ministry of Industry, Science and Tekhnologies, Russian Academy of Science, Russian Ministry of Atomic Energy (Russia), VR and the Wallenberg Foundation (Sweden), the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union, the USHungarian NSF-OTKA-MTA, the US-Israel Binational Science Foundation, and the 5th European Union TMR Marie-Curie Programme. 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C 21, 155 (83). [57] B. Z. Kopeliovich, J. Nemchik, A. Schafer, A. V. Tarasov Phys. Rev. Lett. 88, 232303 (2002). 24 TABLE X: Invariant yields for π + at mid-rapidity in the minimum bias, 0–5%, 5–10%, and 10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] Minimum bias 0–5% 5–10% 10–15% 0.25 1.07e+02 ± 8.8e-01 3.29e+02 ± 2.7e+00 2.76e+02 ± 2.3e+00 2.39e+02 ± 2.0e+00 0.35 6.06e+01 ± 5.0e-01 1.97e+02 ± 1.6e+00 1.64e+02 ± 1.4e+00 1.39e+02 ± 1.2e+00 0.45 3.63e+01 ± 3.1e-01 1.20e+02 ± 1.1e+00 9.93e+01 ± 8.7e-01 8.41e+01 ± 7.4e-01 0.55 2.18e+01 ± 2.0e-01 7.26e+01 ± 6.7e-01 6.02e+01 ± 5.6e-01 5.08e+01 ± 4.7e-01 0.65 1.34e+01 ± 1.3e-01 4.49e+01 ± 4.5e-01 3.74e+01 ± 3.8e-01 3.16e+01 ± 3.2e-01 0.75 8.71e+00 ± 9.5e-02 2.93e+01 ± 3.3e-01 2.43e+01 ± 2.7e-01 2.05e+01 ± 2.3e-01 0.85 5.41e+00 ± 6.3e-02 1.82e+01 ± 2.2e-01 1.53e+01 ± 1.8e-01 1.29e+01 ± 1.6e-01 0.95 3.59e+00 ± 4.5e-02 1.21e+01 ± 1.6e-01 1.01e+01 ± 1.3e-01 8.56e+00 ± 1.1e-01 1.05 2.35e+00 ± 3.1e-02 7.96e+00 ± 1.1e-01 6.56e+00 ± 9.3e-02 5.56e+00 ± 8.0e-02 1.15 1.58e+00 ± 2.2e-02 5.32e+00 ± 8.0e-02 4.47e+00 ± 6.8e-02 3.72e+00 ± 5.7e-02 1.25 1.05e+00 ± 1.5e-02 3.55e+00 ± 5.7e-02 2.99e+00 ± 4.9e-02 2.51e+00 ± 4.2e-02 1.35 7.59e-01 ± 1.2e-02 2.55e+00 ± 4.5e-02 2.15e+00 ± 3.9e-02 1.81e+00 ± 3.3e-02 1.45 5.16e-01 ± 8.3e-03 1.72e+00 ± 3.3e-02 1.45e+00 ± 2.8e-02 1.23e+00 ± 2.5e-02 1.55 3.37e-01 ± 5.6e-03 1.13e+00 ± 2.3e-02 9.36e-01 ± 2.0e-02 7.93e-01 ± 1.7e-02 1.65 2.44e-01 ± 4.2e-03 8.05e-01 ± 1.8e-02 6.68e-01 ± 1.6e-02 5.78e-01 ± 1.4e-02 1.75 1.77e-01 ± 3.3e-03 5.70e-01 ± 1.4e-02 4.84e-01 ± 1.3e-02 4.19e-01 ± 1.1e-02 1.85 1.27e-01 ± 2.4e-03 4.18e-01 ± 1.2e-02 3.42e-01 ± 1.0e-02 2.99e-01 ± 9.1e-03 1.95 9.01e-02 ± 1.9e-03 2.80e-01 ± 9.0e-03 2.50e-01 ± 8.3e-03 2.07e-01 ± 7.3e-03 2.05 6.68e-02 ± 1.2e-03 2.09e-01 ± 6.1e-03 1.82e-01 ± 5.6e-03 1.56e-01 ± 5.0e-03 2.15 4.71e-02 ± 8.9e-04 1.36e-01 ± 4.8e-03 1.27e-01 ± 4.6e-03 1.05e-01 ± 4.1e-03 2.25 3.27e-02 ± 6.8e-04 9.10e-02 ± 3.8e-03 8.06e-02 ± 3.5e-03 8.05e-02 ± 3.5e-03 2.35 2.60e-02 ± 6.2e-04 7.20e-02 ± 3.6e-03 6.28e-02 ± 3.3e-03 5.78e-02 ± 3.1e-03 2.45 1.94e-02 ± 5.3e-04 5.40e-02 ± 3.2e-03 4.57e-02 ± 2.9e-03 4.06e-02 ± 2.7e-03 2.55 1.49e-02 ± 4.7e-04 3.78e-02 ± 2.8e-03 3.59e-02 ± 2.7e-03 3.18e-02 ± 2.5e-03 2.65 1.13e-02 ± 4.2e-04 2.65e-02 ± 2.5e-03 2.50e-02 ± 2.4e-03 2.44e-02 ± 2.3e-03 2.75 9.30e-03 ± 4.0e-04 2.27e-02 ± 2.5e-03 2.19e-02 ± 2.4e-03 1.83e-02 ± 2.1e-03 2.85 6.20e-03 ± 3.2e-04 1.28e-02 ± 1.9e-03 1.21e-02 ± 1.8e-03 1.30e-02 ± 1.8e-03 2.95 5.17e-03 ± 3.1e-04 1.03e-02 ± 1.8e-03 1.08e-02 ± 1.8e-03 1.04e-02 ± 1.8e-03 TABLE XI: Invariant yields for π + at mid-rapidity in 15–20%, 20–30%, 30–40%, and 40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 15–20% 20–30% 30–40% 40–50% 0.25 2.04e+02 ± 1.7e+00 1.57e+02 ± 1.3e+00 1.07e+02 ± 8.9e-01 6.84e+01 ± 5.7e-01 0.35 1.18e+02 ± 9.9e-01 8.82e+01 ± 7.4e-01 5.86e+01 ± 4.9e-01 3.67e+01 ± 3.1e-01 0.45 7.09e+01 ± 6.2e-01 5.27e+01 ± 4.6e-01 3.46e+01 ± 3.0e-01 2.15e+01 ± 1.9e-01 0.55 4.28e+01 ± 4.0e-01 3.17e+01 ± 2.9e-01 2.06e+01 ± 1.9e-01 1.26e+01 ± 1.2e-01 0.65 2.65e+01 ± 2.7e-01 1.95e+01 ± 2.0e-01 1.26e+01 ± 1.3e-01 7.66e+00 ± 8.0e-02 0.75 1.73e+01 ± 2.0e-01 1.27e+01 ± 1.4e-01 8.29e+00 ± 9.4e-02 4.99e+00 ± 5.8e-02 0.85 1.07e+01 ± 1.3e-01 7.94e+00 ± 9.5e-02 5.10e+00 ± 6.3e-02 3.04e+00 ± 3.9e-02 0.95 7.12e+00 ± 9.6e-02 5.31e+00 ± 7.0e-02 3.38e+00 ± 4.6e-02 2.02e+00 ± 2.9e-02 1.05 4.77e+00 ± 6.9e-02 3.49e+00 ± 4.9e-02 2.22e+00 ± 3.2e-02 1.30e+00 ± 2.0e-02 1.15 3.16e+00 ± 5.0e-02 2.34e+00 ± 3.5e-02 1.50e+00 ± 2.4e-02 8.78e-01 ± 1.5e-02 1.25 2.10e+00 ± 3.6e-02 1.56e+00 ± 2.5e-02 9.99e-01 ± 1.7e-02 5.98e-01 ± 1.1e-02 1.35 1.52e+00 ± 2.9e-02 1.12e+00 ± 2.0e-02 7.17e-01 ± 1.4e-02 4.26e-01 ± 9.0e-03 1.45 1.05e+00 ± 2.2e-02 7.57e-01 ± 1.5e-02 4.98e-01 ± 1.0e-02 2.91e-01 ± 6.9e-03 1.55 6.78e-01 ± 1.5e-02 5.07e-01 ± 1.0e-02 3.24e-01 ± 7.4e-03 1.97e-01 ± 5.2e-03 1.65 4.93e-01 ± 1.2e-02 3.67e-01 ± 8.3e-03 2.31e-01 ± 5.9e-03 1.42e-01 ± 4.2e-03 1.75 3.60e-01 ± 1.0e-02 2.67e-01 ± 6.7e-03 1.69e-01 ± 4.9e-03 1.03e-01 ± 3.5e-03 1.85 2.56e-01 ± 8.2e-03 1.92e-01 ± 5.3e-03 1.22e-01 ± 3.9e-03 7.29e-02 ± 2.8e-03 1.95 1.78e-01 ± 6.6e-03 1.38e-01 ± 4.3e-03 8.80e-02 ± 3.3e-03 5.80e-02 ± 2.5e-03 2.05 1.35e-01 ± 4.6e-03 1.00e-01 ± 2.9e-03 6.67e-02 ± 2.3e-03 4.13e-02 ± 1.7e-03 2.15 1.02e-01 ± 4.0e-03 7.41e-02 ± 2.4e-03 4.90e-02 ± 1.9e-03 2.92e-02 ± 1.4e-03 2.25 6.65e-02 ± 3.1e-03 5.16e-02 ± 2.0e-03 3.58e-02 ± 1.6e-03 2.09e-02 ± 1.2e-03 2.35 5.43e-02 ± 3.0e-03 4.12e-02 ± 1.9e-03 2.84e-02 ± 1.5e-03 1.87e-02 ± 1.2e-03 2.45 3.97e-02 ± 2.6e-03 3.28e-02 ± 1.7e-03 2.27e-02 ± 1.4e-03 1.21e-02 ± 9.8e-04 2.55 2.88e-02 ± 2.4e-03 2.41e-02 ± 1.5e-03 1.70e-02 ± 1.3e-03 1.11e-02 ± 1.0e-03 2.65 2.21e-02 ± 2.2e-03 1.85e-02 ± 1.4e-03 1.40e-02 ± 1.2e-03 8.92e-03 ± 9.5e-04 2.75 1.58e-02 ± 2.0e-03 1.55e-02 ± 1.4e-03 1.20e-02 ± 1.2e-03 7.80e-03 ± 9.5e-04 2.85 1.37e-02 ± 1.9e-03 1.03e-02 ± 1.1e-03 7.
69e-03 ± 9.7e-04 5.80e-03 ± 8.3e-04 2.95 1.08e-02 ± 1.8e-03 9.32e-03 ± 1.2e-03 6.39e-03 ± 9.6e-04 4.49e-03 ± 7.9e-04 25 TABLE XII: Invariant yields for π + at mid-rapidity in 50–60%, 60–70%, 70–80%, and 80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 50–60% 60–70% 70–80% 80–92% 0.25 4.10e+01 ± 3.4e-01 2.19e+01 ± 1.9e-01 1.03e+01 ± 9.2e-02 5.20e+00 ± 5.0e-02 0.35 2.17e+01 ± 1.9e-01 1.13e+01 ± 1.0e-01 5.27e+00 ± 5.0e-02 2.75e+00 ± 2.8e-02 0.45 1.24e+01 ± 1.1e-01 6.37e+00 ± 6.0e-02 2.95e+00 ± 3.1e-02 1.49e+00 ± 1.8e-02 0.55 7.20e+00 ± 7.0e-02 3.65e+00 ± 3.8e-02 1.62e+00 ± 1.9e-02 8.20e-01 ± 1.1e-02 0.65 4.33e+00 ± 4.7e-02 2.18e+00 ± 2.6e-02 9.63e-01 ± 1.3e-02 4.72e-01 ± 8.1e-03 0.75 2.78e+00 ± 3.4e-02 1.36e+00 ± 1.9e-02 5.91e-01 ± 9.9e-03 2.69e-01 ± 5.9e-03 0.85 1.67e+00 ± 2.3e-02 8.36e-01 ± 1.3e-02 3.53e-01 ± 7.1e-03 1.63e-01 ± 4.4e-03 0.95 1.11e+00 ± 1.7e-02 5.29e-01 ± 9.6e-03 2.22e-01 ± 5.4e-03 1.02e-01 ± 3.4e-03 1.05 7.11e-01 ± 1.2e-02 3.51e-01 ± 7.3e-03 1.41e-01 ± 4.1e-03 6.51e-02 ± 2.6e-03 1.15 4.71e-01 ± 9.2e-03 2.21e-01 ± 5.4e-03 1.01e-01 ± 3.4e-03 4.48e-02 ± 2.2e-03 1.25 3.14e-01 ± 6.9e-03 1.51e-01 ± 4.3e-03 6.06e-02 ± 2.5e-03 2.63e-02 ± 1.6e-03 1.35 2.31e-01 ± 5.8e-03 1.10e-01 ± 3.6e-03 4.25e-02 ± 2.1e-03 2.07e-02 ± 1.5e-03 1.45 1.59e-01 ± 4.6e-03 7.17e-02 ± 2.8e-03 3.04e-02 ± 1.8e-03 1.30e-02 ± 1.1e-03 1.55 1.02e-01 ± 3.4e-03 4.72e-02 ± 2.2e-03 1.89e-02 ± 1.3e-03 8.48e-03 ± 8.8e-04 1.65 7.47e-02 ± 2.8e-03 3.50e-02 ± 1.8e-03 1.52e-02 ± 1.2e-03 7.00e-03 ± 8.1e-04 1.75 5.60e-02 ± 2.4e-03 2.63e-02 ± 1.6e-03 1.03e-02 ± 1.0e-03 5.37e-03 ± 7.1e-04 1.85 3.80e-02 ± 2.0e-03 1.92e-02 ± 1.3e-03 8.04e-03 ± 8.7e-04 3.87e-03 ± 6.0e-04 1.95 2.86e-02 ± 1.7e-03 1.41e-02 ± 1.2e-03 6.06e-03 ± 7.6e-04 2.26e-03 ± 4.6e-04 2.05 2.26e-02 ± 1.2e-03 1.12e-02 ± 8.4e-04 4.34e-03 ± 5.3e-04 1.56e-03 ± 3.1e-04 2.15 1.60e-02 ± 1.0e-03 6.73e-03 ± 6.6e-04 3.09e-03 ± 4.5e-04 1.23e-03 ± 2.8e-04 2.25 1.13e-02 ± 8.6e-04 5.46e-03 ± 5.9e-04 2.43e-03 ± 4.0e-04 8.48e-04 ± 2.3e-04 2.35 9.73e-03 ± 8.5e-04 4.42e-03 ± 5.7e-04 1.98e-03 ± 3.9e-04 8.16e-04 ± 2.5e-04 2.45 7.73e-03 ± 7.8e-04 3.27e-03 ± 5.0e-04 1.30e-03 ± 3.2e-04 3.19e-04 ± 1.6e-04 2.55 5.77e-03 ± 7.2e-04 3.38e-03 ± 5.5e-04 1.17e-03 ± 3.3e-04 5.92e-04 ± 2.3e-04 2.65 4.48e-03 ± 6.7e-04 2.82e-03 ± 5.2e-04 5.70e-04 ± 2.4e-04 3.37e-04 ± 1.8e-04 2.75 3.84e-03 ± 6.7e-04 1.72e-03 ± 4.4e-04 8.51e-04 ± 3.2e-04 4.22e-04 ± 2.2e-04 2.85 2.30e-03 ± 5.2e-04 1.35e-03 ± 4.0e-04 6.79e-04 ± 2.9e-04 1.65e-04 ± 1.4e-04 2.95 2.16e-03 ± 5.5e-04 1.16e-03 ± 4.0e-04 2.88e-04 ± 2.0e-04 1.90e-04 ± 1.6e-04 TABLE XIII: Invariant yields for π − at mid-rapidity in the minimum bias, 0–5%, 5–10%, and 10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] Minimum bias 0–5% 5–10% 10–15% 0.25 1.02e+02 ± 7.9e-01 3.15e+02 ± 2.4e+00 2.71e+02 ± 2.1e+00 2.27e+02 ± 1.8e+00 0.35 5.92e+01 ± 4.6e-01 1.94e+02 ± 1.5e+00 1.64e+02 ± 1.3e+00 1.35e+02 ± 1.1e+00 0.45 3.56e+01 ± 2.9e-01 1.19e+02 ± 9.8e-01 9.93e+01 ± 8.2e-01 8.18e+01 ± 6.8e-01 0.55 2.18e+01 ± 1.9e-01 7.37e+01 ± 6.5e-01 6.17e+01 ± 5.4e-01 5.04e+01 ± 4.5e-01 0.65 1.34e+01 ± 1.2e-01 4.57e+01 ± 4.3e-01 3.82e+01 ± 3.6e-01 3.15e+01 ± 3.0e-01 0.75 8.36e+00 ± 8.2e-02 2.86e+01 ± 2.9e-01 2.40e+01 ± 2.4e-01 1.96e+01 ± 2.0e-01 0.85 5.44e+00 ± 5.7e-02 1.86e+01 ± 2.0e-01 1.56e+01 ± 1.7e-01 1.28e+01 ± 1.4e-01 0.95 3.58e+00 ± 4.1e-02 1.22e+01 ± 1.4e-01 1.02e+01 ± 1.2e-01 8.47e+00 ± 1.0e-01 1.05 2.35e+00 ± 2.8e-02 8.02e+00 ± 1.0e-01 6.75e+00 ± 8.7e-02 5.57e+00 ± 7.2e-02 1.15 1.62e+00 ± 2.1e-02 5.55e+00 ± 7.7e-02 4.64e+00 ± 6.5e-02 3.83e+00 ± 5.5e-02 1.25 1.04e+00 ± 1.4e-02 3.53e+00 ± 5.2e-02 2.94e+00 ± 4.4e-02 2.46e+00 ± 3.8e-02 1.35 7.54e-01 ± 1.1e-02 2.55e+00 ± 4.1e-02 2.19e+00 ± 3.6e-02 1.80e+00 ± 3.0e-02 1.45 5.07e-01 ± 7.6e-03 1.71e+00 ± 3.0e-02 1.48e+00 ± 2.7e-02 1.22e+00 ± 2.2e-02 1.55 3.61e-01 ± 5.7e-03 1.20e+00 ± 2.3e-02 1.02e+00 ± 2.0e-02 8.63e-01 ± 1.8e-02 1.65 2.46e-01 ± 4.0e-03 8.02e-01 ± 1.7e-02 6.94e-01 ± 1.5e-02 5.86e-01 ± 1.3e-02 1.75 1.73e-01 ± 3.0e-03 5.65e-01 ± 1.3e-02 4.91e-01 ± 1.2e-02 4.10e-01 ± 1.0e-02 1.85 1.25e-01 ± 2.3e-03 4.05e-01 ± 1.1e-02 3.48e-01 ± 9.6e-03 3.00e-01 ± 8.5e-03 1.95 8.97e-02 ± 1.8e-03 2.85e-01 ± 8.8e-03 2.53e-01 ± 8.1e-03 2.12e-01 ± 7.1e-03 2.05 6.10e-02 ± 1.1e-03 1.89e-01 ± 5.8e-03 1.64e-01 ± 5.4e-03 1.42e-01 ± 4.8e-03 2.15 4.43e-02 ± 8.7e-04 1.32e-01 ± 4.8e-03 1.20e-01 ± 4.5e-03 1.01e-01 ± 4.0e-03 2.25 3.20e-02 ± 7.0e-04 9.24e-02 ± 4.0e-03 8.31e-02 ± 3.8e-03 7.21e-02 ± 3.4e-03 2.35 2.52e-02 ± 6.3e-04 7.07e-02 ± 3.7e-03 6.29e-02 ± 3.5e-03 5.95e-02 ± 3.3e-03 2.45 1.79e-02 ± 5.1e-04 4.71e-02 ± 3.0e-03 4.47e-02 ± 2.9e-03 3.97e-02 ± 2.7e-03 2.55 1.41e-02 ± 4.8e-04 3.50e-02 ± 2.8e-03 3.33e-02 ± 2.7e-03 3.28e-02 ± 2.7e-03 2.65 1.06e-02 ± 4.1e-04 2.69e-02 ± 2.5e-03 2.36e-02 ± 2.3e-03 2.22e-02 ± 2.2e-03 2.75 8.05e-03 ± 3.7e-04 1.99e-02 ± 2.3e-03 1.67e-02 ± 2.1e-03 1.61e-02 ± 2.0e-03 2.85 6.45e-03 ± 3.5e-04 1.45e-02 ± 2.1e-03 1.63e-02 ± 2.2e-03 1.21e-02 ± 1.9e-03 2.95 4.95e-03 ± 3.2e-04 1.08e-02 ± 1.9e-03 1.16e-02 ± 2.0e-03 1.03e-02 ± 1.8e-03 26 TABLE XIV: Invariant yields for π − at mid-rapidity in 15–20%, 20–30%, 30–40%, and 40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 15–20% 20–30% 30–40% 40–50% 0.25 1.95e+02 ± 1.5e+00 1.51e+02 ± 1.2e+00 1.02e+02 ± 7.9e-01 6.53e+01 ± 5.1e-01 0.35 1.13e+02 ± 9.0e-01 8.62e+01 ± 6.8e-01 5.68e+01 ± 4.5e-01 3.56e+01 ± 2.8e-01 0.45 6.86e+01 ± 5.7e-01 5.18e+01 ± 4.3e-01 3.36e+01 ± 2.8e-01 2.08e+01 ± 1.7e-01 0.55 4.22e+01 ± 3.7e-01 3.17e+01 ± 2.8e-01 2.04e+01 ± 1.8e-01 1.24e+01 ± 1.1e-01 0.65 2.61e+01 ± 2.5e-01 1.95e+01 ± 1.8e-01 1.26e+01 ± 1.2e-01 7.57e+00 ± 7.4e-02 0.75 1.63e+01 ± 1.7e-01 1.22e+01 ± 1.2e-01 7.81e+00 ± 8.0e-02 4.67e+00 ± 4.9e-02 0.85 1.06e+01 ± 1.2e-01 7.96e+00 ± 8.7e-02 5.06e+00 ± 5.7e-02 3.04e+00 ± 3.5e-02 0.95 7.01e+00 ± 8.6e-02 5.31e+00 ± 6.3e-02 3.37e+00 ± 4.1e-02 1.99e+00 ± 2.6e-02 1.05 4.68e+00 ± 6.2e-02 3.45e+00 ± 4.4e-02 2.18e+00 ± 2.9e-02 1.30e+00 ± 1.8e-02 1.15 3.19e+00 ± 4.6e-02 2.36e+00 ± 3.3e-02 1.52e+00 ± 2.2e-02 8.96e-01 ± 1.4e-02 1.25 2.05e+00 ± 3.2e-02 1.55e+00 ± 2.3e-02 9.75e-01 ± 1.5e-02 5.68e-01 ± 9.8e-03 1.35 1.49e+00 ± 2.6e-02 1.10e+00 ± 1.8e-02 7.11e-01 ± 1.2e-02 4.18e-01 ± 8.2e-03 1.45 9.90e-01 ± 1.9e-02 7.55e-01 ± 1.3e-02 4.76e-01 ± 9.2e-03 2.75e-01 ± 6.1e-03 1.55 7.11e-01 ± 1.5e-02 5.41e-01 ± 1.1e-02 3.42e-01 ± 7.4e-03 2.01e-01 ± 5.0e-03 1.65 4.85e-01 ± 1.2e-02 3.71e-01 ± 7.9e-03 2.37e-01 ± 5.7e-03 1.40e-01 ± 3.9e-03 1.75 3.43e-01 ± 9.2e-03 2.56e-01 ± 6.1e-03 1.68e-01 ± 4.5e-03 9.60e-02 ± 3.1e-03 1.85 2.38e-01 ± 7.3e-03 1.93e-01 ± 5.0e-03 1.20e-01 ± 3.7e-03 7.36e-02 ± 2.7e-03 1.95 1.74e-01 ± 6.2e-03 1.36e-01 ± 4.1e-03 8.73e-02 ± 3.1e-03 5.34e-02 ± 2.3e-03 2.05 1.16e-01 ± 4.2e-03 9.65e-02 ± 2.9e-03 6.46e-02 ± 2.2e-03 3.64e-02 ± 1.6e-03 2.15 8.98e-02 ± 3.7e-03 6.97e-02 ± 2.4e-03 4.55e-02 ± 1.9e-03 2.72e-02 ± 1.4e-03 2.25 6.55e-02 ± 3.2e-03 5.15e-02 ± 2.1e-03 3.60e-02 ± 1.7e-03 1.95e-02 ± 1.2e-03 2.35 5.02e-02 ± 2.9e-03 3.83e-02 ± 1.9e-03 2.83e-02 ± 1.6e-03 1.76e-02 ± 1.2e-03 2.45 3.62e-02 ± 2.5e-03 2.84e-02 ± 1.6e-03 1.94e-02 ± 1.3e-03 1.33e-02 ± 1.0e-03 2.55 2.55e-02 ± 2.3e-03 2.37e-02 ± 1.6e-03 1.57e-02 ± 1.3e-03 1.06e-02 ± 1.0e-03 2.65 2.01e-02 ± 2.1e-03 1.68e-02 ± 1.4e-03 1.30e-02 ± 1.2e-03 8.20e-03 ± 9.1e-04 2.75 1.57e-02 ± 1.9e-03 1.35e-02 ± 1.3e-03 1.06e-02 ± 1.1e-03 6.35e-03 ± 8.5e-04 2.85 1.30e-02 ± 1.9e-03 1.03e-02 ± 1.2e-03 8.61e-03 ± 1.1e-03 5.10e-03 ± 8.3e-04 2.95 9.44e-03 ± 1.7e-03 8.45e-03 ± 1.2e-03 6.16e-03 ± 9.8e-04 3.72e-03 ± 7.5e-04 TABLE XV: Invariant yields for π − at mid-rapidity in 50–60%, 60–70%, 70–80%, and 80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 50–60% 60–70% 70–80% 80–92% 0.25 3.92e+01 ±
3.1e-01 2.07e+01 ± 1.7e-01 9.77e+00 ± 8.2e-02 5.03e+00 ± 4.5e-02 0.35 2.10e+01 ± 1.7e-01 1.09e+01 ± 9.0e-02 5.19e+00 ± 4.6e-02 2.67e+00 ± 2.6e-02 0.45 1.21e+01 ± 1.0e-01 6.21e+00 ± 5.5e-02 2.84e+00 ± 2.8e-02 1.45e+00 ± 1.6e-02 0.55 7.13e+00 ± 6.6e-02 3.59e+00 ± 3.5e-02 1.62e+00 ± 1.8e-02 8.13e-01 ± 1.1e-02 0.65 4.30e+00 ± 4.4e-02 2.16e+00 ± 2.4e-02 9.32e-01 ± 1.2e-02 4.54e-01 ± 7.3e-03 0.75 2.61e+00 ± 2.9e-02 1.30e+00 ± 1.6e-02 5.61e-01 ± 8.6e-03 2.70e-01 ± 5.3e-03 0.85 1.68e+00 ± 2.1e-02 8.30e-01 ± 1.2e-02 3.52e-01 ± 6.4e-03 1.59e-01 ± 3.9e-03 0.95 1.10e+00 ± 1.5e-02 5.26e-01 ± 8.7e-03 2.27e-01 ± 5.0e-03 1.07e-01 ± 3.2e-03 1.05 7.13e-01 ± 1.1e-02 3.45e-01 ± 6.6e-03 1.41e-01 ± 3.8e-03 6.63e-02 ± 2.4e-03 1.15 4.88e-01 ± 8.8e-03 2.32e-01 ± 5.2e-03 9.75e-02 ± 3.1e-03 4.46e-02 ± 2.0e-03 1.25 3.12e-01 ± 6.3e-03 1.47e-01 ± 3.8e-03 6.31e-02 ± 2.4e-03 2.65e-02 ± 1.5e-03 1.35 2.29e-01 ± 5.3e-03 1.05e-01 ± 3.2e-03 4.17e-02 ± 1.9e-03 2.02e-02 ± 1.3e-03 1.45 1.51e-01 ± 4.1e-03 7.32e-02 ± 2.6e-03 2.81e-02 ± 1.6e-03 1.28e-02 ± 1.0e-03 1.55 1.10e-01 ± 3.4e-03 5.15e-02 ± 2.2e-03 2.11e-02 ± 1.4e-03 9.27e-03 ± 8.8e-04 1.65 7.11e-02 ± 2.6e-03 3.83e-02 ± 1.8e-03 1.53e-02 ± 1.1e-03 6.56e-03 ± 7.3e-04 1.75 5.38e-02 ± 2.2e-03 2.51e-02 ± 1.4e-03 1.08e-02 ± 9.5e-04 5.14e-03 ± 6.5e-04 1.85 4.00e-02 ± 1.9e-03 1.87e-02 ± 1.2e-03 8.06e-03 ± 8.2e-04 3.51e-03 ± 5.3e-04 1.95 2.88e-02 ± 1.6e-03 1.30e-02 ± 1.1e-03 6.03e-03 ± 7.3e-04 2.70e-03 ± 4.8e-04 2.05 2.04e-02 ± 1.2e-03 8.63e-03 ± 7.4e-04 4.23e-03 ± 5.3e-04 1.40e-03 ± 3.0e-04 2.15 1.53e-02 ± 1.0e-03 6.88e-03 ± 6.7e-04 3.17e-03 ± 4.6e-04 1.25e-03 ± 2.9e-04 2.25 1.08e-02 ± 8.8e-04 4.71e-03 ± 5.7e-04 1.89e-03 ± 3.7e-04 8.66e-04 ± 2.5e-04 2.35 8.95e-03 ± 8.4e-04 4.42e-03 ± 5.8e-04 1.96e-03 ± 4.0e-04 6.65e-04 ± 2.3e-04 2.45 7.17e-03 ± 7.6e-04 3.04e-03 ± 4.9e-04 1.17e-03 ± 3.1e-04 5.61e-04 ± 2.1e-04 2.55 5.72e-03 ± 7.5e-04 2.96e-03 ± 5.3e-04 1.16e-03 ± 3.4e-04 3.79e-04 ± 1.9e-04 2.65 4.94e-03 ± 7.1e-04 2.21e-03 ± 4.7e-04 8.05e-04 ± 2.9e-04 4.14e-04 ± 2.0e-04 2.75 3.43e-03 ± 6.3e-04 1.54e-03 ± 4.2e-04 3.78e-04 ± 2.1e-04 3.34e-04 ± 2.0e-04 2.85 2.67e-03 ± 6.0e-04 1.24e-03 ± 4.1e-04 2.87e-04 ± 2.0e-04 2.85e-04 ± 2.0e-04 2.95 1.73e-03 ± 5.1e-04 1.25e-03 ± 4.3e-04 6.75e-04 ± 3.2e-04 2.04e-04 ± 1.8e-04 27 TABLE XVI: Invariant yields for K+ at mid-rapidity in the minimum bias, 0–5%, 5–10%, and 10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] Minimum bias 0–5% 5–10% 10–15% 0.45 5.46e+00 ± 1.1e-01 1.83e+01 ± 3.9e-01 1.50e+01 ± 3.3e-01 1.29e+01 ± 2.8e-01 0.55 4.28e+00 ± 7.8e-02 1.48e+01 ± 2.9e-01 1.20e+01 ± 2.4e-01 9.88e+00 ± 2.0e-01 0.65 3.11e+00 ± 5.4e-02 1.05e+01 ± 2.0e-01 8.75e+00 ± 1.7e-01 7.38e+00 ± 1.4e-01 0.75 2.27e+00 ± 3.9e-02 7.97e+00 ± 1.5e-01 6.48e+00 ± 1.2e-01 5.39e+00 ± 1.0e-01 0.85 1.69e+00 ± 3.0e-02 5.96e+00 ± 1.2e-01 4.81e+00 ± 9.5e-02 4.02e+00 ± 8.1e-02 0.95 1.20e+00 ± 2.2e-02 4.19e+00 ± 8.5e-02 3.47e+00 ± 7.2e-02 2.91e+00 ± 6.1e-02 1.05 9.06e-01 ± 1.7e-02 3.20e+00 ± 6.8e-02 2.61e+00 ± 5.7e-02 2.21e+00 ± 5.0e-02 1.15 6.57e-01 ± 1.3e-02 2.31e+00 ± 5.2e-02 1.91e+00 ± 4.4e-02 1.63e+00 ± 3.9e-02 1.25 4.55e-01 ± 8.9e-03 1.64e+00 ± 3.9e-02 1.32e+00 ± 3.3e-02 1.14e+00 ± 2.9e-02 1.35 3.24e-01 ± 6.5e-03 1.13e+00 ± 2.9e-02 9.63e-01 ± 2.5e-02 7.88e-01 ± 2.2e-02 1.45 2.43e-01 ± 5.1e-03 8.52e-01 ± 2.4e-02 7.33e-01 ± 2.1e-02 6.05e-01 ± 1.8e-02 1.55 1.76e-01 ± 3.8e-03 6.03e-01 ± 1.8e-02 5.16e-01 ± 1.6e-02 4.33e-01 ± 1.4e-02 1.65 1.27e-01 ± 2.9e-03 4.43e-01 ± 1.5e-02 3.84e-01 ± 1.3e-02 3.04e-01 ± 1.1e-02 1.75 9.47e-02 ± 2.3e-03 3.61e-01 ± 1.3e-02 2.76e-01 ± 1.1e-02 2.28e-01 ± 9.3e-03 1.85 7.24e-02 ± 1.8e-03 2.64e-01 ± 1.0e-02 2.17e-01 ± 9.0e-03 1.72e-01 ± 7.7e-03 1.95 5.67e-02 ± 1.5e-03 2.12e-01 ± 9.1e-03 1.67e-01 ± 7.8e-03 1.37e-01 ± 6.9e-03 TABLE XVII: Invariant yields for K+ at mid-rapidity in 15–20%, 20–30%, 30–40%, and 40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 15–20% 20–30% 30–40% 40–50% 0.45 1.04e+01 ± 2.3e-01 7.81e+00 ± 1.7e-01 5.11e+00 ± 1.1e-01 3.28e+00 ± 7.8e-02 0.55 8.30e+00 ± 1.7e-01 6.22e+00 ± 1.2e-01 4.06e+00 ± 8.3e-02 2.43e+00 ± 5.3e-02 0.65 6.20e+00 ± 1.2e-01 4.51e+00 ± 8.5e-02 2.89e+00 ± 5.7e-02 1.78e+00 ± 3.8e-02 0.75 4.46e+00 ± 8.8e-02 3.31e+00 ± 6.2e-02 2.07e+00 ± 4.1e-02 1.26e+00 ± 2.7e-02 0.85 3.36e+00 ± 7.0e-02 2.50e+00 ± 4.9e-02 1.60e+00 ± 3.3e-02 9.00e-01 ± 2.1e-02 0.95 2.40e+00 ± 5.2e-02 1.74e+00 ± 3.6e-02 1.08e+00 ± 2.4e-02 6.46e-01 ± 1.6e-02 1.05 1.81e+00 ± 4.2e-02 1.31e+00 ± 2.8e-02 8.42e-01 ± 2.0e-02 4.82e-01 ± 1.3e-02 1.15 1.29e+00 ± 3.2e-02 9.60e-01 ± 2.2e-02 6.01e-01 ± 1.5e-02 3.48e-01 ± 1.0e-02 1.25 8.82e-01 ± 2.4e-02 6.54e-01 ± 1.6e-02 4.22e-01 ± 1.1e-02 2.34e-01 ± 7.5e-03 1.35 6.60e-01 ± 1.9e-02 4.68e-01 ± 1.2e-02 2.99e-01 ± 8.7e-03 1.70e-01 ± 5.9e-03 1.45 4.91e-01 ± 1.5e-02 3.50e-01 ± 9.9e-03 2.22e-01 ± 7.2e-03 1.20e-01 ± 4.8e-03 1.55 3.55e-01 ± 1.2e-02 2.59e-01 ± 7.9e-03 1.63e-01 ± 5.8e-03 9.25e-02 ± 4.0e-03 1.65 2.62e-01 ± 1.0e-02 1.88e-01 ± 6.3e-03 1.14e-01 ± 4.6e-03 6.22e-02 ± 3.1e-03 1.75 1.92e-01 ± 8.3e-03 1.34e-01 ± 5.1e-03 8.52e-02 ± 3.8e-03 4.81e-02 ± 2.7e-03 1.85 1.48e-01 ± 7.0e-03 1.04e-01 ± 4.2e-03 6.58e-02 ± 3.2e-03 3.66e-02 ± 2.3e-03 1.95 1.14e-01 ± 6.1e-03 8.21e-02 ± 3.7e-03 4.87e-02 ± 2.7e-03 2.91e-02 ± 2.0e-03 TABLE XVIII: Invariant yields for K+ at mid-rapidity in 50–60%, 60–70%, 70–80%, and 80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 50–60% 60–70% 70–80% 80–92% 0.45 1.93e+00 ± 5.0e-02 9.56e-01 ± 2.9e-02 4.06e-01 ± 1.7e-02 1.88e-01 ± 1.1e-02 0.55 1.36e+00 ± 3.3e-02 6.72e-01 ± 2.0e-02 2.89e-01 ± 1.2e-02 1.48e-01 ± 7.8e-03 0.65 1.01e+00 ± 2.4e-02 4.81e-01 ± 1.4e-02 1.88e-01 ± 8.0e-03 1.02e-01 ± 5.6e-03 0.75 6.82e-01 ± 1.7e-02 3.40e-01 ± 1.1e-02 1.24e-01 ± 5.8e-03 5.88e-02 ± 3.9e-03 0.85 4.77e-01 ± 1.3e-02 2.33e-01 ± 8.1e-03 9.39e-02 ± 4.8e-03 3.87e-02 ± 3.0e-03 0.95 3.51e-01 ± 1.0e-02 1.69e-01 ± 6.4e-03 5.66e-02 ± 3.5e-03 2.99e-02 ± 2.5e-03 1.05 2.54e-01 ± 8.2e-03 1.19e-01 ± 5.1e-03 4.40e-02 ± 3.0e-03 2.07e-02 ± 2.0e-03 1.15 1.80e-01 ± 6.4e-03 7.84e-02 ± 3.9e-03 3.12e-02 ± 2.4e-03 1.64e-02 ± 1.7e-03 1.25 1.28e-01 ± 5.1e-03 5.43e-02 ± 3.1e-03 2.07e-02 ± 1.9e-03 7.94e-03 ± 1.1e-03 1.35 8.53e-02 ± 3.9e-03 3.85e-02 ± 2.5e-03 1.38e-02 ± 1.5e-03 6.53e-03 ± 9.9e-04 1.45 6.40e-02 ± 3.3e-03 2.94e-02 ± 2.1e-03 1.34e-02 ± 1.4e-03 5.70e-03 ± 9.2e-04 1.55 4.73e-02 ± 2.7e-03 2.10e-02 ± 1.8e-03 6.85e-03 ± 1.0e-03 2.84e-03 ± 6.4e-04 1.65 3.39e-02 ± 2.2e-03 1.60e-02 ± 1.5e-03 5.62e-03 ± 8.9e-04 2.67e-03 ± 6.1e-04 1.75 2.31e-02 ± 1.8e-03 1.04e-02 ± 1.2e-03 4.19e-03 ± 7.6e-04 1.85e-03 ± 5.0e-04 1.85 1.72e-02 ± 1.5e-03 8.75e-03 ± 1.1e-03 3.39e-03 ± 6.7e-04 2.09e-03 ± 5.2e-04 1.95 1.53e-02 ± 1.4e-03 6.49e-03 ± 9.2e-04 2.75e-03 ± 6.1e-04 1.16e-03 ± 3.9e-04 28 TABLE XIX: Invariant yields for K− at mid-rapidity in the minimum bias, 0–5%, 5–10%, and 10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] Minimum bias 0–5% 5–10% 10–15% 0.45 4.87e+00 ± 9.3e-02 1.64e+01 ± 3.4e-01 1.36e+01 ± 2.8e-01 1.12e+01 ± 2.4e-01 0.55 3.88e+00 ± 6.7e-02 1.31e+01 ± 2.4e-01 1.09e+01 ± 2.0e-01 8.91e+00 ± 1.7e-01 0.65 2.96e+00 ± 4.9e-02 1.01e+01 ± 1.8e-01 8.57e+00 ± 1.5e-01 6.94e+00 ± 1.3e-01 0.75 2.20e+00 ± 3.6e-02 7.69e+00 ± 1.4e-01 6.27e+00 ± 1.1e-01 5.14e+00 ± 9.5e-02 0.85 1.59e+00 ± 2.6e-02 5.61e+00 ± 1.0e-01 4.55e+00 ± 8.4e-02 3.82e+00 ± 7.2e-02 0.95 1.14e+00 ± 1.9e-02 4.11e+00 ± 7.7e-02 3.36e+00 ± 6.5e-02 2.76e+00 ± 5.4e-02 1.05 8.50e-01 ± 1.5e-02 3.03e+00 ± 6.0e-02 2.53e+00 ± 5.2e-02 2.05e+00 ± 4.3e-02 1.15 5.96e-01 ± 1.0e-02 2.11e+00 ± 4.4e-02 1.79e+00 ± 3.8e-02 1.44e+00 ± 3.2e-02 1.25 4.29e-01 ± 7.8e-03 1.53e+00 ± 3.4e-02 1.25e+00 ± 2.9e-02 1.05e+00 ± 2.5e-02 1.35 3.23e-01 ± 6.2e-03 1.15e+00 ± 2.8e-02 9.45e-01 ± 2.4e-02 8.03e-
01 ± 2.1e-02 1.45 2.32e-01 ± 4.6e-03 8.42e-01 ± 2.2e-02 6.97e-01 ± 1.9e-02 5.62e-01 ± 1.6e-02 1.55 1.67e-01 ± 3.4e-03 5.86e-01 ± 1.7e-02 4.97e-01 ± 1.5e-02 4.16e-01 ± 1.3e-02 1.65 1.21e-01 ± 2.6e-03 4.42e-01 ± 1.4e-02 3.82e-01 ± 1.2e-02 2.93e-01 ± 1.0e-02 1.75 8.78e-02 ± 2.0e-03 3.17e-01 ± 1.1e-02 2.64e-01 ± 9.6e-03 2.11e-01 ± 8.2e-03 1.85 6.76e-02 ± 1.6e-03 2.52e-01 ± 9.4e-03 2.10e-01 ± 8.4e-03 1.61e-01 ± 7.0e-03 1.95 5.10e-02 ± 1.3e-03 1.83e-01 ± 7.9e-03 1.53e-01 ± 7.1e-03 1.22e-01 ± 6.1e-03 TABLE XX: Invariant yields for K− at mid-rapidity in 15–20%, 20–30%, 30–40%, and 40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 15–20% 20–30% 30–40% 40–50% 0.45 9.24e+00 ± 2.0e-01 7.05e+00 ± 1.5e-01 4.60e+00 ± 9.9e-02 2.79e+00 ± 6.4e-02 0.55 7.61e+00 ± 1.5e-01 5.62e+00 ± 1.0e-01 3.68e+00 ± 7.1e-02 2.25e+00 ± 4.7e-02 0.65 5.78e+00 ± 1.1e-01 4.29e+00 ± 7.7e-02 2.74e+00 ± 5.1e-02 1.69e+00 ± 3.4e-02 0.75 4.33e+00 ± 8.1e-02 3.22e+00 ± 5.8e-02 2.04e+00 ± 3.8e-02 1.19e+00 ± 2.5e-02 0.85 3.13e+00 ± 6.0e-02 2.29e+00 ± 4.2e-02 1.49e+00 ± 2.9e-02 8.47e-01 ± 1.8e-02 0.95 2.23e+00 ± 4.5e-02 1.61e+00 ± 3.1e-02 1.04e+00 ± 2.1e-02 6.04e-01 ± 1.4e-02 1.05 1.70e+00 ± 3.7e-02 1.21e+00 ± 2.5e-02 7.74e-01 ± 1.7e-02 4.49e-01 ± 1.1e-02 1.15 1.17e+00 ± 2.7e-02 8.78e-01 ± 1.9e-02 5.39e-01 ± 1.3e-02 3.11e-01 ± 8.4e-03 1.25 8.58e-01 ± 2.1e-02 6.29e-01 ± 1.4e-02 3.87e-01 ± 9.9e-03 2.25e-01 ± 6.8e-03 1.35 6.26e-01 ± 1.7e-02 4.76e-01 ± 1.2e-02 2.97e-01 ± 8.3e-03 1.64e-01 ± 5.5e-03 1.45 4.56e-01 ± 1.4e-02 3.41e-01 ± 9.2e-03 2.09e-01 ± 6.5e-03 1.21e-01 ± 4.5e-03 1.55 3.25e-01 ± 1.1e-02 2.50e-01 ± 7.3e-03 1.43e-01 ± 5.0e-03 8.71e-02 ± 3.7e-03 1.65 2.36e-01 ± 8.9e-03 1.72e-01 ± 5.7e-03 1.07e-01 ± 4.2e-03 6.17e-02 ± 3.0e-03 1.75 1.83e-01 ± 7.4e-03 1.29e-01 ± 4.6e-03 7.79e-02 ± 3.4e-03 4.42e-02 ± 2.4e-03 1.85 1.29e-01 ± 6.0e-03 1.01e-01 ± 4.0e-03 5.84e-02 ± 2.8e-03 3.24e-02 ± 2.0e-03 1.95 1.05e-01 ± 5.5e-03 7.67e-02 ± 3.4e-03 4.31e-02 ± 2.4e-03 2.46e-02 ± 1.8e-03 TABLE XXI: Invariant yields for K− at mid-rapidity in 50–60%, 60–70%, 70–80%, and 80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 50–60% 60–70% 70–80% 80–92% 0.45 1.73e+00 ± 4.3e-02 8.11e-01 ± 2.5e-02 3.89e-01 ± 1.6e-02 1.82e-01 ± 9.9e-03 0.55 1.25e+00 ± 2.9e-02 6.37e-01 ± 1.8e-02 2.80e-01 ± 1.1e-02 1.37e-01 ± 7.1e-03 0.65 9.30e-01 ± 2.1e-02 4.43e-01 ± 1.3e-02 1.83e-01 ± 7.5e-03 1.02e-01 ± 5.4e-03 0.75 6.59e-01 ± 1.6e-02 3.16e-01 ± 9.5e-03 1.40e-01 ± 5.9e-03 6.21e-02 ± 3.8e-03 0.85 4.65e-01 ± 1.2e-02 2.31e-01 ± 7.4e-03 8.42e-02 ± 4.2e-03 3.81e-02 ± 2.7e-03 0.95 3.22e-01 ± 9.0e-03 1.56e-01 ± 5.7e-03 5.67e-02 ± 3.2e-03 2.57e-02 ± 2.1e-03 1.05 2.32e-01 ± 7.2e-03 1.09e-01 ± 4.5e-03 4.26e-02 ± 2.7e-03 1.73e-02 ± 1.7e-03 1.15 1.60e-01 ± 5.5e-03 7.06e-02 ± 3.4e-03 2.98e-02 ± 2.1e-03 1.32e-02 ± 1.4e-03 1.25 1.15e-01 ± 4.4e-03 5.72e-02 ± 2.9e-03 1.84e-02 ± 1.6e-03 9.79e-03 ± 1.2e-03 1.35 8.85e-02 ± 3.8e-03 3.67e-02 ± 2.3e-03 1.59e-02 ± 1.5e-03 7.78e-03 ± 1.0e-03 1.45 5.83e-02 ± 3.0e-03 2.38e-02 ± 1.8e-03 1.12e-02 ± 1.2e-03 4.22e-03 ± 7.5e-04 1.55 4.60e-02 ± 2.5e-03 1.89e-02 ± 1.6e-03 7.86e-03 ± 1.0e-03 3.92e-03 ± 7.1e-04 1.65 3.05e-02 ± 2.0e-03 1.53e-02 ± 1.4e-03 6.44e-03 ± 9.0e-04 2.92e-03 ± 6.0e-04 1.75 2.07e-02 ± 1.6e-03 1.00e-02 ± 1.1e-03 3.65e-03 ± 6.6e-04 1.27e-03 ± 3.9e-04 1.85 1.84e-02 ± 1.5e-03 7.82e-03 ± 9.5e-04 2.81e-03 ± 5.8e-04 1.44e-03 ± 4.1e-04 1.95 1.46e-02 ± 1.3e-03 6.14e-03 ± 8.6e-04 2.12e-03 ± 5.1e-04 1.30e-03 ± 4.0e-04 29 TABLE XXII: Invariant yields for protons at mid-rapidity in the minimum bias, 0–5%, 5–10%, and 10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] Minimum bias 0–5% 5–10% 10–15% 0.65 9.51e-01 ± 2.7e-02 2.90e+00 ± 9.3e-02 2.44e+00 ± 8.0e-02 2.09e+00 ± 6.9e-02 0.75 8.47e-01 ± 2.4e-02 2.65e+00 ± 8.5e-02 2.24e+00 ± 7.3e-02 1.87e+00 ± 6.2e-02 0.85 7.08e-01 ± 2.0e-02 2.28e+00 ± 7.3e-02 1.91e+00 ± 6.3e-02 1.60e+00 ± 5.3e-02 0.95 6.06e-01 ± 1.8e-02 2.00e+00 ± 6.6e-02 1.66e+00 ± 5.5e-02 1.41e+00 ± 4.8e-02 1.05 5.05e-01 ± 1.5e-02 1.68e+00 ± 5.7e-02 1.43e+00 ± 4.9e-02 1.16e+00 ± 4.1e-02 1.15 4.23e-01 ± 1.3e-02 1.46e+00 ± 5.1e-02 1.22e+00 ± 4.3e-02 9.85e-01 ± 3.6e-02 1.25 3.30e-01 ± 1.0e-02 1.16e+00 ± 4.2e-02 9.51e-01 ± 3.5e-02 7.92e-01 ± 3.0e-02 1.35 2.71e-01 ± 8.8e-03 9.72e-01 ± 3.7e-02 7.96e-01 ± 3.1e-02 6.55e-01 ± 2.6e-02 1.45 2.04e-01 ± 6.7e-03 7.42e-01 ± 2.9e-02 6.09e-01 ± 2.5e-02 5.07e-01 ± 2.1e-02 1.55 1.68e-01 ± 5.8e-03 6.05e-01 ± 2.5e-02 5.08e-01 ± 2.2e-02 4.21e-01 ± 1.9e-02 1.65 1.25e-01 ± 4.4e-03 4.55e-01 ± 2.0e-02 3.77e-01 ± 1.7e-02 3.02e-01 ± 1.4e-02 1.75 9.38e-02 ± 3.4e-03 3.51e-01 ± 1.6e-02 2.76e-01 ± 1.4e-02 2.29e-01 ± 1.2e-02 1.85 7.50e-02 ± 2.8e-03 2.85e-01 ± 1.4e-02 2.28e-01 ± 1.2e-02 1.79e-01 ± 1.0e-02 1.95 5.37e-02 ± 2.1e-03 1.99e-01 ± 1.1e-02 1.61e-01 ± 9.3e-03 1.36e-01 ± 8.2e-03 2.10 3.71e-02 ± 9.4e-04 1.35e-01 ± 5.0e-03 1.12e-01 ± 4.4e-03 9.18e-02 ± 3.8e-03 2.30 2.15e-02 ± 5.9e-04 7.69e-02 ± 3.5e-03 6.73e-02 ± 3.2e-03 5.39e-02 ± 2.7e-03 2.50 1.21e-02 ± 4.2e-04 4.39e-02 ± 2.5e-03 3.67e-02 ± 2.2e-03 3.05e-02 ± 2.0e-03 2.70 7.26e-03 ± 2.8e-04 2.44e-02 ± 1.8e-03 2.27e-02 ± 1.7e-03 1.78e-02 ± 1.5e-03 2.90 4.17e-03 ± 1.9e-04 1.54e-02 ± 1.4e-03 1.16e-02 ± 1.2e-03 1.04e-02 ± 1.1e-03 3.25 1.70e-03 ± 8.3e-05 5.98e-03 ± 5.5e-04 5.17e-03 ± 5.0e-04 4.04e-03 ± 4.3e-04 3.75 5.79e-04 ± 4.4e-05 2.05e-03 ± 3.1e-04 1.68e-03 ± 2.8e-04 1.45e-03 ± 2.5e-04 4.25 2.21e-04 ± 2.7e-05 8.96e-04 ± 2.2e-04 7.04e-04 ± 1.9e-04 4.70e-04 ± 1.5e-04 TABLE XXIII: Invariant yields for protons at mid-rapidity in 15–20%, 20–30%, 30–40%, and 40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 15–20% 20–30% 30–40% 40–50% 0.65 1.76e+00 ± 6.0e-02 1.37e+00 ± 4.4e-02 9.68e-01 ± 3.2e-02 6.31e-01 ± 2.2e-02 0.75 1.59e+00 ± 5.4e-02 1.24e+00 ± 4.0e-02 8.52e-01 ± 2.9e-02 5.39e-01 ± 1.9e-02 0.85 1.34e+00 ± 4.6e-02 1.02e+00 ± 3.3e-02 7.06e-01 ± 2.4e-02 4.33e-01 ± 1.6e-02 0.95 1.16e+00 ± 4.1e-02 8.90e-01 ± 2.9e-02 5.79e-01 ± 2.0e-02 3.60e-01 ± 1.4e-02 1.05 9.75e-01 ± 3.5e-02 7.41e-01 ± 2.5e-02 4.83e-01 ± 1.7e-02 2.96e-01 ± 1.2e-02 1.15 8.38e-01 ± 3.1e-02 6.27e-01 ± 2.2e-02 3.93e-01 ± 1.5e-02 2.33e-01 ± 9.7e-03 1.25 6.47e-01 ± 2.5e-02 4.83e-01 ± 1.8e-02 3.09e-01 ± 1.2e-02 1.77e-01 ± 7.9e-03 1.35 5.35e-01 ± 2.2e-02 3.93e-01 ± 1.5e-02 2.46e-01 ± 1.0e-02 1.40e-01 ± 6.7e-03 1.45 4.04e-01 ± 1.8e-02 2.90e-01 ± 1.2e-02 1.89e-01 ± 8.3e-03 1.05e-01 ± 5.4e-03 1.55 3.33e-01 ± 1.6e-02 2.42e-01 ± 1.0e-02 1.49e-01 ± 7.1e-03 8.39e-02 ± 4.7e-03 1.65 2.60e-01 ± 1.3e-02 1.80e-01 ± 8.1e-03 1.10e-01 ± 5.6e-03 6.02e-02 ± 3.7e-03 1.75 1.86e-01 ± 1.0e-02 1.36e-01 ± 6.6e-03 8.52e-02 ± 4.7e-03 4.64e-02 ± 3.1e-03 1.85 1.51e-01 ± 8.9e-03 1.08e-01 ± 5.7e-03 6.68e-02 ± 4.0e-03 3.64e-02 ± 2.7e-03 1.95 1.06e-01 ± 6.9e-03 7.98e-02 ± 4.5e-03 4.72e-02 ± 3.2e-03 2.53e-02 ± 2.1e-03 2.10 7.41e-02 ± 3.3e-03 5.63e-02 ± 2.1e-03 3.32e-02 ± 1.5e-03 1.82e-02 ± 1.0e-03 2.30 4.46e-02 ± 2.4e-03 3.19e-02 ± 1.5e-03 1.96e-02 ± 1.1e-03 9.61e-03 ± 7.2e-04 2.50 2.52e-02 ± 1.7e-03 1.79e-02 ± 1.1e-03 1.07e-02 ± 7.8e-04 5.83e-03 ± 5.5e-04 2.70 1.55e-02 ± 1.3e-03 1.08e-02 ± 8.0e-04 6.78e-03 ± 6.1e-04 3.73e-03 ± 4.4e-04 2.90 8.35e-03 ± 9.5e-04 6.05e-03 ± 5.8e-04 4.10e-03 ± 4.7e-04 2.20e-03 ± 3.3e-04 3.25 3.51e-03 ± 3.9e-04 2.54e-03 ± 2.4e-04 1.64e-03 ± 1.9e-04 8.36e-04 ± 1.3e-04 3.75 1.18e-03 ± 2.2e-04 8.20e-04 ± 1.3e-04 5.66e-04 ± 1.1e-04 3.25e-04 ± 7.8e-05 4.25 4.64e-04 ± 1.4e-04 3.07e-04 ± 8.3e-05 1.93e-04 ± 6.4e-05 1.07e-04 ± 4.7e-05 30 TABLE XXIV: Invariant yields for protons at mid-rapidity in 50–60%, 60–70%, 70–80%, and 80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 50–60% 60–70% 70–80% 80–92% 0.65 3.82e-01 ± 1.5e-02 2.04e-01 ± 9.7e-03 9.09e-02 ± 5.9e-03 4
.96e-02 ± 4.2e-03 0.75 3.25e-01 ± 1.3e-02 1.65e-01 ± 8.1e-03 7.04e-02 ± 4.9e-03 3.79e-02 ± 3.4e-03 0.85 2.60e-01 ± 1.1e-02 1.27e-01 ± 6.5e-03 5.41e-02 ± 4.0e-03 2.62e-02 ± 2.7e-03 0.95 2.08e-01 ± 9.1e-03 1.00e-01 ± 5.5e-03 4.11e-02 ± 3.3e-03 2.06e-02 ± 2.3e-03 1.05 1.61e-01 ± 7.5e-03 7.43e-02 ± 4.5e-03 3.14e-02 ± 2.8e-03 1.54e-02 ± 1.9e-03 1.15 1.24e-01 ± 6.2e-03 5.88e-02 ± 3.8e-03 2.40e-02 ± 2.3e-03 8.08e-03 ± 1.3e-03 1.25 9.20e-02 ± 5.0e-03 3.98e-02 ± 3.0e-03 1.68e-02 ± 1.9e-03 6.94e-03 ± 1.2e-03 1.35 7.34e-02 ± 4.4e-03 3.41e-02 ± 2.7e-03 1.21e-02 ± 1.6e-03 5.84e-03 ± 1.1e-03 1.45 4.98e-02 ± 3.3e-03 2.41e-02 ± 2.2e-03 9.02e-03 ± 1.3e-03 3.61e-03 ± 8.1e-04 1.55 4.43e-02 ± 3.1e-03 1.69e-02 ± 1.8e-03 6.98e-03 ± 1.1e-03 2.19e-03 ± 6.3e-04 1.65 3.29e-02 ± 2.6e-03 1.30e-02 ± 1.5e-03 4.57e-03 ± 9.0e-04 1.36e-03 ± 4.8e-04 1.75 2.37e-02 ± 2.1e-03 9.76e-03 ± 1.3e-03 3.81e-03 ± 8.0e-04 1.40e-03 ± 4.8e-04 1.85 1.80e-02 ± 1.8e-03 7.16e-03 ± 1.1e-03 2.56e-03 ± 6.6e-04 8.09e-04 ± 3.7e-04 1.95 1.24e-02 ± 1.4e-03 5.34e-03 ± 9.1e-04 2.04e-03 ± 5.7e-04 8.46e-04 ± 3.6e-04 2.10 9.33e-03 ± 7.2e-04 3.47e-03 ± 4.2e-04 1.34e-03 ± 2.7e-04 4.08e-04 ± 1.5e-04 2.30 4.86e-03 ± 5.0e-04 2.28e-03 ± 3.4e-04 6.06e-04 ± 1.8e-04 2.88e-04 ± 1.2e-04 2.50 3.01e-03 ± 3.9e-04 9.91e-04 ± 2.2e-04 3.91e-04 ± 1.4e-04 2.19e-04 ± 1.0e-04 2.70 1.66e-03 ± 2.9e-04 6.31e-04 ± 1.7e-04 2.37e-04 ± 1.1e-04 1.12e-04 ± 7.4e-05 2.90 1.03e-03 ± 2.2e-04 4.62e-04 ± 1.5e-04 1.06e-04 ± 7.3e-05 3.22e-05 ± 4.0e-05 3.25 4.01e-04 ± 8.7e-05 1.66e-04 ± 5.5e-05 6.73e-05 ± 3.6e-05 2.02e-05 ± 2.0e-05 3.75 1.45e-04 ± 5.2e-05 5.72e-05 ± 3.2e-05 2.13e-05 ± 1.9e-05 2.89e-06 ± 7.7e-06 4.25 4.94e-05 ± 3.2e-05 2.40e-05 ± 2.2e-05 1.02e-05 ± 1.5e-05 2.43e-06 ± 6.7e-06 TABLE XXV: Invariant yields for anti-protons at mid-rapidity in the minimum bias, 0–5%, 5–10%, and 10–15% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] Minimum bias 0–5% 5–10% 10–15% 0.65 6.73e-01 ± 2.0e-02 2.00e+00 ± 6.8e-02 1.73e+00 ± 6.0e-02 1.48e+00 ± 5.2e-02 0.75 6.16e-01 ± 1.8e-02 1.89e+00 ± 6.2e-02 1.61e+00 ± 5.4e-02 1.34e+00 ± 4.6e-02 0.85 5.28e-01 ± 1.5e-02 1.67e+00 ± 5.4e-02 1.42e+00 ± 4.7e-02 1.19e+00 ± 4.1e-02 0.95 4.52e-01 ± 1.3e-02 1.47e+00 ± 4.8e-02 1.25e+00 ± 4.2e-02 1.05e+00 ± 3.6e-02 1.05 3.65e-01 ± 1.1e-02 1.21e+00 ± 4.1e-02 1.04e+00 ± 3.6e-02 8.82e-01 ± 3.1e-02 1.15 3.19e-01 ± 9.7e-03 1.10e+00 ± 3.9e-02 9.28e-01 ± 3.4e-02 7.39e-01 ± 2.8e-02 1.25 2.53e-01 ± 7.9e-03 8.90e-01 ± 3.3e-02 7.47e-01 ± 2.8e-02 6.15e-01 ± 2.4e-02 1.35 2.01e-01 ± 6.5e-03 7.24e-01 ± 2.8e-02 6.08e-01 ± 2.4e-02 4.88e-01 ± 2.0e-02 1.45 1.66e-01 ± 5.6e-03 6.12e-01 ± 2.5e-02 5.01e-01 ± 2.1e-02 4.09e-01 ± 1.8e-02 1.55 1.22e-01 ± 4.1e-03 4.43e-01 ± 1.9e-02 3.69e-01 ± 1.6e-02 3.04e-01 ± 1.4e-02 1.65 9.61e-02 ± 3.4e-03 3.46e-01 ± 1.6e-02 3.00e-01 ± 1.4e-02 2.43e-01 ± 1.2e-02 1.75 7.19e-02 ± 2.7e-03 2.70e-01 ± 1.3e-02 2.17e-01 ± 1.1e-02 1.84e-01 ± 9.9e-03 1.85 5.57e-02 ± 2.1e-03 2.07e-01 ± 1.1e-02 1.68e-01 ± 9.5e-03 1.45e-01 ± 8.4e-03 1.95 4.04e-02 ± 1.7e-03 1.53e-01 ± 9.2e-03 1.19e-01 ± 7.7e-03 1.02e-01 ± 6.9e-03 2.10 2.61e-02 ± 7.3e-04 9.75e-02 ± 4.2e-03 7.95e-02 ± 3.7e-03 6.64e-02 ± 3.2e-03 2.30 1.54e-02 ± 4.8e-04 5.99e-02 ± 3.1e-03 4.59e-02 ± 2.7e-03 3.87e-02 ± 2.4e-03 2.50 8.66e-03 ± 3.4e-04 3.16e-02 ± 2.2e-03 2.69e-02 ± 2.0e-03 2.29e-02 ± 1.8e-03 2.70 4.79e-03 ± 2.2e-04 1.79e-02 ± 1.6e-03 1.46e-02 ± 1.4e-03 1.19e-02 ± 1.2e-03 2.90 2.91e-03 ± 1.6e-04 1.04e-02 ± 1.2e-03 8.43e-03 ± 1.1e-03 7.25e-03 ± 9.6e-04 3.25 1.16e-03 ± 6.7e-05 4.14e-03 ± 4.7e-04 3.55e-03 ± 4.3e-04 3.02e-03 ± 3.8e-04 3.75 3.71e-04 ± 3.5e-05 1.29e-03 ± 2.5e-04 1.30e-03 ± 2.5e-04 1.09e-03 ± 2.2e-04 4.25 1.35e-04 ± 2.1e-05 5.44e-04 ± 1.7e-04 3.98e-04 ± 1.4e-04 3.57e-04 ± 1.3e-04 31 TABLE XXVI: Invariant yields for anti-protons at mid-rapidity in 15–20%, 20–30%, 30–40%, and 40-50% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 15–20% 20–30% 30–40% 40–50% 0.65 1.25e+00 ± 4.5e-02 9.68e-01 ± 3.2e-02 6.98e-01 ± 2.4e-02 4.51e-01 ± 1.7e-02 0.75 1.16e+00 ± 4.1e-02 8.94e-01 ± 2.9e-02 6.35e-01 ± 2.2e-02 4.06e-01 ± 1.5e-02 0.85 1.02e+00 ± 3.5e-02 7.83e-01 ± 2.5e-02 5.21e-01 ± 1.8e-02 3.37e-01 ± 1.3e-02 0.95 8.85e-01 ± 3.1e-02 6.61e-01 ± 2.2e-02 4.42e-01 ± 1.5e-02 2.70e-01 ± 1.0e-02 1.05 7.26e-01 ± 2.6e-02 5.25e-01 ± 1.8e-02 3.54e-01 ± 1.3e-02 2.05e-01 ± 8.4e-03 1.15 6.43e-01 ± 2.5e-02 4.63e-01 ± 1.6e-02 2.99e-01 ± 1.2e-02 1.79e-01 ± 7.7e-03 1.25 4.99e-01 ± 2.0e-02 3.65e-01 ± 1.4e-02 2.33e-01 ± 9.5e-03 1.37e-01 ± 6.4e-03 1.35 4.11e-01 ± 1.8e-02 2.88e-01 ± 1.1e-02 1.80e-01 ± 7.8e-03 1.03e-01 ± 5.2e-03 1.45 3.40e-01 ± 1.5e-02 2.41e-01 ± 1.0e-02 1.42e-01 ± 6.7e-03 8.40e-02 ± 4.6e-03 1.55 2.45e-01 ± 1.2e-02 1.77e-01 ± 7.8e-03 1.06e-01 ± 5.3e-03 6.14e-02 ± 3.6e-03 1.65 1.90e-01 ± 1.0e-02 1.43e-01 ± 6.7e-03 8.53e-02 ± 4.6e-03 4.50e-02 ± 3.0e-03 1.75 1.45e-01 ± 8.4e-03 1.02e-01 ± 5.2e-03 6.32e-02 ± 3.8e-03 3.49e-02 ± 2.6e-03 1.85 1.20e-01 ± 7.4e-03 7.97e-02 ± 4.4e-03 4.76e-02 ± 3.1e-03 2.66e-02 ± 2.2e-03 1.95 8.41e-02 ± 6.0e-03 5.83e-02 ± 3.7e-03 3.56e-02 ± 2.7e-03 1.84e-02 ± 1.8e-03 2.10 5.22e-02 ± 2.8e-03 3.90e-02 ± 1.7e-03 2.30e-02 ± 1.3e-03 1.27e-02 ± 8.8e-04 2.30 3.19e-02 ± 2.1e-03 2.24e-02 ± 1.2e-03 1.34e-02 ± 9.2e-04 7.39e-03 ± 6.6e-04 2.50 1.83e-02 ± 1.5e-03 1.22e-02 ± 9.0e-04 7.78e-03 ± 6.9e-04 4.11e-03 ± 4.8e-04 2.70 9.79e-03 ± 1.1e-03 6.65e-03 ± 6.4e-04 4.66e-03 ± 5.2e-04 2.30e-03 ± 3.5e-04 2.90 6.28e-03 ± 8.7e-04 4.33e-03 ± 5.1e-04 2.57e-03 ± 3.8e-04 1.67e-03 ± 3.0e-04 3.25 2.55e-03 ± 3.4e-04 1.64e-03 ± 2.0e-04 1.05e-03 ± 1.5e-04 5.44e-04 ± 1.1e-04 3.75 8.03e-04 ± 1.9e-04 5.39e-04 ± 1.1e-04 2.59e-04 ± 7.3e-05 1.75e-04 ± 5.9e-05 4.25 2.92e-04 ± 1.2e-04 1.74e-04 ± 6.3e-05 1.12e-04 ± 4.9e-05 5.56e-05 ± 3.5e-05 TABLE XXVII: Invariant yields for anti-protons at mid-rapidity in 50–60%, 60–70%, 70–80%, and 80-92% centrality bins, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] 50–60% 60–70% 70–80% 80–92% 0.65 2.84e-01 ± 1.2e-02 1.58e-01 ± 8.1e-03 6.22e-02 ± 4.7e-03 3.55e-02 ± 3.4e-03 0.75 2.50e-01 ± 1.1e-02 1.25e-01 ± 6.6e-03 5.43e-02 ± 4.0e-03 2.77e-02 ± 2.8e-03 0.85 1.89e-01 ± 8.3e-03 9.50e-02 ± 5.2e-03 4.16e-02 ± 3.3e-03 2.06e-02 ± 2.2e-03 0.95 1.58e-01 ± 7.1e-03 7.38e-02 ± 4.3e-03 3.13e-02 ± 2.7e-03 1.56e-02 ± 1.8e-03 1.05 1.19e-01 ± 5.8e-03 5.50e-02 ± 3.5e-03 2.12e-02 ± 2.1e-03 1.01e-02 ± 1.4e-03 1.15 9.60e-02 ± 5.1e-03 4.34e-02 ± 3.1e-03 1.73e-02 ± 1.9e-03 7.94e-03 ± 1.2e-03 1.25 7.11e-02 ± 4.1e-03 3.19e-02 ± 2.5e-03 1.22e-02 ± 1.5e-03 6.05e-03 ± 1.1e-03 1.35 5.31e-02 ± 3.4e-03 2.40e-02 ± 2.1e-03 9.65e-03 ± 1.3e-03 4.08e-03 ± 8.4e-04 1.45 4.43e-02 ± 3.1e-03 1.90e-02 ± 1.9e-03 7.69e-03 ± 1.2e-03 3.31e-03 ± 7.6e-04 1.55 3.13e-02 ± 2.4e-03 1.28e-02 ± 1.4e-03 4.43e-03 ± 8.5e-04 2.02e-03 ± 5.6e-04 1.65 2.39e-02 ± 2.1e-03 9.29e-03 ± 1.2e-03 3.09e-03 ± 7.0e-04 1.70e-03 ± 5.2e-04 1.75 1.79e-02 ± 1.7e-03 6.92e-03 ± 1.0e-03 2.79e-03 ± 6.6e-04 1.21e-03 ± 4.3e-04 1.85 1.28e-02 ± 1.4e-03 5.66e-03 ± 9.3e-04 1.27e-03 ± 4.4e-04 7.33e-04 ± 3.3e-04 1.95 1.00e-02 ± 1.3e-03 3.93e-03 ± 7.8e-04 1.54e-03 ± 4.9e-04 7.92e-04 ± 3.5e-04 2.10 6.03e-03 ± 5.9e-04 2.58e-03 ± 3.8e-04 6.91e-04 ± 2.0e-04 3.59e-04 ± 1.4e-04 2.30 3.46e-03 ± 4.4e-04 1.37e-03 ± 2.7e-04 5.66e-04 ± 1.8e-04 2.03e-04 ± 1.1e-04 2.50 2.04e-03 ± 3.4e-04 7.56e-04 ± 2.0e-04 2.85e-04 ± 1.3e-04 1.35e-04 ± 8.5e-05 2.70 1.20e-03 ± 2.5e-04 3.92e-04 ± 1.4e-04 2.26e-04 ± 1.1e-04 2.67e-05 ± 3.8e-05 2.90 6.21e-04 ± 1.8e-04 2.92e-04 ± 1.2e-04 1.40e-04 ± 8.8e-05 8.76e-06 ± 2.2e-05 3.25 2.61e-04 ± 7.3e-05 1.10e-04 ± 4.7e-05 3.63e-05 ± 2.8e-05 9.16e-06 ± 1.4e-05 3.75 6.52e-05 ± 3.6e-05 2.77e-05 ± 2.3e-05 5.76e-06 ± 1.1e-05 4.25 4.82e-05 ± 3.2e-05 1.23e-05 ± 1.6e-05 2.71e-06 ± 8.1e-06 32 TABLE XXVIII: Invariant yields for π ± and K± at mid-rapidity in 60–92% centrality bin, normalized to
one unit rapidity. Errors are statistical only. pT [GeV/c] π + π − K+ K− 0.25 1.28e+01 ± 1.1e-01 1.21e+01 ± 9.5e-02 0.35 6.61e+00 ± 5.7e-02 6.42e+00 ± 5.2e-02 0.45 3.71e+00 ± 3.4e-02 3.59e+00 ± 3.1e-02 5.35e-01 ± 1.5e-02 4.74e-01 ± 1.3e-02 0.55 2.09e+00 ± 2.1e-02 2.06e+00 ± 1.9e-02 3.83e-01 ± 9.7e-03 3.62e-01 ± 8.8e-03 0.65 1.24e+00 ± 1.4e-02 1.21e+00 ± 1.3e-02 2.66e-01 ± 6.8e-03 2.50e-01 ± 6.2e-03 0.75 7.63e-01 ± 9.6e-03 7.31e-01 ± 8.4e-03 1.81e-01 ± 4.9e-03 1.78e-01 ± 4.6e-03 0.85 4.64e-01 ± 6.6e-03 4.60e-01 ± 5.9e-03 1.26e-01 ± 3.7e-03 1.21e-01 ± 3.4e-03 0.95 2.93e-01 ± 4.8e-03 2.95e-01 ± 4.3e-03 8.85e-02 ± 2.9e-03 8.21e-02 ± 2.5e-03 1.05 1.91e-01 ± 3.5e-03 1.89e-01 ± 3.2e-03 6.34e-02 ± 2.3e-03 5.80e-02 ± 2.0e-03 1.15 1.26e-01 ± 2.6e-03 1.28e-01 ± 2.5e-03 4.35e-02 ± 1.8e-03 3.91e-02 ± 1.5e-03 1.25 8.15e-02 ± 2.0e-03 8.12e-02 ± 1.8e-03 2.87e-02 ± 1.4e-03 2.94e-02 ± 1.3e-03 1.35 5.96e-02 ± 1.7e-03 5.71e-02 ± 1.5e-03 2.03e-02 ± 1.1e-03 2.07e-02 ± 1.0e-03 1.45 3.95e-02 ± 1.3e-03 3.91e-02 ± 1.2e-03 1.68e-02 ± 9.7e-04 1.35e-02 ± 8.2e-04 1.55 2.56e-02 ± 9.7e-04 2.81e-02 ± 9.7e-04 1.06e-02 ± 7.5e-04 1.05e-02 ± 7.0e-04 1.65 1.96e-02 ± 8.4e-04 2.07e-02 ± 8.1e-04 8.39e-03 ± 6.5e-04 8.47e-03 ± 6.2e-04 1.75 1.44e-02 ± 7.1e-04 1.41e-02 ± 6.5e-04 5.68e-03 ± 5.2e-04 5.15e-03 ± 4.6e-04 1.85 1.07e-02 ± 6.0e-04 1.04e-02 ± 5.6e-04 4.91e-03 ± 4.7e-04 4.15e-03 ± 4.1e-04 1.95 7.68e-03 ± 5.1e-04 7.42e-03 ± 4.8e-04 3.59e-03 ± 4.1e-04 3.29e-03 ± 3.7e-04 2.05 5.87e-03 ± 3.6e-04 4.87e-03 ± 3.3e-04 2.15 3.78e-03 ± 2.9e-04 3.87e-03 ± 3.0e-04 2.25 2.99e-03 ± 2.6e-04 2.55e-03 ± 2.5e-04 2.35 2.47e-03 ± 2.5e-04 2.41e-03 ± 2.6e-04 2.45 1.68e-03 ± 2.1e-04 1.63e-03 ± 2.1e-04 2.55 1.77e-03 ± 2.3e-04 1.54e-03 ± 2.3e-04 2.65 1.28e-03 ± 2.1e-04 1.18e-03 ± 2.0e-04 2.75 1.02e-03 ± 2.0e-04 7.74e-04 ± 1.7e-04 2.85 7.49e-04 ± 1.7e-04 6.23e-04 ± 1.7e-04 2.95 5.61e-04 ± 1.6e-04 7.27e-04 ± 1.9e-04 TABLE XXIX: Invariant yields for protons and anti-protons at mid-rapidity in 60–92% centrality bin, normalized to one unit rapidity. Errors are statistical only. pT [GeV/c] p p 0.65 1.17e-01 ± 4.8e-03 8.63e-02 ± 3.8e-03 0.75 9.26e-02 ± 3.9e-03 7.00e-02 ± 3.1e-03 0.85 7.01e-02 ± 3.1e-03 5.31e-02 ± 2.5e-03 0.95 5.48e-02 ± 2.6e-03 4.07e-02 ± 2.0e-03 1.05 4.10e-02 ± 2.1e-03 2.92e-02 ± 1.6e-03 1.15 3.09e-02 ± 1.7e-03 2.32e-02 ± 1.4e-03 1.25 2.16e-02 ± 1.3e-03 1.70e-02 ± 1.1e-03 1.35 1.77e-02 ± 1.2e-03 1.27e-02 ± 9.4e-04 1.45 1.25e-02 ± 9.4e-04 1.02e-02 ± 8.3e-04 1.55 8.85e-03 ± 7.8e-04 6.51e-03 ± 6.2e-04 1.65 6.42e-03 ± 6.3e-04 4.76e-03 ± 5.2e-04 1.75 5.08e-03 ± 5.5e-04 3.69e-03 ± 4.5e-04 1.85 3.58e-03 ± 4.6e-04 2.60e-03 ± 3.7e-04 1.95 2.79e-03 ± 3.9e-04 2.11e-03 ± 3.4e-04 2.10 1.77e-03 ± 1.8e-04 1.23e-03 ± 1.5e-04 2.30 1.08e-03 ± 1.4e-04 7.22e-04 ± 1.2e-04 2.50 5.42e-04 ± 9.5e-05 3.97e-04 ± 8.5e-05 2.70 3.32e-04 ± 7.4e-05 2.17e-04 ± 6.2e-05 2.90 2.04e-04 ± 5.8e-05 1.49e-04 ± 5.2e-05 3.25 8.58e-05 ± 2.3e-05 5.24e-05 ± 1.9e-05 3.75 2.76e-05 ± 1.3e-05 1.14e-05 ± 8.7e-06 4.25 1.24e-05 ± 9.1e-06 5.08e-06 ± 6.1e-06

arXiv:nucl-ex/0307010v1 10 Jul 2003 Single Identified Hadron Spectra from √ sNN = 130 GeV Au+Au Collisions K. Adcox,40 S.S. Adler, 4 N.N. Ajitanand,33 Y. Akiba,14 J. Alexander,33 L. Aphecetche,35 Y. Arai,14 S.H. Aronson, 4 R. Averbeck,34 T.C. Awes,27 K.N. Barish, 5 P.D. Barnes,19 J. Barrette,21 B. Bassalleck,25 S. Bathe,22 V. Baublis,28 A. Bazilevsky,12, 30 S. Belikov,12, 13 F.G. Bellaiche,27 S.T. Belyaev,16 M.J. Bennett,19 Y. Berdnikov,31 S. Botelho,32 M.L. Brooks,19 D.S. Brown,26 N. Bruner,25 D. Bucher,22 H. Buesching,22 V. Bumazhnov,12 G. Bunce,4, 30 J.M. Burward-Hoy,34 S. Butsyk,34, 28 T.A. Carey,19 P. Chand, 3 J. Chang, 5 W.C. Chang, 1 L.L. Chavez,25 S. Chernichenko,12 C.Y. Chi, 8 J. Chiba,14 M. Chiu, 8 R.K. Choudhury, 3 T. Christ,34 T. Chujo,4, 39 M.S. Chung,15, 19 P. Chung,33 V. Cianciolo,27 B.A. Cole, 8 D.G. d’Enterria,35 G. David, 4 H. Delagrange,35 A. Denisov,12 A. Deshpande,30 E.J. Desmond, 4 O. Dietzsch,32 B.V. Dinesh, 3 A. Drees,34 A. Durum,12 D. Dutta, 3 K. Ebisu,24 Y.V. Efremenko,27 K. El Chenawi,40 H. En’yo,17, 29 S. Esumi,39 L. Ewell, 4 T. Ferdousi, 5 D.E. Fields,25 S.L. Fokin,16 Z. Fraenkel,42 A. Franz, 4 A.D. Frawley, 9 S.-Y. Fung, 5 S. Garpman,20, ∗ T.K. Ghosh,40 A. Glenn,36 A.L. Godoi,32 Y. Goto,30 S.V. Greene,40 M. Grosse Perdekamp,30 S.K. Gupta, 3 W. Guryn, 4 H.- ˚A. Gustafsson,20 J.S. Haggerty, 4 H. Hamagaki, 7 A.G. Hansen,19 H. Hara,24 E.P. Hartouni,18 R. Hayano,38 N. Hayashi,29 X. He,10 T.K. Hemmick,34 J.M. Heuser,34 M. Hibino,41 J.C. Hill,13 D.S. Ho,43 K. Homma,11 B. Hong,15 A. Hoover,26 T. Ichihara,29, 30 K. Imai,17, 29 M.S. Ippolitov,16 M. Ishihara,29, 30 B.V. Jacak,34, 30 W.Y. Jang,15 J. Jia,34 B.M. Johnson, 4 S.C. Johnson,18, 34 K.S. Joo,23 S. Kametani,41 J.H. Kang,43 M. Kann,28 S.S. Kapoor, 3 S. Kelly, 8 B. Khachaturov,42 A. Khanzadeev,28 J. Kikuchi,41 D.J. Kim,43 H.J. Kim,43 S.Y. Kim,43 Y.G. Kim,43 W.W. Kinnison,19 E. Kistenev, 4 A. Kiyomichi,39 C. Klein-Boesing,22 S. Klinksiek,25 L. Kochenda,28 V. Kochetkov,12 D. Koehler,25 T. Kohama,11 D. Kotchetkov, 5 A. Kozlov,42 P.J. Kroon, 4 K. Kurita,29, 30 M.J. Kweon,15 Y. Kwon,43 G.S. Kyle,26 R. Lacey,33 J.G. Lajoie,13 J. Lauret,33 A. Lebedev,13 D.M. Lee,19 M.J. Leitch,19 X.H. Li, 5 Z. Li,6, 29 D.J. Lim,43 M.X. Liu,19 X. Liu, 6 Z. Liu, 6 C.F. Maguire,40 J. Mahon, 4 Y.I. Makdisi, 4 V.I. Manko,16 Y. Mao,6, 29 S.K. Mark,21 S. Markacs, 8 G. Martinez,35 M.D. Marx,34 A. Masaike,17 F. Matathias,34 T. Matsumoto,7, 41 P.L. McGaughey,19 E. Melnikov,12 M. Merschmeyer,22 F. Messer,34 M. Messer, 4 1 Y. Miake,39 T.E. Miller,40 A. Milov,42 S. Mioduszewski,4, 36 R.E. Mischke,19 G.C. Mishra,10 J.T. Mitchell,4 A.K. Mohanty,3 D.P. Morrison,4 J.M. Moss,19 F. M¨uhlbacher,34 M. Muniruzzaman,5 J. Murata,29 S. Nagamiya,14 Y. Nagasaka,24 J.L. Nagle,8 Y. Nakada,17 B.K. Nandi,5 J. Newby,36 L. Nikkinen,21 P. Nilsson,20 S. Nishimura,7 A.S. Nyanin,16 J. Nystrand,20 E. O’Brien,4 C.A. Ogilvie,13 H. Ohnishi,4, 11 I.D. Ojha,2, 40 M. Ono,39 V. Onuchin,12 A. Oskarsson,20 L. Osterman, ¨ 20 I. Otterlund,20 K. Oyama,7, 38 L. Paffrath,4, ∗ A.P.T. Palounek,19 V.S. Pantuev,34 V. Papavassiliou,26 S.F. Pate,26 T. Peitzmann,22 A.N. Petridis,13 C. Pinkenburg,4, 33 R.P. Pisani,4 P. Pitukhin,12 F. Plasil,27 M. Pollack,34, 36 K. Pope,36 M.L. Purschke,4 I. Ravinovich,42 K.F. Read,27, 36 K. Reygers,22 V. Riabov,28, 31 Y. Riabov,28 M. Rosati,13 A.A. Rose,40 S.S. Ryu,43 N. Saito,29, 30 A. Sakaguchi,11 T. Sakaguchi,7, 41 H. Sako,39 T. Sakuma,29, 37 V. Samsonov,28 T.C. Sangster,18 R. Santo,22 H.D. Sato,17, 29 S. Sato,39 S. Sawada,14 B.R. Schlei,19 Y. Schutz,35 V. Semenov,12 R. Seto,5 T.K. Shea,4 I. Shein,12 T.-A. Shibata,29, 37 K. Shigaki,14 T. Shiina,19 Y.H. Shin,43 I.G. Sibiriak,16 D. Silvermyr,20 K.S. Sim,15 J. Simon-Gillo,19 C.P. Singh,2 V. Singh,2 M. Sivertz,4 A. Soldatov,12 R.A. Soltz,18 S. Sorensen,27, 36 P.W. Stankus,27 N. Starinsky,21 P. Steinberg,8 E. Stenlund,20 A. Ster,44 S.P. Stoll,4 M. Sugioka,29, 37 T. Sugitate,11 J.P. Sullivan,19 Y. Sumi,11 Z. Sun,6 M. Suzuki,39 E.M. Takagui,32 A. Taketani,29 M. Tamai,41 K.H. Tanaka,14 Y. Tanaka,24 E. Taniguchi,29, 37 M.J. Tannenbaum,4 J. Thomas,34 J.H. Thomas,18 T.L. Thomas,25 W. Tian,6, 36 J. Tojo,17, 29 H. Torii,17, 29 R.S. Towell,19 I. Tserruya,42 H. Tsuruoka,39 A.A. Tsvetkov,16 S.K. Tuli,2 H. Tydesj¨o,20 N. Tyurin,12 T. Ushiroda,24 H.W. van Hecke,19 C. Velissaris,26 J. Velkovska,34 M. Velkovsky,34 A.A. Vinogradov,16 M.A. Volkov,16 A. Vorobyov,28 E. Vznuzdaev,28 H. Wang,5 Y. Watanabe,29, 30 S.N. White,4 C. Witzig,4 F.K. Wohn,13 C.L. Woody,4 W. Xie,5, 42 K. Yagi,39 S. Yokkaichi,29 G.R. Young,27 I.E. Yushmanov,16 W.A. Zajc,8, † Z. Zhang,34 and S. Zhou6 (PHENIX Collaboration) 1 Institute of Physics, Academia Sinica, Taipei 11529, Taiwan 2Department of Physics, Banaras Hindu University, Varanasi 221005, India 3Bhabha Atomic Research Centre, Bombay 400 085, India 4Brookhaven National Laboratory, Upton, NY 11973-5000, USA 2 5University of California – Riverside, Riverside, CA 92521, USA 6China Institute of Atomic Energy (CIAE), Beijing, People´s Republic of China 7Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan 8Columbia University, New York, NY 10027 and Nevis Laboratories, Irvington, NY 10533, USA 9Florida State University, Tallahassee, FL 32306, USA 10Georgia State University, Atlanta, GA 30303, USA 11Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan 12Institute for High Energy Physics (IHEP), Protvino, Russia 13Iowa State University, Ames, IA 50011, USA 14KEK, High Energy Accelerator Research Organization, Tsukuba-shi, Ibaraki-ken 305-0801, Japan 15Korea University, Seoul, 136-701, Korea 16Russian Research Center “Kurchatov Institute”, Moscow, Russia 17Kyoto University, Kyoto 606, Japan 18Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 19Los Alamos National Laboratory, Los Alamos, NM 87545, USA 20Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden 21McGill University, Montreal, Quebec H3A 2T8, Canada 22Institut fuer Kernphysik, University of Muenster, D-48149 Muenster, Germany 23Myongji University, Yongin, Kyonggido 449-728, Korea 24Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan 25University of New Mexico, Albuquerque, NM, USA 26New Mexico State University, Las Cruces, NM 88003, USA 27Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 28PNPI, Petersburg Nuclear Physics Institute, Gatchina, Russia 29RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, JAPAN 30RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, USA 31St. Petersburg State Technical University, St. Petersburg, Russia 3 32Universidade de S˜ao Paulo, Instituto de F´isica, Caixa Postal 66318, S˜ao Paulo CEP05315-970, Brazil 33Chemistry Department, State University of New York – Stony Brook, Stony Brook, NY 11794, USA 34Department of Physics and Astronomy, State University of New York – Stony Brook, Stony Brook, NY 11794, USA 35SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Universit´e de Nantes) BP 20722 – 44307, Nantes, France 36University of Tennessee, Knoxville, TN 37996, USA 37Department of Physics, Tokyo Institute of Technology, Tokyo, 152-8551, Japan 38University of Tokyo, Tokyo, Japan 39Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan 40Vanderbilt University, Nashville, TN 37235, USA 41Waseda University, Advanced Research Institute for Science and Engineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan 42Weizmann Institute, Rehovot 76100, Israel 43Yonsei University, IPAP, Seoul 120-749, Korea 44 KFKI Research Institute for Particle and Nuclear Physics (RMKI), Budapest, Hungary (Dated: February 8, 2008) 4 Abstract Transverse momentum spectra and yields of hadrons are measured by the PHENIX collaboration in Au + Au collisions at √ sNN = 130 GeV at the Relativistic Heavy Ion Collider (RHIC). The timeof-flight resolution allows identification of pions to transverse momenta of 2 GeV/c and protons and antiprotons to 4 GeV/c. The yield of pions rises approximately linearly with the number of nucleons participating in the c
ollision, while the number of kaons, protons, and antiprotons increases more rapidly. The shape of the momentum distribution changes between peripheral and central collisions. Simultaneous analysis of all the pT spectra indicates radial collective expansion, consistent with predictions of hydrodynamic models. Hydrodynamic analysis of the spectra shows that the expansion velocity increases with collision centrality and collision energy. This expansion boosts the particle momenta, causing the yield from soft processes to exceed that for hard to large transverse momentum, perhaps as large as 3 GeV/c. ∗Deceased †PHENIX Spokesperson:zajc@nevis.columbia.edu 5 I. INTRODUCTION Heavy ion reactions at ultrarelativistic energies provide information on strongly interacting matter under extreme conditions. Lattice QCD and phenomenological predictions indicate that at high enough energy density a deconfined state of quarks and gluons, the quark-gluon-plasma, is formed. It is expected that conditions in ultrarelativistic heavy ion reactions may produce this new state of matter, the study of which is the major goal of the experiments at the Relativistic Heavy Ion Collider (RHIC). The high energy density state thus created will cool down and expand, undergoing a phase transition to “ordinary” hadronic matter. While the tools of choice to study the earliest phase of the reactions, and thereby the new state, are probes that do not interact via the strong force, such as photons, electrons, or muons, the global properties and dynamics of later stages in the system are best studied via hadronic observables. Hadron momentum spectra in proton-proton reactions are often separated into two parts, a soft part at low transverse momentum (pT ), where the shape is roughly exponential in transverse mass mT = q p 2 T + m2 0 , and a high pT region where the shape more closely resembles a power law. Soft production (low pT ) is attributed to fragmentation of a string [1, 2] between components of the struck nucleons, while hard (high pT ) hadrons are expected to originate predominantly from fragmentation of hard-scattered partons. The transition between these two regimes is not sharply defined, but is commonly believed to be near pT ≈ 2 GeV/c [3]. In proton-nucleus (p+A) scattering, these two regimes depend on the colliding system size in different ways. The soft production depends on the number of nucleons struck, or participating in the collision (Npart). The number of hard scatterings should increase proportionally to the number of binary nucleon-nucleon encounters (Ncoll) since these processes have a small elementary cross section and may be considered as incoherent. Hard scattering also produces color strings which fragment and produce some low pT particles, though these are much fewer in number than those from the much more frequent soft scatterings. In p+A these Npart and Ncoll are connected by a very simple relation, namely Npart = Ncoll + 1. In nucleus-nucleus collisions, the number of participant nucleons does not scale simply with A, so it is more useful to study scaling with Ncoll or Npart. Collisions are sorted according to centrality, allowing control of the geometry and determination of Ncoll or Npart. In heavy ion collisions, one expects secondary collisions of particles (rescattering) to 6 take place, especially among particles with low and intermediate transverse momentum. Rescattering may occur among partons early in the collision, and also among hadrons later in the collision. Both kinds of rescattering can lead to collective behavior among the particles, and the presence of elliptic flow ([4, 5, 6, 7, 8, 9]) indicates that partonic rescattering is important at RHIC. In the extreme, rescattering can lead to thermalization. Rescattering has observable consequences on the final hadron momentum spectra, causing them to be broadened as shown in this paper. This relates to some of the key questions regarding the evolution of the collision: Are the size and lifetime sufficient to attain local equilibrium? Are the momentum distributions thermal, and if so, what are the chemical and kinetic freezeout temperatures? Can expansion be described by hydrodynamic models? Momentum distributions of hadrons as a function of centrality provide a means to investigate these questions and permit extraction of thermodynamic quantities which govern the predicted phase transition. This paper reports semi-inclusive momentum spectra and yields of π, K, and p from AuAu collisions at √ sNN = 130 GeV. The data are measured and analyzed by the PHENIX Collaboration in the first year of the physics program at RHIC (Run-1). The paper is organized as follows. In Section II the PHENIX detectors used in the analysis are described. The data reduction techniques using the Time-of-Flight and Drift Chamber detectors, along with the corrections applied to the spectra, are described in Section III. Functions that describe the shape of the spectra are used to extrapolate the unmeasured portion in order to determine the total average momentum and particle yield for each particle. The overall systematic uncertainties in the spectra are discussed. The resulting minimum bias and centrality-selected particle spectra are presented in Section IV. In Section V a description of the particle production within a hydrodynamic picture is investigated. For each centrality selection, a hydrodynamic parameterization of the mT distribution is fit simultaneously to the spectra of different species. The data are compared to full hydrodynamic calculations. The transition region in pT between hard (perturbative QCD) and soft (hydrodynamic behavior) physics is investigated by comparison of extrapolated soft spectra to the data. Finally, we study the dependence of the particle yields on the number of nucleons participating in the collision. 7 II. EXPERIMENT The PHENIX [10, 11] experiment at RHIC identifies hadrons over a large momentum range, by the addition of excellent time-of-flight capability to the detector suite optimized for photons, electrons, and muons. PHENIX has four spectrometer arms, two that are positioned about midrapidity (the central arms) and two at more forward rapidities (the Muon Arms). A cross-sectional view of the PHENIX detector, transverse to the beamline is shown in Figure 1. Within the two central arm spectrometers, the detectors that were instrumented and operational during the √ sNN = 130 GeV run (Run-1) are shown. The detector systems in PHENIX are discussed in detail elsewhere [12]. The detector systems used for the measurements reported in this paper are described in detail in the following sections. A. CENTRAL ARM DETECTORS The central arm spectrometers use a central magnet that produces an approximately axially symmetric field that focuses charged particles into the detector acceptance. The two central arms are labeled as East and West Arms. The East Arm contains the following subsystems used in this analysis: drift chamber (DC), pad chamber (PC), and a Time-ofFlight (TOF) wall. The PHENIX hadron acceptance using the TOF system in the East Arm is illustrated in Figure 2 where the transverse momentum is plotted as a function of the particle rapidity (the phase space) within the central arm acceptance subtending the polar angle θ from 70 to 110 degrees for pions, kaons, and protons. The vertical lines are the equivalent pseudorapidity edges, corresponding to |η| < 0.35. More details are discussed elsewhere [13]. 1. TRACKING CHAMBERS The charged particle tracking chambers include three layers of pad chambers and two drift chambers. The chambers are designed to operate in a high particle multiplicity environment. The drift chambers are the first tracking detectors that charged particles encounter as they travel from the collision vertex through the central arms. Each is 1.8 m in width in the beam direction, subtends 90-degrees in azimuthal angle φ, centered at a radius RDC = 2.2 m, 8 West BeamView PHENIX Detector – First Year Physics Run East BB MVD Installed PbSc PbSc Active PbSc PbSc PbSc PbGl PbSc PbGl TOF PC1 PC1 Central Magnet TEC PC3 RICH RICH DC DC FIG. 1:
A cross-sectional view of the PHENIX detector, transverse to the beamline. Within the two central arm spectrometers the detectors that were instrumented and operational during the √ sNN = 130 GeV run are shown. and is filled with a 50-50 Argon-Ethane gas mixture. It consists of 40 planes of sense wires arranged in 80 drift cells placed cylindrically symmetric about the beamline. The wire planes are placed in an X-U-V configuration in the following order (moving outward radially): 12 X planes (X1), 4 U planes (U1), 4 V planes (V1), 12 X planes (X2), 4 U planes (U2), and 4 V planes (V2). The U and V planes are tilted by a small ±5 o stereo angle to allow for full three-dimensional track reconstruction. The field wire design is such that the electron drift to each sense wire is only from one side, thus removing most left-right ambiguities everywhere except within 2 mm of the sense wire. The wires are divided electrically in the middle at the beamline center. The occupancy for a central RHIC Au+Au collision is about 9 0 0.5 1 1.5 2 2.5 π 0 < θ < 110 0 70 (GeV/c) T p 0 0.5 1 1.5 2 2.5 K y -0.5 -0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.5 0 0.5 1 1.5 2 2.5 p FIG. 2: The central arm spectrometer acceptance in rapidity and transverse momentum for pions (top), kaons (middle), and protons (bottom). two hits per wire. At the drift chamber location, the field of the central magnet is nearly zero, so the DC determines (nearly) straight-line track segments in the r-φ plane. Each track segment is intersected with a circle at RDC, where it is characterized by two angles: the angular deflection 10 in the main bend plane, and the azimuthal position in φ. A combinatorial Hough transform technique (CHT) is used to identify track segments by searching for location maxima in this angular space/citehough. The DCs are calibrated with respect to the event collision time measurement (see Section II B). With this calibration, the single-wire resolution in the r-φ plane is 160 µm. The single-track wire efficiency is 99% and the two-track resolution is better than 1.5 mm. The drift chambers are used to measure the momentum of charged particles and the direction vector for charged particles traversing the spectrometer. The angular deflection is inversely proportional to the component of momentum in the bend plane only. Both the bend angle and the measured track points are used in the momentum reconstruction and track model, which uses a look-up table of the measured central magnet field grid. For this data set, the drift chamber momentum resolution is σp/p = 0.6% ⊕ 3.6%p, where the first term is multiple scattering up to the drift chambers and the second is the angular resolution of the detector. In Run-1, there were three pad chambers in PHENIX. Each pad chamber measures a three-dimensional space point of a charged track. The pad chambers are pixel-based detectors with effective readout sizes of 8.45 mm along the beamline by 8.40 mm in the plane transverse to the beamline. The first pad chamber layer (PC1) is fixed to the outer edge radially of each drift chamber at a radial distance of 2.49 m, while the third layer (PC3) is positioned at 4.98 m from the beamline. Both arms include PC1 chambers, while only the East Arm is instrumented with PC3. The second layer (PC2) is located at an inner inscribed radius of 4.19 m in the West Arm and was not installed for Run-1. The position resolution of PC1 is 1.6 mm along the beam axis and 2.3 mm in the plane transverse to the beam axis. The position resolutions of PC3 are 3.2 mm and 4.8 mm, respectively. The PC3 is used to reject background from albedo and non-vertex decay particles; however, only the PC1 is used for the results presented here. The PC1 is used in the global track reconstruction with the measured vertex position using the beamline detectors (see Section II B) to determine the polar angle of each charged track. Both PC1 and the beamline detectors provide z-coordinate information with a 1.89 mm resolution. 11 2. TIME OF FLIGHT The Time-of-Flight detector (TOF) serves as the primary particle identification device for charged hadrons by the measurement of their arrival time at the TOF wall 5.1 m from the collision vertex. The TOF wall spans 30◦ in azimuth in the East Arm. It consists of 10 panels of 96 scintillator slats each with an intrinsic timing resolution better than 100 ps. Each slat is oriented along the r-φ direction and provides timing as well as beam-axis position information for each particle hit recorded. The slats are viewed by two photomultiplier tubes, attached to either end of the scintillator. A ±2σ π/K separation at momenta up to 2.0 GeV/c, and a ±2σ (π+K)/proton separation up to 4.0 GeV/c can be achieved. For each particle, the time, energy loss in the scintillator, and geometrical position are determined. The total time offset is calibrated slat by slat. A particle hit in the scintillator is defined by a measured pulse height which is also used to correct the time recorded at each end of the slat (slewing correction). After calibration, the average of the times at either end of the slat is the measured time for a particle. The azimuthal position is proportional to the time difference across the slat and the known velocity of light propagation in the scintillator (for Bicron BC404, this is 14 cm/ns). The slat position along the beamline determines the longitudinal coordinate position of the particle. The total time of flight is measured relative to the Beam-Beam counter initial time (see Section II B), the measured time in the Time-of-Flight detector, and a global time offset from the RHIC clock. Positive pions in the momentum range 1.4 < pT < 1.8 GeV/c are used to determine the TOF resolution. The timing calibration in this analysis results in a resolution of σ = 115 ps.1 Particle identification for charged hadrons is performed by combining the information from the tracking system with the timing information from the BBC and the TOF. Tracks at 1 GeV/c in momentum point to the TOF with a projected resolution σproj of 5 mrad in azimuthal angle and 2 cm along the beam axis. Tracks that point to the TOF with less than 2.0 σproj were selected. Figure 3 shows the resulting time-of-flight as a function of the reciprocal momentum in minimum-bias Au+Au collisions. 1 Ultimately, 96 ps results after further calibration, as reported in [12]. 12 FIG. 3: Scaled Time-of-Flight versus reciprocal momentum in minimum-bias Au+Au collisions at √ sNN = 130 GeV. The distribution demonstrates the particle identification capability using the TOF for the Run-1 data taking period. B. BEAMLINE DETECTORS The beamline detectors determine the collision vertex position along the beam direction, and the trigger and timing information for each event. These detectors include the Zero Degree Calorimeters (ZDCs), the Beam-Beam Counters (BBC), and the Multiplicity Vertex Detector (MVD) and are positioned in PHENIX as shown in Figure 4. The Zero Degree Calorimeters are small transverse area hadron calorimeters that are installed at each of the four RHIC experiments. They measure the fraction of the energy 13 South Side View North BB MuID MuID MVD Central Magnet North Muon Magnet ZDC South ZDC North Installed Active PHENIX Detector – First Year Physics Run FIG. 4: A side view of the PHENIX detector, parallel to the beamline. The beamline detectors determine the collision vertex position along the beam direction, and the trigger and timing information for each event. deposited by spectator neutrons from the collisions and serve as an event trigger for each RHIC experiment. The ZDCs measure the unbound neutrons in small forward cones (θ <2 mrad) around each beam axis. Each ZDC is positioned 18 m up and downstream from the interaction point along the beam axis. A single ZDC consists of 3 modules each with a depth of 2 hadronic interaction lengths and read out by a single PMT. Both time and amplitude are digitized for each of the 3 PMTs as well as an analog sum of the PMTs for each ZDC. [14] There are two Beam-Beam counters each positioned 1.4 m from the interaction point, just behind the cent
ral magnet poles along the beam axis (see Figure 4). The BBC consists of two identical sets of counters installed on both sides of the interaction point along the beam. Each counter consists of 64 Cherenkov telescopes, arranged radially about the collision axis and situated north and south of the MVD. The BBCs measure the fast secondary particles produced in each collision at forward angles, with 3.0 ≤ η ≤ 3.9, and full azimuthal coverage. 14 For both the ZDC and the BBC, the time and vertex position are determined using the measured time difference between the north and the south detectors and the known distance between the two detectors. The start time (T0) and the vertex position along the beam axis (Zvertex) are calculated as T0 = (T1 + T2)/2 and Zvertex = (T1 − T2)/2c, where T1 and T2 are the average timing of particles in each counter and c is the speed of light. With an intrinsic timing resolution of 150 ps, the ZDC vertex is measured to within 3 cm. In Run-1, the BBC timing resolution of 70 ps results in a vertex position resolution of 1.5 cm. Event centrality is determined using a correlation measurement between neutral energy deposited in the ZDCs and fast particles recorded in the BBCs as shown in Figure 5. The spectator nucleons are unaffected by the interaction and travel at their initial momentum from each respective ion. The number of neutrons measured by the ZDC is proportional to the number of spectators, while the BBC signal increases with the number of participants. III. DATA REDUCTION AND ANALYSIS A. DATA REDUCTION The PHENIX Level-1 trigger selected events with hits coincident in both the ZDC and BBC detectors, and in time with the RHIC clock. A total of 5M events were recorded at √ sNN = 130 GeV in the ZDCs [11]. The collision position along the beam direction was required to be within ± 30 cm of the center of PHENIX, using the collision vertex reconstructed by the BBC. The trigger on both BBC and both ZDC counters includes 92 ± 4% of the total inelastic cross section (6.8 ±0.4 barns). A Monte Carlo Glauber model [15] is used with a simulation of the BBC and ZDC responses to determine the number of nucleons participating in the collisions for the minimum bias events. The Woods-Saxon parameters determined from electron scattering experiments are: radius = 6.38±0.06 fm, diffusivity = 0.54±0.01 fm [16], and the nucleon-nucleon inelastic cross-section, σ inel N+N = 40±3 mb. An additional systematic uncertainty enters the radius parameter since the radial distribution of neutrons in large nuclei should be larger than for protons and is not well determined [17]. The centrality selections used in this paper are 0-5%, 5-15%, 15-30%, 30-60%, and 60-92% of the total geometrical cross section, where 0-5% corresponds to the most central collisions. 15 max BBC QBBC/Q 0 0.2 0.4 0.6 0.8 1 max ZDC /E ZDC E 0 0.2 0.4 0.6 0.8 1 BBC vs ZDC analog response 0-5% 5-10% 10-15% 15-20% Number of tracks 0 20 40 60 80 100 120 140 160 180 Yield 1 10 10 2 10 3 10 4 0 200 400 600 η=0 /dη| ch dN Minimum bias multiplicity distribution at mid-rapidity FIG. 5: The event centrality (upper plot) is determined using a correlation measurement of the fraction of neutron energy recorded in the ZDCs (vertical scale) and the fractional charge measured in the BBCs (horizontal scale). The equivalent track multiplicity in each centrality selection is shown in the lower plot. 16 Only tracks which are reconstructed in all three dimensions are included in the spectra. These tracks are then matched within 2σproj to the measured positions in the TOF detector. For each TOF hit, the time, position, and energy loss are measured in the TOF detector. The widths of residual distance distributions between projected tracks and TOF hit positions, σproj , increase at lower momentum due to multiple scattering. Therefore, a momentumdependent hit association criterion was defined. Finally, a requirement on energy loss in the TOF is applied to each track to exclude false hits by requiring the energy deposit of at least minimum ionizing particle energy. A β- dependent energy loss cut whose form is a parameterization of the Bethe-Bloch formula[18] is used, where dE/dx ≈ β −5/3 (1) and β = L/ct, where L is the pathlength of the particle’s trajectory from the BBC vertex to the TOF detector, t is the particle’s time-of-flight, and c is the speed of light. The approximate Bethe-Bloch formula is scaled by a factor to fall below the data and thereby serve as a cut. The resulting equation is ∆E = Aβ−5/3 where A is a scaling factor equal to 1.6 MeV. The energy loss cut reduces low momentum background under the kaon and proton mass peaks. The fraction of tracks excluded after the energy loss cut is less than 5.5%. The measured momentum (p), pathlength (L), and time of flight (t) in the spectrometer are used to calculate the particle mass, which is used for particle identification: m2 = p 2 c 2   1 β !2 − 1   . (2) The width of the peaks in the mass-squared distribution depend on both the momentum and time-of-flight resolutions. An analytic form for the width of m2 as a function of momentum resolution σp and time of flight resolution is determined using Equation 2. The error in the particle’s pathlength L results in an effective time width that is included with the TOF resolution, σT , σ 2 m2 = 4m4σp p 2 + 4p 4 1 β 2 σT t 2 . (3) The momentum resolution of the drift chambers is expressed in the following form σ 2 p = C1p 1 β !2 + C2p 2 2 , (4) 17 C1 = δφms K1 , (5) C2 = δφα K1 , (6) where C1 and C2 are the multiple scattering and angular resolution terms, respectively. The units of δφms are mrad GeV/c. The constant K1 is the momentum kick on the particle from the magnetic field and is equal to 87.3 mrad GeV/c. The constant C1 is the width in φ due to the multiple scattering (ms) of a charged particle with materials of the spectrometer up to the drift chambers. The C2 term is the angular resolution of the bend angle (α), which is the angular deflection in φ of the track segment relative to the radius to the collision vertex. Equation 4 is used in Equation 3 with β = p/q p 2 + m2 0 , where m0 is the mass centroid of the particle’s mass-squared distribution. The mass centroid is close to the rest mass of the particle; however due to residual misalignments and timing calibration, the centroid of the distribution is a fit parameter in order to avoid cutting into the distribution. The m2 width for each particle is written as follows: σ 2 m2 = (7) C 2 1 · 4m4 (1 + m2 0 p 2 ) + C 2 2 · 4m4 0p 2 + C 2 3 · (4p 2 (m2 0 + p 2 )) where the coefficient C3 is related to the combined TOF, C3 = σT c L , (8) and pathlength contributions to the time width, σT in Equation 8. From the measured drift chamber momentum resolution, C1 = 0.006 and C2 = 0.036 c/GeV. While the TOF resolution is 115±5 ps, the pathlength uncertainty introduces a width of ≈ 20-40 ps, so 145 ps is used for σT in C3. The pions, kaons, and protons are identified using the measured peak centroids of the m2 distribution and selecting 2σ bands; shown as shaded regions in Figure 6 for two different momentum slices. The 2σ bands for pions and kaons do not overlap up to pT =2 GeV/c. The protons are identified up to pT = 4 GeV/c. By studying variations in the m2 centroid and width before the particle identification cut is applied, the uncertainty in the particle identification is estimated to be 5% for all particles. Kaons are depleted by decays in flight and geometrical acceptance. For the low momentum protons, energy loss and geometrical acceptance cause a drop in the raw yield for pT < 0.5 GeV/c, as seen in Figure 2. 18 Entries (a.u.) 10-1 1 10 102 103 0.7 < p < 0.8 GeV/c ) 4 /c2 (GeV m2 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Entries (a.u.) 10-1 1 10 10 2 103 1.3 < p < 1.5 GeV/c FIG. 6: The mass-squared distributions of positive pions, kaons, and protons for two different momentum slices. The momentum slice 0.7 < p < 0.8 GeV/c is the upper panel and 1.3 < p < 1.5 GeV/c is the lower panel. The shaded regions correspond to the 2σ particle id
entification bands based on the calculated mass-squared width, the measured mass-squared centroids, and the known detector resolutions. The remaining background contribution was determined by reflecting the track about the midpoint of PHENIX along the beamline and repeating the association and PID cuts used in the TOF detector. This random background was evaluated separately for each particle type. The background contribution is ≈ 30% for the kaon spectra at 0.2 < pT < 0.4 GeV/c 19 and defines the low pT limit in the spectra. The background is < 5% in all other cases, and negligible above 0.8 GeV/c in the measured momentum range in this analysis. The background was not subtracted but is instead treated as a systematic uncertainty. This uncertainty is 2, 5, and 3% for pions, kaons, and protons, respectively, at pT < 0.6 GeV/c and is negligible at higher momenta. B. ANALYSIS The raw spectra include inefficiencies from detector acceptance, resolution, particle decays in flight and track reconstruction. The baseline efficiencies are determined by simulating and reconstructing single hadrons. Multiplicity dependent effects are then evaluated by embedding simulated single hadrons into real events and calculating the degradation of the reconstruction efficiency. 1. CORRECTIONS: ACCEPTANCE, DECAYS IN FLIGHT, AND DETECTOR RESPONSE The corrections for the finite detector aperture, pion and kaon decays in flight, and the detector response are determined using single particles in the the GEANT [19] simulation of the detector. All details of each detector are modeled, including dead channels in the drift chambers, pad chambers, and Time-of-Flight detector. All physics processes are automatically taken into account, resulting in corrections for multiple scattering, anti-proton annihilation, pion and kaon decays in flight, finite geometrical acceptance of the detector, and momentum resolution, which affects the spectral shape above 2.5 GeV/c. The drift chamber simulated response is tuned to describe the response of the real drift chambers on the single-wire level. This is done using a simple geometrical model of the drift chamber and the straight-line trajectories of particles from the zero-field data. This simple model of the drift cell in the drift chamber is sufficient to describe the observed drift distance distribution, the pulse width, the single wire efficiency, and the detector resolution. The TOF response is simulated by smearing the true time of flight using a Gaussian distribution with a width as measured in the data. Figure 7 shows the momentum dependence of the residual distance between projected 20 tracks and TOF hits for the real (solid line) and simulated (dashed) events. These residuals are parameterized in the azimuthal angle φ and the beamline direction z, separately for data and simulation. For each case, tracks that fall outside 2σ of the parameterized width are rejected, thus allowing use of the Monte Carlo to evaluate the correction for the 2σ match requirement for real tracks. p (GeV/c) 0 0.5 1 1.5 2 (mrad) φ σ 0 2 4 6 8 10 12 14 16 18 20 Monte Carlo Data p (GeV/c) 0 0.5 1 1.5 2 (cm) z σ 0 1 2 3 4 5 6 7 8 9 10 FIG. 7: Comparison of the momentum-dependent residuals of DC tracks matched to TOF hits in azimuthal angle φ (left) and z (right) between data (solid) and simulation (dashed). A fiducial cut is made in both the simulation and in the data to ensure the same fiducial volume. The systematic uncertainty in the acceptance correction is approximately 5%. The simulated distributions are generated uniformly in pT , φ, and y. For each hadron, sufficient Monte Carlo events are generated to obtain the correction factor for every measured pT bin. The statistical errors from the correction factors were smaller than those in the data and both are added in quadrature. The distribution of the number of particles generated in each pT slice, dN/dpT , is the “ideal” input distribution without detector and reconstruction effects. This distribution is 21 normalized to 2π and 1 unit of rapidity. After detector response and track reconstruction, the output distribution is the number of particles found in each pT slice. The final corrections are determined after an iterative weighting procedure. First, the flat input and output distributions are weighted by exponential functions for all particles using an inverse slope of 300 MeV. The ratio of input to output distributions is determined as a function of momentum. In each pT slice, the corresponding ratio is applied to the data. The corrected data are next fitted with exponentials for kaons and protons (see Equation 11), and a power-law for the pions (see Equation 9). The original flat input and output distributions are weighted by these resulting functions. The procedure is repeated until the functions remain constant in their parameters. The weighted input and output distributions are divided to produce acceptance correction factors. The corrections are larger for kaons due to the decays in flight. The statistical error in determination of the correction factor is added in quadrature to the statistical error in the data. 2. HIGH TRACK-DENSITY EFFICIENCY CORRECTION A final multiplicity dependent correction is determined using simulated single-particles embedded into real events. This correction depends on both the quality of the track reconstruction in a high multiplicity environment and the type of particle measured. Depending on the centrality of the event, the correction factor is determined for each particle in the raw transverse momentum distribution and is applied as a weight. The final efficiency corrections are shown in Figure 8, where the correction for pions is shown as solid circles and for (anti)protons as open circles. The horizontal axis ranges from the most central to the most peripheral events in increments of 5%. The systematic uncertainty in the multiplicity efficiency correction is 9%. The difference between pions (solid) and (anti)protons (open) is due to the different TOF efficiencies for each particle (protons are slower than pions). In a small fraction of cases two particles may hit the same TOF slat at different times, and the slower particle is assigned an incorrect time. The particle will then fall outside the particle identification cuts. This effect depends on the type of particle. For each particle, two curves are shown, representing the DC tracking inefficiency for two types of tracks: fully reconstructed and partially reconstructed tracks. Fully reconstructed 22 tracks include X1 and X2 sections. In a high track-density environment, tracks may be partially reconstructed or hits may be incorrectly associated. There are two cases when this incorrect hit association occurs. In the first case, the direction vector in the azimuth prevents the track from pointing properly to the PC1 detector, and the correct hit cannot be associated. In the second case, the track is reconstructed properly, but there are two possible PC1 points. If no UV hits are found, then the wrong PC1 point can be associated to the track and the track’s beamline coordinate is mis-reconstructed. In both of these cases, the track fails the matching criteria in the TOF detector and is lost. Centrality (%) 0 10 20 30 40 50 60 70 80 90 100 Efficiency 0.5 0.6 0.7 0.8 0.9 1 1.1 – π p Fully reconstructed tracks Partially reconstructed tracks FIG. 8: The multiplicity dependent efficiency correction for pions (solid) and (anti)protons (open) for two types of tracks. The upper set of points correspond to fully reconstructed tracks in the drift chambers; while the lower set of points correspond to partially reconstructed tracks in the drift chambers. 3. DETERMINING THE YIELD AND MEAN pT The dN/dy and hpT i are determined using the data in the measured region and an extrapolation to the unmeasured region after integrating a functional form fit to the data. 23 A function describing the spectral shape is fit to the data, with varying pT ranges to control systematic uncertainties in the fit parameters. The fitted shape is extrapolated, integrated over the unmeasured range, and then co
mbined with the measured data to get the full yield. Two different functions are used to estimate upper and lower bounds for each spectrum. The average between the upper and lower bounds is used for dN/dy and hpT i. The statistical error is determined from the data, and the systematic uncertainty is taken as 1/2 the difference between the upper and lower bounds. For pions, a power-law in pT (Equation 9) and an exponential in mT (= q p 2 T + m2 0 ) (Equation 10) are fit to the data. For kaons and (anti)protons, two exponentials, one in pT (Equation 11) and the other in mT are used. The pT exponential provides an upper limit for the extrapolated yield, which is most important for the (anti)protons. The power-law function has three parameters labeled A, p0, and n in Equation 9. The exponentials have two parameters, A and T. d 2N 2πpT dpT dy = A p0 p0 + pT !n (9) d 2N 2πmT dmT dy = Ae−mT /T (10) d 2N 2πpT dpT dy = Ae−pT /T (11) C. SYSTEMATIC UNCERTAINTIES In Table I, the sources of systematic uncertainties in both hpT i and dN/dy are tabulated. The sources of uncertainty include the extrapolation in pT , the background, and the Monte Carlo corrections and cuts. The uncertainty in the Monte Carlo corrections is 11% and includes: the multiplicity efficiency correction of 9%, the particle identification cut of 5%, and the fiducial cuts of 5%. The uncertainties in the correction functions are added in quadrature to the statistical error in the data. Background is only relevant for pT < 0.6 GeV/c in the spectra. The total systematic uncertainty in the hpT i depends on the extrapolation and background uncertainties; the uncertainties are 7%, 10%, and 8% for pions, kaons, and protons, respectively. The overall uncertainty on dN/dy includes the uncertainties on hpT i in addition to the uncertainties from the corrections and cuts; the uncertainties are 13%, 15%, and 14% for pions, kaons, and protons, respectively [20]. 24 The hadron yields and hpT i values include an additional uncertainty arising from the fitting function used for extrapolation to the unmeasured region at low and high pT . The magnitude of the extrapolation is 30 ± 6% of the spectrum for pions, 40 ± 8% for kaons, and 25 ± 7.5% for protons [20]. The systematic uncertainty quoted here is taken as 1/2 the difference between the results from the two different functional forms. TABLE I: The sources of systematic uncertainties in hpT i and dN/dy. π (%) K (%) (anti)p (%) Extrapolation 6 8 7.5 Background (pT < 0.6 GeV/c) 2 5 3 hpT i total 7 10 8 Corrections and cuts 11 11 11 dN/dy total 13 15 14 The momentum scale is known to better than 2%, and the momentum resolution affects the spectra shape, primarily for protons, above 2.5 GeV/c. The momentum resolution is corrected by the Monte Carlo. As other sources of uncertainty on the number of particles at any given momentum are much larger, momentum resolution effects are neglected in determining the overall systematic uncertainty from the data reduction. IV. RESULTS A. TRANSVERSE MOMENTUM DISTRIBUTIONS The invariant yields as a function of pT for identified hadrons are shown in Figure 9, while Figure 10 provides the centrality dependence of the spectra. The spectra are tabulated in Appendix B. The π ±, K±, p, and p invariant yields for the most central, mid-central, and the most peripheral collisions, were reported previously [21]. Pion and (anti-)proton invariant yields are comparable for pT >1 GeV in the most central collisions. As can be seen already from Figure 10 all the spectra seem to be exponential; however, upon closer inspection, small deviations from an exponential form are apparent for the more peripheral collisions. The spectrum in the most peripheral collisions is noticeably power- 25 (GeV/c) pT 0 0.5 1 1.5 2 2.5 3 3.5 ) 2 /GeV 2 dy (c T N/dp 2 ) d T p π 1/(2 10 -4 10 -3 10 -2 10 -1 1 10 10 2 ± π ± K p and p Minimum bias Au+Au sNN = 130 GeV positive (GeV/c) pT 0 0.5 1 1.5 2 2.5 3 3.5 negative FIG. 9: The spectra of positive particles (left) and negative (right) in minimum-bias collisions from Au+Au collisions at √ sNN =130 GeV. The errors include both statistical and systematic errors from the corrections. law-like when compared to the more exponential-like spectrum in central collisions. This is especially apparent for the pions. The effect can be seen more clearly in the ratio of the spectra for a given particle species in two different centrality classes. Such ratios are shown in Figure 11 for the 5% central and the most peripheral positive spectra (60-92% centrality). The ratios for protons and antiprotons as well as for π + have a maximum at intermediate pT and are lower both at low and high pT . The kaon shape change is not very significant, given the current statistics. The change in slope at low-pT in central collisions compared to peripheral is consistent with a more substantial hydrodynamic, pressure-driven transverse flow existing in central collisions, since the increased boost would tend to deplete particles at the lowest pT (see Section IV C). This is observed at lower energies at the CERN SPS [22, 23]. It is in contrast to results obtained at the ISR [24] for p+p collisions at √ s = 63 GeV, where a shallow 26 0 0.5 1 1.5 2 2.5 10 -3 10 -2 10 -1 1 10 10 2 + π 0 0.5 1 1.5 2 2.5 0-5% 5-15 15-30 30-60 60-92 – π 0 0.5 1 1.5 2 ) 2 2/GeV dy (c T 2N/dp ) d T pπ 1/(2 10 -3 10 -2 10 -1 1 10 + K 0 0.5 1 1.5 2 – K (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 3.5 10 -4 10 -3 10 -2 10 -1 1 10 p (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 3.5 p FIG. 10: The hadron spectra for five centralities from the most central 0-5% to the most peripheral 60-92% at √ sNN = 130 GeV. Errors include both the statistical and point-by-point error in the corrections added in quadrature. maximum or minimum exists at low pT (in the range 0.3 − 0.6 GeV/c). 1. FEED-DOWN CONTRIBUTION TO p AND p FROM INCLUSIVE Λ and Λ Inclusive Λ and Λ transverse momentum distributions have been measured in the west arm of the PHENIX spectrometer using the tracking detectors (DC, PC1) and a lead-scintillator electromagnetic calorimeter (EMCal) [25]. The invariant mass is reconstructed from the weak decays Λ → p + π − and Λ → p + π +. The tracks from the tracking detectors are required to fall within 3σ of EMCal measured space-points. The EMCal timing resolution of the daughter particles is ≈ 700 ps. Using the DC momentum and the EMCal time-of-flight, the particle mass is calculated, and protons, antiprotons, and pions are identified using 2σ momentum-dependent mass-squared cuts. A 27 0 0.5 1 1.5 2 0 20 40 60 80 100 + π 0 0.5 1 1.5 2 – π 0 0.5 1 1.5 2 central/peripheral 0 20 40 60 80 100 120 140 160 180 + K 0 0.5 1 1.5 2 – K (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 0 20 40 60 80 100 120 140 160 180 p (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 p FIG. 11: The ratio of the most central to the most peripheral yields as a function of pT for pions (top), kaons (middle) and (anti)protons (bottom). clean particle separation is obtained using an upper momentum cut of 0.6 GeV/c and 1.4 GeV/c for pions and protons, respectively. The momentum is determined assuming the primary decay vertex is positioned at the event vertex and results in a momentum shift of 1-2% based on a Monte Carlo study. Using all combinations of pions and protons, the invariant mass is determined. The mass distribution shows a Λ peak on top of a random combinatorial background, which is determined by combining protons and pions from different collisions with the same centrality. A signal-to-background ratio of 1/2 is obtained after applying a decay kinematic cut on the daughter particles. Fitting a Gaussian function to the mass distribution in the range 1.05 < mpπ < 1.20 GeV/c 2 , 12000 Λ and 9000 Λ are observed, with mass resolution δm/m ≈ 2%. The reconstructed Λ and Λ spectra are corrected for the acceptance, pion decay-in- flight, momentum resolution, and reconstruction efficiency [25]. The systematic uncertainty 28 on the pT spectra is 13% from the corrections and 3% from the combinatorial background subtraction. The feed-down contributions from heavier hyperons Σ0 and
Ω are not measured but are estimated to be < 5%. In Figure 12, the transverse momentum spectra of inclusive protons (left) and antiprotons (right) are shown with the inclusive Λ and Λ transverse momentum distributions. The solid points are the (anti)proton spectra after the feed-down correction from Λ and Λ weak decays. From here forward, the data that are presented and discussed are not corrected for this feeddown effect; inclusive p and p yields are given. More details on the Λ and Λ measurement are included in [25]. (GeV/c) pT 0 0.5 1 1.5 2 2.5 3 3.5 ) 2 /GeV 2 dy (c T N/dp 2 ) d T p π 1/(2 10 -3 10-2 10-1 1 inclusive Λ direct p inclusive p Minimum bias Au+Au sNN=130 GeV positive (GeV/c) pT 0 0.5 1 1.5 2 2.5 3 3.5 inclusive Λ direct p inclusive p negative FIG. 12: For minimum-bias collisions, the inclusive Λ, inclusive p, and direct p transverse momentum distributions are plotted together in the left panel. The equivalent comparison for inclusive Λ, p, and direct p transverse momentum distributions is in the right panel. B. YIELD AND hpT i The yield, dN/dy, and the average transverse momentum, hpT i, are determined for each particle as described in the preceding section and have been previously published in [21]. For each centrality, the rapidity density dN/dy and average transverse momentum hpT i are tabulated in Tables II and III, respectively. 29 The Npart and Ncoll in each centrality selection are determined using a Glauber-model calculation in [26]. The resulting values of Npart and Ncoll are also tabulated in Table II. (See Appendix A for more detail). The errors on Npart and Ncoll include the uncertainties in the model parameters as well as in the fraction of the total geometrical cross section (92% ±4%) seen by the interaction trigger. The error due to model uncertainties is 2% [26]. An additional 3.5% error results from time dependencies in the centrality selection over the large data sample. TABLE II: The dN/dy at midrapidity for hadrons produced at midrapidity in each centrality class. The errors are statistical only. The systematic errors are 13%, 15% and 14% for pions, kaons, and (anti)protons, respectively. The Npart and Ncoll in each centrality selection are from a Glauber-model calculation in [26], also shown with systematic errors based on a 92±4% coverage. 0-5% 5-15% 15-30% 30-60% 60-92% Npart 347.7 ± 10 271.3 ± 8.4 180.2 ± 6.6 78.5 ± 4.6 14.3 ± 3.3 Ncoll 1008.8 712.2 405.5 131.5 14.2 π + 276 ± 3 216 ± 2 141 ± 1.5 57.0 ± 0.6 9.6 ± 0.2 π − 270 ± 3.5 200 ± 2.2 129 ± 1.4 53.3 ± 0.6 8.6 ± 0.2 K+ 46.7 ± 1.5 35 ± 1.3 22.2 ± 0.8 8.3 ± 0.3 0.97 ± 0.11 K− 40.5 ± 2.3 30.4 ± 1.4 15.5 ± 0.7 6.2 ± 0.3 0.98 ± 0.1 p 28.7 ± 0.9 21.6 ± 0.6 13.2 ± 0.4 5.0 ± 0.2 0.73 ± 0.06 p 20.1 ± 1.0 13.8 ± 0.6 9.2 ± 0.4 3.6 ± 0.1 0.47 ± 0.05 Pions dominate the charged particle multiplicity, but a large number of kaons and (anti)protons are produced. The inclusive yield of antiprotons is nearly comparable to that of protons. In the most central Au+Au collisions, the particle density at midrapidity (dN/dy) is ≈ 20 for antiprotons and 28 for protons, not corrected for feed-down from strange baryons. The average transverse momenta increase with particle mass and with decreasing impact parameter. The mean transverse momentum increases with the number of participant nucleons by 20±5% for pions and protons, as shown in Figure 13. The hpT i of particles produced in p + p and pp collisions, extrapolated to RHIC energies, are consistent with the most peripheral pion and kaon data; however, the hpT i of protons produced in Au+Au collisions is 30 TABLE III: The hpT i in MeV/c for hadrons produced at midrapidity in each centrality class. The errors are statistical only. The systematic uncertainties are 7%, 10%, and 8% for pions, kaons, and (anti)protons, respectively. 0-5% 5-15% 15-30% 30-60% 60-92% π + 390 ± 10 380 ± 10 380 ± 20 360 ± 10 310 ± 30 π − 380 ± 20 390 ± 10 380 ± 10 370 ± 20 320 ± 20 K+ 560 ± 40 580 ± 40 570 ± 40 550 ± 40 470 ± 90 K− 570 ± 50 590 ± 40 610 ± 40 550 ± 50 460 ± 90 p 880 ± 40 870 ± 30 850 ± 30 800 ± 30 710 ± 80 p 900 ± 50 890 ± 40 840 ± 40 820 ± 40 800 ± 100 significantly higher. This dependence on the number of participant nucleons may be due to radial expansion. Npart 0 50 100 150 200 250 300 350 > (GeV/c) T

(GeV/c) T

0.38 GeV to avoid the resonance contribution to the low pT region (see Section V A 2). The radial flow velocity and freeze-out temperature for all centralities are determined in the same way. The results are plotted together with the spectra in Figure 19. The hydrodynamic form clearly describes the spectra better than the simple exponential in Figure 14. The values for Tf o and β max T are tabulated in Table VI. TABLE VI: The minimum χ 2 and the parameters Tf o and β max T for each of the five centrality selections. The best fit parameters are determined by averaging all parameter pairs within the 1σ contour. The errors correspond to the standard deviation of the parameter pairs within the 1σ χ2 contour. It is important to note that the fit range in Figure 19 is the same as was used to fit mT exponentials to the spectra in Figure 14. Centrality (%) χ 2/dof Tf o (MeV) β max T < βT > 0-5 34.0/40 121 ± 4 0.70 ± 0.01 0.47±0.01 5-15 34.7/40 125 ± 2 0.69 ± 0.01 0.46±0.01 15-30 36.2/40 134 ± 2 0.65 ± 0.01 0.43±0.01 30-60 68.9/40 140 ± 4 0.58 ± 0.01 0.39±0.01 60-92 36.3/40 161±19 12 0.24±0.16 0.2 0.16±0.16 0.2 Figure 20 shows χ 2 contours for the temperature and velocity parameters for the 5% most central collisions. The n-sigma contours are labeled up to 8σ. The χ 2 contours indicate 40 0 0.5 1 1.5 2 2.5 10 -3 10 -2 10 -1 1 10 10 2 10 3 10 4 + π 0 0.5 1 1.5 2 2.5 0-5% (x 5) 5-15 (x 2) 15-30 30-60 60-92 – π 0 0.5 1 1.5 2 ) 2 2/GeV dy (c T 2N/dp ) d T pπ 1/(2 10 -3 10 -2 10 -1 1 10 10 2 + K 0 0.5 1 1.5 2 – K (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 3.5 10 -4 10 -3 10 -2 10 -1 1 10 10 2 p (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 3.5 p FIG. 19: The parameterization and the pT hadron spectra for all five centrality selections. strong anti-correlation of the two parameters. If the freeze-out temperature decreases, the flow velocity increases. The minimum χ 2 is 34 and the total number of degrees of freedom (dof) is 40. The parameters that correspond to this minimum are Tf o = 121 ± 4MeV and β max T = 0.70 ± 0.01. The quoted errors are the 1σ contour widths of ∆β max T and ∆Tf o. Within 3σ, the Tf o range is 106 − 141 MeV and the β max T range is 0.75 − 0.64. As a linear velocity profile (n = 1 in Equation 13) is assumed, the mean flow velocity in the transverse plane is hβT i = 2β max T /3. If a different particle density distribution (for instance, a Gaussian function for f(ξ)) were used, then the average should be determined after weighting accordingly [44]. A similar analysis for Pb+Pb collisions at 158 A GeV, was reported by the NA49 Collaboration in [45]. Using the same hydrodynamic parameterization, simultaneous fits of several hadron species for the highest energy results in Tf o = 127 ± 1 MeV and β max T = 0.48 ± 0.01 with χ 2/NDF = 120/43 for positive particles and Tf o = 114±2 MeV and β max T = 0.50±0.01 41 max T β 0.4 0.5 0.6 0.7 0.8 (GeV) fo T 0.08 0.1 0.12 0.14 0.16 0.18 0.2 1σ 2σ 3σ 4σ 5σ 6σ 7σ 8σ max T β 0.1 0.2 0.3 0.4 0.5 (GeV) fo T 0.08 0.1 0.12 0.14 0.16 0.18 0.2 FIG. 20: The χ 2 contours in the parameter space Tf o and β max T that result after simultaneously fitting hadrons in the 0 − 5% centrality (top) and 60 − 92% (bottom). The n-sigma contours are 42 with χ 2/NDF = 91/41 for negative particles (statistical errors only). Pions and deuterons are excluded from the fits to avoid dealing with resonance contributions to the pion yield and formation of deuterons by coalescence. The φ meson is included in the fit together with the negative particles. Previously, NA49 used a different parameterization to fit the charged hadron and deuteron spectra, as well as the mT dependence of measured HBT source radii, resulting in overlapping χ 2 contours with Tf o = 120 ± 12 MeV and β max T = 0.55 ± 0.12 [46]. 1. VELOCITY AND PARTICLE DENSITY PROFILE In order to use β max T and Tf o from the fits described above, one needs to know their sensitivity to the assumed velocity and particle density profiles in the emitting source. The choice of a linear velocity profile within the source is motivated by the profile observed in a full hydrodynamic calculation [47], which shows a nearly perfect linear increase of β(r) with r. Nevertheless, we also used a parabolic profile to check the sensitivity of the results to details of the velocity profile. For a parabolic velocity profile (n = 2 in Equation 13), β max T increases by ≈ 13% and Tf o increases by ≈ 5%. A Gaussian density profile used with a linear velocity profile increases β max T by ≈ 2%, with a neglible difference in the temperature Tf o. As a test of the assumption that all the particles freeze out at a common temperature, the simultaneous fits were repeated without the kaons. The difference in Tf o is within the measured uncertainties. 2. INFLUENCE OF RESONANCE PRODUCTION The functional forms given by Equations 10 and 17 do not include particles arising from resonance or weak decays. As resonance decays are known to result in pions at low transverse momenta [48, 49, 50], we place a pT threshold of 500 MeV/c on pions included in the hydrodynamic fit. A similar approach was followed by NA44, E814, and other experiments at lower energies, which performed in-depth studies of resonance decays feeding hadron spectra. However, these were for systems with higher baryon density, so we performed a cross check on possible systematic uncertainties arising from the pion threshold used in the fits. To estimate the effect of resonance decays were they not excluded from the fit, we calculate resonance contributions following Wiedemann [51]. 43 In order to reproduce the relative yields of different particle types, a chemical freeze-out temperature – different from the kinetic freeze-out temperature – and a baryonic chemical potential are introduced. Direct production and resonance contribution are calculated for pions and (anti)protons assuming a kinetic freeze-out temperature of 123 MeV, a transverse flow velocity of 0.612 (equivalent to hβT i = 0.44), a baryon chemical potential of 37 MeV, and a chemical freeze-out temperature (when particle production stops) of 172 MeV. These parameters are chosen as they provide a reasonable description of the (anti)proton and pion spectra and yields (10% most central) and are in good agreement with chemical freezeout analyses [52]. Most spectra from resonance decays show a steeper fall-off than the direct production, which should lead to a smaller apparent inverse slope, depending on what fraction of the low pT part of the spectrum is included in the fits. To measure the effect of resonance production on the spectral shape, the local slope is determined. For a given mT bin number i, the local slope is defined as Tlocal (i) = − mT (i + 1) − mT (i − 1) log[N(i + 1)] − log[N(i − 1)], (17) which is identical to the inverse slope independent of mT for an exponential. The difference in the local slope, ∆Tlocal = T direct local − T incl local, (18) is determined for direct and inclusive pions and (anti)protons. The differences are plotted as a function of mT − m0 in Figure 21. The difference in local slope for protons is below 13 MeV for the full transverse mass range; the non-monotonic behavior for protons is caused by the relatively strong transverse flow. For pions, ∆Tlocal decreases monotonically with mT and is below 10 MeV above mT = 1GeV/c. A fit of an exponential to the pion spectra for (mT −m0) > 0.38 GeV (which corresponds to pT > 0.5 GeV/c) yields a difference in inverse slope of 16 MeV with and without resonances. B. COMPARISON WITH HYDRODYNAMIC MODELS Hydrodynamic parameterizations as used in the previous Section rely upon many simplifying assumptions. Another approach to the study of collective flow is to compare the data to hydrodynamic models. Such models assume rapid equilibration in the collision and describe the subsequent motion of the matter using the laws of hydrodynamics. Large pressure 44 0 5 10 15 20 25 ∆ Tlocal (MeV) 30 mT-m0 (GeV/c) 0 0.5 1 1.5 2 2.5 3 π± p, p FIG. 21: The difference in the local slope for direct and inclusive pions (solid
) and (anti)protons (dashed). buildup is found, and we investigate this ansatz by checking the consistency of the data with calculations using a reasonable set of initial conditions. We compare to two separate models, the hydrodynamics model of Kolb and Heinz [53, 54, 55] and the “Hydro to Hadrons” (H2H) model of Teaney and Shuryak [56, 57]. The H2H model consists of a hydrodynamics calculation, followed by a hadronic cascade after chemical freeze-out. The cascade step utilizes the Relativistic Quantum Molecular Dynamics (RQMD) model, developed for lower energy 45 heavy ion collisions [58]. In both models, initial conditions are tuned to reproduce the shape of the transverse momentum spectra measured in the most central collisions, along with the charged particle yield. Each model also includes the formation and decay of resonances. In the Kolb and Heinz model, the initial parameters are the entropy density, baryon number density, the equilibrium time, and the freeze-out temperature which controls the duration of the expansion. The chemical freeze-out temperature is the temperature at which particle production ceases. The initial entropy or energy density and maximum temperature are fixed to match the measured multiplicity for the most central collisions using a parameterization that is tuned to produce the measured dNch/dη dependence on both Npart and Ncoll. A kinetic freeze-out temperature of Tf o = 128 MeV is used. Spectra from the Kolb-Heinz hydrodynamic model are shown in Figure 22 for pions (upper) and for protons (lower) as dotted lines. The solid lines are the results from the fits described in the previous sections. The figure thus allows two comparisons. The similarity of the dashed and solid lines shows that the hydrodynamic-inspired parameterization used to fit the data results in a pT distribution similar to this hydrodynamic calculation. Comparing the dashed lines to the data points shows that the hydrodynamic model agrees quite well for most of the centrality ranges. It is important to note that the model parameters are uncertain at the level of 10%, and, more importantly, the application of hydrodynamics to peripheral collisions may be less reasonable than for central collisions, as hydrodynamic calculations assume strong rescattering and a sufficiently large system size (discussed in [55]). In reference [56, 59], the PHENIX p spectrum shape is well described by the H2H model with the LH8 equation of state. The cascade step in the H2H model removes the requirement that all particles freeze out at a common temperature. Thus the freeze-out temperature and its profile are predicted, rather than input parameters. Furthermore, following the hadronic interactions explicitly with RQMD removes the need to rescale the particle ratios at the end of the calculation, as they are fixed by the hadronic cross sections rather than at some particular freeze-out temperature. The LH8 equation of state includes a phase transition with a latent heat of 0.8 GeV. In [56, 59], the Ω and the φ are shown to decouple from the expanding system at T = 160 MeV, and they receive a flow velocity boost of 0.45c. Pions and kaons decouple at T = 135 MeV with flow velocity = 0.55c, while protons have T = 120 MeV and flow velocity ≥ 0.6. These temperatures and flow velocities are consistent with 46 0 0.5 1 1.5 2 2.5 ) 2 2/GeV dy (c T N/dp 2 ) d T p π 1/(2 10 -3 10 -2 10 -1 1 10 10 2 10 3 10 4 + π Hydro Param. Fit 0 0.5 1 1.5 2 2.5 0-5% (x 5) 5-15 (x 2) 15-30 30-60 60-92 – π (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 3.5 ) 2 /c 2 dy (GeV T N/dp 2 ) d T p π 1/(2 10 -4 10 -3 10 -2 10 -1 1 10 10 2 p (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 3.5 p FIG. 22: The hydrodynamics calculation with initial parameters tuned to match the most central spectra in the pT range 0.3 − 2.0 GeV/c. the values extracted from the data for the most central events. However, the average initial energy density exceeds the experimental estimate using formation time τ0 =1 fm/c. In Figure 23, radial flow from the fits of the previous section are shown as a function of the number of participants for Tf o (top) and hβT i (bottom). There is a slight decrease of Tf o, while hβT i increases with Npart, saturating at 0.45. The value of hβT i from Kolb and Heinz is also shown, and agrees with the data reasonably well. In the plot of hβT i, the dashed line indicates the results of fitting the parameterization to the data while keeping Tf o fixed at 128 MeV to agree with the value used by Kolb and Heinz. Radial flow values for central collisions remain unchanged, while those in peripheral collisions increase. Even with the extreme assumption that all collisions freeze out at the same temperature, regardless of centrality, the trend in centrality dependence of the radial flow does not change. 47 (MeV) fo T 60 80 100 120 140 160 180 200 Param. Fit Hydro Npart 0 50 100 150 200 250 300 350 400 > T β < 0.1 0.2 0.3 0.4 0.5 0.6 T = 128 MeV Param. Fit Hydro FIG. 23: The expansion parameters Tf o and β max T as a function of the number of participants. As a comparison, the results from a hydrodynamic model calculation are also shown (Ref. [53, 54, 55]). The dashed line corresponds to a fixed temperature of 128 MeV for all centralities in the parameterized fit to the data. C. HYDRODYNAMIC CONTRIBUTIONS AT HIGHER pT We use the parameters extracted from the fit to the charged hadron spectra in the low pT region to extrapolate the effect of the soft physics to higher pT . This yields a prediction for the spectra of hadrons should a collective expanding thermal source be the only mechanism for particle production in heavy ion collisions. Comparing this prediction to the measured spectrum of charged particles or neutral pions should indicate the pT range over which soft thermal processes dominate the cross section. Where the data deviate from the hydrodynamic extrapolation, other contributions, as e.g. from hard processes or non-equilibrium production become visible. The approach described here differs from hydrodynamic fits to 48 (GeV/c) T p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 dy (GeV/c) T N/dp 2 ) d T p π 1/(2 10 -5 10 -4 10 -3 10 -2 10 -1 1 10 10 2 – +h + h ± +p ± radial flow fit π ±+K – +π + radial flow fit π – +K + radial flow fit K radial flow fit p+ p = 0.70 max T β Tfo = 121 MeV FIG. 24: The high pT hadron spectra in Reference [38] compared to the fit results assuming radial flow from the πKp spectra in the 5% central events. the entire hadron spectrum, as we fix the parameters from the low pT region alone, where soft physics should be dominant. The hadron spectrum is calculated using the fit parameters from the low pT region fits shown in the preceding section, and extrapolated to higher pT . Figure 24 shows the calculated spectrum for each particle type, and the sum of the extrapolated spectra is compared to the measured charged hadrons (h + + h −) in the 5% most central collisions. As nonidentified charged hadrons are measured in η rather than in y, the extrapolated spectra are converted to units of η. This conversion is most important in the low pT region. No additional scale factor is applied – the extrapolation and data are compared absolutely. Below ≈ 2.5 GeV/c pT , the agreement is very good, while at higher pT the data begin to exceed the hydrodynamic extrapolation. Other hydrodynamic calculations have been successful in describing the distributions 49 over the full pT range [60] with different parameter values. There are clear indications that particle production from a hydrodynamic source, if invoked to explain the spectra at low pT , will have a non-negligible influence even at relatively large pT . Furthermore, the range of pT populated by hydrodynamically boosted hadrons is species dependent. This is clearly visible in Figure 24, which shows that the extrapolated proton spectra have a flatter pT distribution than the extrapolated pions and kaons. The yield of the “soft” protons reaches, and even exceeds, that of the extrapolated “soft” pions at 2 GeV/c pT . Therefore the transition from soft to hard processes must also be species dependent, and the b
oost of the protons causes the region where hard processes dominate the inclusive charged particle spectrum to be at significantly higher transverse momenta in central Au+Au than in p+p collisions. Our analysis suggests this occurs not lower than pT = 3 GeV/c. D. HADRON YIELDS AS A FUNCTION OF CENTRALITY The previous discussion focused on the hadron spectra; now we turn to the centrality dependence of the pion, kaon, proton, and antiproton yields, which can shed further light on the importance of different mechanisms in particle production. It is instructive to see whether yields of the different hadrons scale with the number of participant nucleons, Npart, the number of binary nucleon-nucleon collisions, Ncoll, or some combination of the two. The total yields of the hadrons may be expected to be dominated by soft processes, and the wounded nucleon model of soft interactions suggests that the yields should scale as the number of participants, Npart. If each participant loses a certain fraction of its incoming energy, like e.g. in string models, where each pair of participants (or wounded nucleons) contributes a color flux tube, the total energy of the fireball formed at central rapidity would be proportional to the number of participants Npart. If, furthermore, the fireball is locally thermalized and particle production is determined at a single temperature, the multiplicity would scale with Npart. On the other hand, at very high pT , particle production may be dominated by hard processes and scale with Ncoll[61, 62]. In order to investigate the existence of scaling, the multiplicities are parameterized as: dN dy = C · (Npart) αpart (19) 50 TABLE VII: Fit parameters for each particle species using equations 19 and 20. particle αpart αcoll π + 1.06 ± 0.01 0.79 ± 0.01 π − 1.08 ± 0.01 0.80 ± 0.01 K+ 1.18 ± 0.02 0.88 ± 0.02 K− 1.20 ± 0.03 0.89 ± 0.02 p + 1.16 ± 0.02 0.86 ± 0.02 p − 1.14 ± 0.03 0.84 ± 0.02 and dN dy = C ′ · (Ncoll) αcoll . (20) Fit results for these parameterizations are shown in Table VII. As can be seen, the exponents αpart are > 1 for all species, while αcoll is consistently < 1. The production of all particles increases more strongly than with Npart, but not as strongly as with Ncoll. Small differences between the different particle species are apparent: The (anti-)proton yield increases more strongly than the pion yield, and the kaon yield shows the strongest centrality dependence. Remarkably, the yield fraction scaling beyond linear with Npart is larger for kaons, protons, and antiprotons than for pions. Perhaps it is not surprising that the yields do not scale simply with Npart; the collective flow seen in the pT spectra already shows that the nucleonnucleon collisions cannot be independent. We next check whether the simple model of hadron yields can be brought into agreement with the data by adding a component of the yields scaling as the number of binary collisions, Ncoll. Such an admixture inspires simple two-component models [61, 62]. The nonlinearity of dN/dy on the number of participants is illustrated by the ratio (dN/dy)/Npart, shown in Figure 25 as a function of centrality. The yields are seen to depend linearly on Ncoll/Npart. As seen already from the exponents in Table VII, the increase with centrality is strongest for kaons, intermediate for (anti-)protons, and weakest for pions. This indicates that protons and antiprotons have a larger component scaling with Ncoll than pions. We fit the yields per participant with Equation 21. As in [61, 62] we parameterize the multiplicity using two free parameters: npp, the multiplicity in p+p collisions, and x, the 51 relative strength of the component scaling with Ncoll. R ≡ dN/dy Npart = (1 − x) · npp 1 2 + x · npp Ncoll Npart = npp ” 1 2 + x Ncoll Npart − 1 2 !# . (21) The results of the fit are shown as solid lines in Figure 25. The fit parameter values are given in Table VIII. All hadron species are well fit. The importance of the component scaling as Ncoll is largest for kaons and smallest for pions. TABLE VIII: Values of the parameters npp and x from fitting Equation 21 to the observed dN/dy per Npart. npp x π + 1.41 ± 0.11 0.028 ± 0.020 π − 1.10 ± 0.11 0.085 ± 0.030 K+ 0.130 ± 0.021 0.232 ± 0.076 K− 0.089 ± 0.020 0.326 ± 0.132 p 0.089 ± 0.013 0.181 ± 0.062 p 0.062 ± 0.010 0.172 ± 0.068 We check the consistency of the fits in Figure 25 with known hadron yields in p+p collisions by extrapolating the fits down to two participants (and one binary nucleon-nucleon collision). Isospin differences between p+p and Au+Au are ignored. The check is done by separately extrapolating the fitted fraction of yield which scales with Ncoll and the fraction scaling with Npart down to one nucleon-nucleon collision and two participant nucleons, and summing the result. One obtains particle ratios of K/π = (8.7 ± 2.6)% and ¯p/π = (4.9 ± 0.8)%. These values fall between those measured at lower √ s at the ISR [63] and those at higher √ s at the Tevatron [64], as expected since the RHIC energy lies in between. Thus the Au+Au data are shown to scale down to p+p reasonably. One may expect that the particle ratios at very high pT should be dominated by hard scattering, and therefore scale with the number of binary collisions. Consequently, we look at ratios of the Ncoll scaling components alone, extrapolated down to one binary collision. The values are compared to measurements of hadron ratios at the ISR [65] in Figures 26 52 0.5 1 1.5 2 2.5 3 0.5 1 1.5 2 2.5 3 Ncoll/Npart (dN X/dy) / Npart K – (x20) π – p (x20) K + (x20) π + p (x20) FIG. 25: dN/dy per participant of different particle species as a function of the number of collisions per participant. Kaon and (anti-)proton multiplicities are scaled by a factor of 20. and 27. The ratio of the extrapolated Au+Au yield fractions scaling as Ncoll are shown as solid lines for pT ≥ 2 GeV/c. The agreement with the p+p data at high pT is quite good. Finally, we directly compare p/π and p/π ratios in central Au+Au collisions with p+p, as a function of pT . These ratios from the 10% most central data, using the charged particle measurement from this paper and neutral pions from [38], are shown in Figure 28. The ratios show a steady increase up to 2.5 GeV/c in pT . Even though the simple extrapolation 53 (GeV/c) T p 0 1 2 3 4 5 kaon / pion 0 0.2 0.4 0.6 0.8 1 1.2 Alper et.al. NP B100,237,(1975) 23 GeV 31 GeV 45 GeV 53 GeV 63 GeV FIG. 26: Kaon to pion ratio as a function of pT . The different points are measured in p+p collisions (data from ref. [65]). The solid line is the asymptotic value for high pT in p+p derived from the hard scattering component of the fits using Equation 21 to the measured centrality dependence of dN/dy in Au-Au collisions at √ sNN = 130 GeV. The dashed lines indicate the corresponding uncertainty. of the Ncoll scaling yield fraction agreed with p+p, the ratios of the full yield significantly exceed those in the ISR measurements [65]. According to Gyulassy and collaborators, [66], this result may give insight into baryon number transport and the interplay between soft and hard processes. Of course, splitting the observed yields into portions which scale with Npart and Ncoll is by no means a unique explanation of the data. The spectra and yields can also be well reproduced by thermal models, which break such simple scalings due to the multiple interactions suffered by the constituents. Simple thermal models that ignore transverse and longitudinal flow [67] are able to describe the centrality dependence of the mid-rapidity π ±, K±, p, and p yields by tuning the chemical freeze-out temperature Tch, the baryon chemical potential µB and by introducing a strangeness saturation factor γs. It was found that µB is independent of centrality, while both γs and Tch increase from peripheral to central collisions. Within the same model, the centrality dependence of the particle yields at lower energy (√ sNN = 17 GeV [68, 69]) are described by constant Tch and µB. The strong centrality dependence in kaon production at both energies is accounted for
by the increase in the strangeness saturation factor γs. Although the integrated particle yields are very well described, such simple thermal models 54 (GeV/c) T p 0 1 2 3 4 5 anti-proton / pion 0 0.2 0.4 0.6 0.8 1 1.2 Alper et.al. NP B100,237,(1975) 23 GeV 31 GeV 45 GeV 53 GeV 63 GeV FIG. 27: Antiproton to π − ratio as a function of pT . The different points are measured in p + p collisions (data from ref. [65]). The solid line is the asymptotic value for high pT in p+p derived from the hard scattering component of the fits using Equation 21 to the measured centrality dependence of dN/dy in Au-Au collisions at √ sNN = 130 GeV. The dashed lines indicate the corresponding uncertainty. (GeV/c) T p 0 1 2 3 4 5 0 1 2 3 4 5 proton / pion 0 1 2 3 4 5 + p / π 0 p / π , pp @53 GeV, ISR + p / π (GeV/c) T p anti-proton / pion 0 1 2 3 4 5 – p / π 0 p / π , pp @53 GeV, ISR – p / π FIG. 28: a) Proton to pion ratio as a function of pT . b) Antiproton to pion ratio as a function of pT . The open circles represent measurements in p + p collisions (data from ref. [65]). The filled circles show the 10 % most central Au+Au collisions. The neutral pion spectra are from the data published in [38]. do not attempt a comparison to the single particle spectra, which clearly indicate centrality dependent flow effects not included in the model. Thermal models which include hydrodynamical parameters on a freeze-out hypersurface to account for longitudinal and transverse flow can reproduce the absolutely normalized 55 particle spectra by introducing only two thermal parameters Tch and µB [70, 71]. In this approach, the thermal parameters are independent of centrality, while the geometric parameters are adjusted to reproduce the spectra. Good agreement with the data is obtained up to pT ≈ 2 − 3 GeV/c, however an explicit comparison with the centrality dependence of the integrated mid-rapidity yields has not yet been made. This section shows that the yields of all hadrons increase more rapidly than linearly with the number of participants, but the increase is weaker than scaling with the number of binary collisions. The excess beyond linear scaling with Npart is strongest for kaons, intermediate for (anti-)protons, and weakest for pions. The centrality dependence of the total yields can be well fit with a sum of these two kinds of scaling. At high pT , the baryon and anti-baryon yields greatly exceed expectations from p+p collisions. Thermal models, which do not invoke strict scaling rules, can successfully reproduce the data as well, providing that they include the radial flow required by the pT spectra. VI. SUMMARY AND CONCLUSION We have presented the spectra and yields of identified hadrons produced in √ sNN = 130 GeV Au + Au collisions. The yields of pions increase approximately linearly with the number of participant nucleons, while the yield increase is faster than linear for kaons, protons, and antiprotons. Hydrodynamic analyses of the particle spectra are performed: the spectra are fit with a hydrodynamic-inspired parameterization to extract freeze-out temperature and radial flow velocity of the particle source. The data are also compared to two full hydrodynamics calculations. The simultaneous fits of pion, kaon, proton, and antiproton spectra show that radial flow in central collisions at RHIC exceeds that at lower energies and increases with centrality of the collision. The hydrodynamic models are consistent with the measured spectral shapes, extracted freeze-out temperature Tf o, and the flow velocity βT in central collisions. Extrapolating the fits to estimate thermal particle production at higher pT allows us to study the soft-hard physics boundary by comparing to measured spectra at high pT . The yield of the “soft” protons reaches, and even exceeds, that of the extrapolated “soft” pions at 2 GeV/c pT . The sum of the extrapolated “soft” spectra agree with the measured 56 inclusive data to pT ≈ 2.5 − 3 GeV/c. The transition from soft to hard processes must be species dependent, and the admixture of boosted nucleons implies that hard processes do not dominate the inclusive charged particle spectra until approximately 3 GeV/c. APPENDIX A: DETERMINING Npart AND Ncoll As only the fraction of the total cross section is measured in both the ZDC and BBC detectors, a model-dependent calculation is used to map collision centrality to the number of participant nucleons, Npart, and the number of nucleons undergoing binary collisions, Ncoll. A discussion of this calculation at RHIC can be found elsewhere [61]. Using a Glauber model combined with a simulation of the BBC and ZDC responses, Npart and Ncoll are determined in each centrality. The model provides the thickness of nuclear matter in the direct path of each oncoming nucleon, and uses the inelastic nucleon-nucleon cross section σ inel N+N to determine whether or not a nucleon-nucleon collision occurs. We assume the following: • The nucleons travel in straight-line paths, parallel to the velocity of its respective nucleus. • An inelastic collision occurs if the relative distance between two nucleons is less than q σ inel N+N /π. • Fluctuations are introduced by using the simulated detector response for both the ZDC and BBC. In this calculation, the Woods-Saxon nuclear density distribution (ρ(r)) is used for each nucleus with three parameters, the nuclear radius R = 6.38+0.27 −0.13 fm, diffusivity d = 0.53±0.01 fm [15], and the inelastic nucleon-nucleon cross section σ inel N+N = 40 ± 3 mb, ρ(r) = ρ0 1 + e r−rn d . (A1) APPENDIX B: INVARIANT CROSS SECTIONS Tabulated here are the measured invariant yields of pions, kaons, and (anti)protons produced in Au+Au collisions at 130 GeV. The first set of tables (Tables IX- XII) are the 57 TABLE IX: Invariant yields for π ±, K±, and (anti)p measured in minimum bias events at midrapidity and normalized to one rapidity unit. The errors are statistical only. pT (GeV/c) π ± K± p(p) 0.25 112±2 109±2 0.35 56 ±1 49.9 ±0.9 0.45 28.0 ±0.5 6.1±0.4 24.1 ±0.5 4.6±0.4 0.55 15.7 ±0.3 4.0±0.3 2.3± 0.1 14.6 ±0.3 3.2±0.2 1.2±0.1 0.65 9.1 ±0.2 2.8±0.2 1.8± 0.1 8.7 ±0.2 2.1 ±0.2 1.17± 0.09 0.75 5.8 ±0.1 1.7±0.1 1.38± 0.08 5.6 ±0.2 1.6±0.1 0.98±0.07 0.85 3.8 ±0.1 1.30±0.08 1.18±0.07 3.6±0.1 1.17±0.09 0.95±0.07 0.95 2.40 ±0.08 0.87±0.06 0.98± 0.06 2.28 ±0.08 0.69±0.06 0.65± 0.05 1.05 1.61 ±0.06 0.62±0.04 0.70± 0.04 1.61 ±0.06 0.53±0.05 0.50± 0.04 1.15 1.03 ±0.04 0.43±0.03 0.60± 0.04 1.17 ±0.05 0.38±0.04 0.35± 0.03 1.25 0.71±0.03 0.33±0.03 0.41± 0.03 0.76 ±0.04 0.27±0.03 0.34±0.03 1.35 0.46 ±0.02 0.20±0.02 0.32±0.02 0.54±0.03 0.16±0.02 0.22±0.02 1.45 0.35±0.02 0.17±0.02 0.23± 0.02 0.31 ±0.02 0.13±0.02 0.18± 0.02 1.55 0.24 ±0.02 0.10±0.01 0.17± 0.02 0.22 ±0.02 0.10±0.01 0.15± 0.02 1.65 0.16 ±0.01 0.08±0.01 0.15 ±0.01 0.07±0.01 58 invariant cross sections plotted in Figures 9 and 10. The second set of tables (Tables XIIIXVI) are the invariant cross sections in equal pT bins as used in Figure 11. APPENDIX C: FREEZE-OUT SURFACE ASSUMPTIONS The freeze-out surface is σ (r, φ, η), where the radius r is between zero and R, the radius at freeze-out, the azimuthal angle φ is between zero and 2π, and the longitudinal space-time rapidity variable η varies between −ηmax and ηmax. In the Bjorken scenario, the freeze-out surface in space-time is hyperbolic, with contours of constant proper time τ = √ t 2 − z 2 . Assuming instantaneous freeze-out in the radial direction and longitudinal boost-invariance, the model-dependence factors out of Equation 17 and is included in the normalization constant A. At 130 GeV, the PHOBOS experiment measures the total charged particle pseudorapidity distribution to be flat over 2 units of pseudorapidity [42]. The measured rapidity in PHOBOS is taken to be the same as the rapidity of the fireball, defined here as z. The rapidity variables in the integrand vanish for |z| > 2. Therefore, the integration over the fireball rapidity is generally taken to be from −∞ to +∞ using the modified K1 Bessel function K1(mT
/T) = Z ∞ 0 cosh(z)e −mT cosh(z)/T dz (C1) where the variable z is the fireball rapidity variable. The K1 bessel function can also result by integration over the measured rapidity y with the assumption that the freeze-out is instantaneous in the radial direction. In this case, no assumption is made on the shape of the freeze-out hypersurface. This also assumes that the total rapidity distribution is measured in the detector. What results is the single differential 1/mT dN/dmT . 2 ACKNOWLEDGMENTS We thank the staff of the RHIC Project, Collider-Accelerator, and Physics Departments at Brookhaven National Laboratory and the staff of the other PHENIX participating institutions for their vital contributions. We acknowledge support from the Department of Energy, Office of Science, Nuclear Physics Division, the National Science Foundation, and Dean of the 2 Private communication with U. Heinz. 59 TABLE X: Pion invariant yields in each event centrality and pT bin measured at midrapidity, normalized to one rapidity unit. For each measured pT bin, the positive pion cross section is the top row and the negative pion cross section is the bottom row. Errors are statistical only. pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92% 0.25 355 ± 9 282 ± 6 186 ± 4 81 ± 2 13.2 ± 0.5 371 ± 10 275 ± 7 180 ± 4 74 ± 2 12.1 ± 0.5 0.35 188 ± 5 146 ± 3 93 ± 2 36.6 ± 0.8 5.3 ± 0.2 169 ± 5 128 ± 3 82 ± 2 34.3 ± 0.9 5.0 ± 0.2 0.45 95 ± 3 74 ± 2 48 ± 1 17.5 ± 0.5 2.7 ± 0.1 86 ± 3 63 ± 2 40 ± 1 15.7 ± 0.5 2.1 ± 0.1 0.55 56 ± 2 41 ± 1 26.0 ± 0.7 10.1 ± 0.3 1.32 ± 0.09 51 ± 2 38 ± 1 24.5 ± 0.8 9.6 ± 0.3 1.18 ± 0.09 0.65 32± 1 25.6 ± 0.8 15.0 ± 0.5 5.3 ± 0.2 30 ± 1 22.6 ± 0.8 14.5 ± 0.5 5.7 ± 0.2 0.70 0.62± 0.04 0.57± 0.04 0.75 21.1 ± 0.9 15.4 ± 0.6 9.9 ± 0.4 3.6 ± 0.1 20 ± 1 15.3 ± 0.6 9.5 ± 0.4 3.5 ± 0.2 0.85 14.0 ± 0.7 10.3 ± 0.4 6.4 ± 0.3 2.3 ± 0.1 12.8 ± 0.8 9.6 ± 0.5 6.1 ± 0.3 2.1 ± 0.1 0.90 0.19 ± 0.02 0.24 ± 0.02 1.00 7.1 ± 0.3 5.3± 0.2 3.4 ± 0.1 1.25 ± 0.05 6.5 ± 0.3 5.0 ± 0.2 3.4 ± 0.1 1.25 ± 0.05 1.20 3.2 ± 0.2 2.2 ± 0.1 1.47 ± 0.07 0.55 ± 0.03 0.064 ± 0.006 3.3 ± 0.2 2.6 ± 0.1 1.51 ± 0.08 0.63 ± 0.04 0.061 ± 0.007 1.40 1.3 ± 0.1 1.01 ± 0.07 0.72 ± 0.04 0.27 ± 0.02 1.3 ± 0.1 1.25 ± 0.09 0.72 ± 0.05 0.26 ± 0.02 1.60 0.55 ± 0.07 0.57 ± 0.05 0.33 ± 0.03 0.14 ± 0.01 0.015 ± 0.003 0.51 ± 0.07 0.57 ± 0.05 0.30 ± 0.03 0.12 ± 0.01 0.014 ± 0.003 1.80 0.35 ± 0.05 0.25 ± 0.03 0.15 ± 0.02 0.060 ± 0.008 0.40 ± 0.06 0.27 ± 0.03 0.14 ± 0.02 0.075 ± 0.009 2.00 0.18 ± 0.03 0.13 ± 0.02 0.10 ± 0.01 0.023 ± 0.004 0.005 ± 0.001 60 TABLE XI: Kaon invariant yields in each event centrality and pT bin, measured at midrapidity and normalized to one rapidity unit. The top row in each pT bin is K+, and the bottom row is K−. Errors are statistical only. pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92% 0.44 0.5 ± 0.1 0.4 ± 0.1 0.45 21± 3 16 ± 2 10 ± 1 4.3 ± 0.5 21± 3 13 ± 2 7 ± 1 2.5 ± 0.4 0.54 0.20 ± 0.07 0.3 ± 0.1 0.55 15± 2 11 ± 1 6.6 ± 0.7 2.4 ± 0.3 13± 2 8 ± 1 4.8 ± 0.6 2.3 ± 0.3 0.65 9 ± 1 7.5 ± 0.7 4.7 ± 0.4 1.9 ± 0.2 8 ± 1 7.0 ± 0.8 3.1 ± 0.4 1.1 ± 0.2 0.69 0.18 ± 0.03 0.14 ± 0.03 0.75 5.3 ± 0.7 4.6 ± 0.5 3.1 ± 0.3 0.9 ± 0.1 5.1 ± 0.8 5.0 ± 0.6 2.5 ± 0.3 0.9 ± 0.1 0.85 5.7 ± 0.7 3.6 ± 0.4 2.1 ± 0.2 0.67 ± 0.08 3.6 ± 0.6 3.7 ± 0.4 2.0 ± 0.2 0.64 ± 0.09 0.89 0.07 ± 0.02 0.09 ± 0.02 0.95 3.0 ± 0.4 2.3 ± 0.2 1.5 ± 0.2 0.51 ± 0.07 2.4 ± 0.4 2.3 ± 0.3 1.0 ± 0.2 0.35 ± 0.06 1.05 2.3 ± 0.3 1.5 ± 0.2 1.2 ± 0.1 0.37 ± 0.05 1.8 ± 0.3 1.8 ± 0.2 0.8 ± 0.1 0.27 ± 0.05 1.15 1.6 ± 0.3 1.3 ± 0.2 0.62 ± 0.09 0.29 ± 0.04 1.4 ± 0.3 0.9 ± 0.2 0.7 ± 0.1 0.23 ± 0.04 1.17 0.012± 0.004 0.015± 0.005 1.25 1.1 ± 0.2 1.0 ± 0.1 0.66 ± 0.09 0.15 ± 0.03 1.2 ± 0.2 0.8 ± 0.1 0.41 ± 0.08 0.15 ± 0.03 1.35 0.6 ± 0.1 0.6 ± 0.1 0.35 ± 0.05 0.12 ± 0.02 61 TABLE XII: (Anti)proton invariant yields in each event centrality and pT bin, measured at midrapidity and normalized to one rapidity unit. The top row in each pT is the proton cross section, and the bottom row the antiproton. The errors are statistical only. pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92% 0.545 0.26 ± 0.06 0.12 ± 0.05 0.55 8 ± 1 4.9 ± 0.5 4.0 ± 0.4 1.6 ± 0.2 4.2 ± 0.8 2.8 ± 0.5 2.0 ± 0.3 0.8 ± 0.1 0.65 6.3 ± 0.7 4.7 ± 0.4 2.7 ± 0.2 1.2 ± 0.1 4.3 ± 0.7 2.6 ± 0.4 1.9 ± 0.3 0.9 ± 0.1 0.695 0.14 ± 0.02 0.14 ± 0.03 0.75 4.4 ± 0.5 4.0 ± 0.4 2.2 ± 0.2 0.90 ± 0.08 3.6 ± 0.5 2.5 ± 0.3 1.7 ± 0.2 0.60 ± 0.08 0.85 3.9 ± 0.4 3.3 ± 0.3 1.9 ± 0.2 0.75 ± 0.07 2.9 ± 0.5 2.5 ± 0.3 1.8 ± 0.2 0.62± 0.08 0.895 0.10± 0.02 0.06± 0.01 1.00 3.1 ± 0.2 2.4 ± 0.2 1.37 ± 0.09 0.46 ± 0.03 2.1 ± 0.2 1.5 ± 0.1 0.91 ± 0.08 0.41 ± 0.04 1.18 0.031± 0.005 0.018± 0.004 1.20 2.0 ± 0.2 1.4 ± 0.1 0.82 ± 0.06 0.28 ± 0.02 1.4± 0.2 1.0 ± 0.1 0.54 ± 0.05 0.19 ± 0.02 1.40 1.1 ± 0.1 0.74 ± 0.07 0.46 ± 0.04 0.14 ± 0.01 0.9 ± 0.1 0.50 ± 0.06 0.32 ± 0.04 0.13 ± 0.02 1.58 0.005± 0.002 0.007± 0.002 1.60 0.54 ± 0.07 0.49 ± 0.05 0.25 ± 0.03 0.09 ± 0.01 0.49 ± 0.08 0.37 ± 0.05 0.20 ± 0.03 0.053 ± 0.009 1.80 0.34 ± 0.05 0.25 ± 0.03 0.16 ± 0.02 0.047 ± 0.007 0.27 ± 0.06 0.11 ± 0.02 0.10 ± 0.02 0.021 ± 0.005 1.98 0.003 ± 0.001 62 TABLE XIII: Minimum bias invariant yields for all particles in equal pT bins. For each pT , the first line are the positive particle yields, and the second are the negative particle yields. The units are c 2/GeV 2 . pT (GeV /c) π ± K± (anti)p 0.25 112±2 109±2 0.35 56 ±1 49.9 ±0.9 0.45 28.0 ±0.5 6.1±0.4 24.1 ±0.5 4.6±0.4 0.55 15.7 ±0.3 4.0±0.3 2.3±0.1 14.6 ±0.3 3.2±0.2 0.38±0.02 0.70 7.3 ±0.1 2.18±0.09 1.55±0.06 7.0 ±0.1 1.9±0.1 1.07±0.06 0.90 3.06 ±0.06 1.07±0.05 1.08±0.04 2.89 ±0.07 0.91±0.05 0.79±0.04 1.20 0.91 ±0.02 0.38±0.02 0.49±0.02 0.98 ±0.02 0.32±0.02 0.35±0.01 1.60 0.208 ±0.007 0.104±0.006 0.157±0.007 0.193 ±0.007 0.093±0.006 0.119±0.007 2.00 0.050 ±0.003 0.051±0.003 0.053 ±0.003 0.031±0.003 2.45 0.0028 ±0.0005 0.013±0.001 0.0034 ±0.0006 0.009±0.001 2.95 0.0036±0.0006 0.0022±0.0005 3.55 0.0007±0.0002 0.0006±0.0002 63 TABLE XIV: Pion invariant yields in each event centrality normalized to one rapidity unit at midrapidity. The first line corresponds to positive pions, and the second to negative pions. pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92% 0.25 355±9 282±6 186±4 81±2 13.2±0.5 371±10 275±7 180± 4 74 ± 2 12.1 ± 0.5 0.35 188±5 146±3 93± 2 36.6± 0.8 5.3 ± 0.2 169±5 128±3 82± 2 34.3± 0.9 5.0 ± 0.2 0.45 95±3 74±2 48± 1 17.5± 0.5 2.7 ± 0.1 86±3 63±2 40± 1 15.7± 0.5 2.1 ± 0.1 0.55 56±2 41±1 26.0± 0.7 10.1± 0.3 1.32 ± 0.09 51±2 38±1 24.5± 0.8 9.6 ± 0.3 1.18 ± 0.09 0.70 26.3±0.8 20.2±0.5 12.3± 0.3 4.4 ± 0.1 0.62 ± 0.04 24.7±0.9 18.6±0.6 11.8± 0.4 4.5 ± 0.1 0.57 ± 0.04 0.90 11.0±0.4 7.9 ±0.2 5.1 ± 0.2 1.79 ± 0.06 0.19 ± 0.02 10.0±0.5 7.9 ±0.3 5.0 ± 0.2 1.76 ± 0.07 0.24 ± 0.02 1.20 3.1±0.1 2.37 ±0.09 1.50 ± 0.05 0.58 ± 0.02 0.064 ± 0.006 3.4±0.2 2.7 ±0.1 1.67 ± 0.07 0.64 ± 0.03 0.061 ± 0.007 1.60 0.62±0.05 0.54 ±0.03 0.34 ± 0.02 0.142 ± 0.009 0.015 ± 0.003 0.63±0.06 0.58 ±0.04 0.32 ± 0.02 0.129 ± 0.009 0.014 ± 0.003 2.00 0.17±0.02 0.14 ±0.01 0.083 ± 0.009 0.027 ± 0.003 0.005 ± 0.001 0.20±0.03 0.14 ±0.02 0.09 ± 0.01 0.035 ± 0.004 0.004 ± 0.001 2.45 0.005 ±0.003 0.009 ±0.003 0.006 ± 0.002 0.0017 ± 0.0006 0.011±0.005 0.011 ±0.004 0.005 ± 0.002 0.0025 ± 0.0009 College of Arts and Sciences, Vanderbilt University (U.S.A), Ministry of Education, Culture, Sports, Science, and Technology and the Japan Society for the Promotion of Science (Japan), Russian Academy of Science, Ministry of Atomic Energy of Russian Federation, Ministry of Industry, Science, and Technologies of Russian Federation (Russia), Bundesministerium fuer Bildung und Forschung, Deutscher Akademischer Auslandsdienst, and Alexander von Humboldt Stiftung (Germany), VR and the Wallenberg Foundation (Sweden), MIST and 64 TABLE XV: Kaon invariant yields in each event centrality normalized to one rapidity unit at mi
drapidity. The first line corresponds to positive kaons, and the second to negative kaons. pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92% 0.45 21±3 16± 2 10± 1 4.3 ± 0.5 0.5 ± 0.1 21±3 13± 2 7 ± 1 2.5 ± 0.4 0.4 ± 0.1 0.55 15±2 11± 1 6.6 ± 0.7 2.4 ± 0.3 0.20 ± 0.07 13±2 8 ± 1 4.8 ± 0.6 2.3 ± 0.3 0.3 ± 0.1 0.70 8.0±0.7 6.6 ± 0.5 4.3 ± 0.3 1.5 ± 0.1 0.18 ± 0.03 7.0±0.8 6.5 ± 0.6 3.1 ± 0.3 1.1 ± 0.1 0.14 ± 0.03 0.90 4.5±0.4 3.1 ± 0.2 1.9 ± 0.1 0.62 ± 0.06 0.06 ± 0.02 3.3±0.4 3.3 ± 0.3 1.6 ± 0.2 0.5 ± 0.06 0.09 ± 0.02 1.20 1.4±0.1 1.10 ± 0.08 0.68 ± 0.05 0.22 ± 0.02 0.012 ± 0.004 1.3±0.1 0.97 ± 0.08 0.50 ± 0.05 0.17 ± 0.02 0.015 ± 0.005 1.60 0.36±0.05 0.29 ± 0.03 0.17 ± 0.02 0.062 ± 0.007 0.008 ± 0.002 0.29±0.05 0.27 ± 0.03 0.20 ± 0.02 0.058 ± 0.008 0.004 ± 0.002 the Natural Sciences and Engineering Research Council (Canada), Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico and Funda¸c˜ao de Amparo `a Pesquisa do Estado de S˜ao Paulo (Brazil), Natural Science Foundation of China (People’s Republic of China), Centre National de la Recherche Scientifique, Commissariat `a l’Energie Atomique, Insti- ´ tut National de Physique Nucl´aire et de Physique des Particules, and Association pour la Recherche et le D´eveloppement des M´ethodes et Processus Industriels (France), Department of Atomic Energy and Department of Science and Technology (India), Israel Science Foundation (Israel), Korea Research Foundation and Center for High Energy Physics (Korea), the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union, and the US-Israel Binational Science Foundation. 65 TABLE XVI: (Anti)proton invariant yields in each event centrality normalized to one rapidity unit at midrapidity. The first line corresponds to protons, and the second to antiprotons. pT (GeV/c) 0-5% 5-15% 15-30% 30-60% 60-92% 0.55 8±1 4.9 ± 0.5 4.0 ± 0.4 1.6 ± 0.2 0.26 ± 0.06 4.2±0.8 2.8± 0.5 2.0± 0.3 0.8± 0.1 0.12± 0.05 0.70 5.4±0.4 4.5± 0.3 2.5± 0.2 1.06± 0.07 0.14± 0.02 4.4±0.5 2.9± 0.3 2.0± 0.2 0.80± 0.08 0.14± 0.03 0.90 3.9±0.3 3.1± 0.2 1.9± 0.1 0.71± 0.05 0.10± 0.02 2.8±0.3 2.1± 0.2 1.4± 0.1 0.58± 0.05 0.06± 0.01 1.20 1.9±0.1 1.37± 0.08 0.78± 0.04 0.26± 0.02 0.031± 0.005 1.3±0.1 0.96± 0.07 0.56± 0.04 0.21± 0.02 0.018± 0.004 1.60 0.60±0.06 0.44± 0.03 0.27± 0.02 0.087± 0.008 0.005± 0.002 0.49±0.06 0.34± 0.03 0.19± 0.02 0.062± 0.007 0.007± 0.002 2.00 0.20±0.03 0.15± 0.02 0.09± 0.01 0.025± 0.003 0.003± 0.001 0.15±0.03 0.07± 0.01 0.055± 0.009 0.019 ± 0.003 0.0005± 0.0005 2.45 0.06±0.01 0.040± 0.007 0.020 ± 0.004 0.006± 0.001 0.0010± 0.0006 0.04±0.01 0.028± 0.006 0.011± 0.003 0.005± 0.001 0.0020 ± 0.0008 2.95 0.015±0.005 0.007± 0.002 0.005± 0.002 0.0023± 0.0007 0.0006± 0.0004 0.013±0.005 0.008± 0.003 0.002± 0.001 0.0003± 0.0003 0.0005± 0.0003 3.55 0.003 ±0.002 0.0012 ± 0.0007 0.0014± 0.0006 0.0005± 0.0002 0.002±0.001 0.0011± 0.0007 0.0013± 0.0006 0.0002± 0.0002 66 [1] B. 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arXiv:0808.2041v2 [nucl-ex] 11 Apr 2009 Systematic Measurements of Identified Particle Spectra in pp, d+Au and Au+Au Collisions from STAR B. I. Abelev,9 M. M. Aggarwal,30 Z. Ahammed,46 B. D. Anderson,19 D. Arkhipkin,13 G. S. Averichev,12 Y. Bai,28 J. Balewski,23 O. Barannikova,9 L. S. Barnby,2 J. Baudot,17 S. Baumgart,51 D. R. Beavis,3 R. Bellwied,49 F. Benedosso,28 R. R. Betts,9 S. Bhardwaj,35 A. Bhasin,18 A. K. Bhati,30 H. Bichsel,48 J. Bielcik,11 J. Bielcikova,11 B. Biritz,6 L. C. Bland,3 M. Bombara,2 B. E. Bonner,36 M. Botje,28 J. Bouchet,19 E. Braidot,28 A. V. Brandin,26 Bruna,51 S. Bueltmann,3 T. P. Burton,2 M. Bystersky,11 X. Z. Cai,39 H. Caines,51 M. Calder´on de la Barca S´anchez,5 J. Callner,9 O. Catu,51 D. Cebra,5 R. Cendejas,6 M. C. Cervantes,41 Z. Chajecki,29 P. Chaloupka,11 S. Chattopadhyay,46 H. F. Chen,38 J. H. Chen,39 J. Y. Chen,50 J. Cheng,43 M. Cherney,10 A. Chikanian,51 K. E. Choi,34 W. Christie,3 S. U. Chung,3 R. F. Clarke,41 M. J. M. Codrington,41 J. P. Coffin,17 T. M. Cormier,49 M. R. Cosentino,37 J. G. Cramer,48 H. J. Crawford,4 D. Das,5 S. Dash,14 M. Daugherity,42 C. De Silva,49 T. G. Dedovich,12 M. DePhillips,3 A. A. Derevschikov,32 R. Derradi de Souza,7 L. Didenko,3 P. Djawotho,16 S. M. Dogra,18 X. Dong,22 J. L. Drachenberg,41 J. E. Draper,5 F. Du,51 J. C. Dunlop,3 M. R. Dutta Mazumdar,46 W. R. Edwards,22 L. G. Efimov,12 E. Elhalhuli,2 M. Elnimr,49 V. Emelianov,26 J. Engelage,4 G. Eppley,36 B. Erazmus,40 M. Estienne,17 L. Eun,31 P. Fachini,3 R. Fatemi,20 J. Fedorisin,12 A. Feng,50 P. Filip,13 E. Finch,51 V. Fine,3 Y. Fisyak,3 C. A. Gagliardi,41 L. Gaillard,2 D. R. Gangadharan,6 M. S. Ganti,46 E. Garcia-Solis,9 V. Ghazikhanian,6 P. Ghosh,46 Y. N. Gorbunov,10 A. Gordon,3 O. Grebenyuk,22 D. Grosnick,45 B. Grube,34 S. M. Guertin,6 K. S. F. F. Guimaraes,37 A. Gupta,18 N. Gupta,18 W. Guryn,3 B. Haag,5 T. J. Hallman,3 A. Hamed,41 J. W. Harris,51 W. He,16 M. Heinz,51 S. Heppelmann,31 B. Hippolyte,17 A. Hirsch,33 E. Hjort,22 A. M. Hoffman,23 G. W. Hoffmann,42 D. J. Hofman,9 R. S. Hollis,9 H. Z. Huang,6 T. J. Humanic,29 G. Igo,6 A. Iordanova,9 P. Jacobs,22 W. W. Jacobs,16 P. Jakl,11 F. Jin,39 P. G. Jones,2 J. Joseph,19 E. G. Judd,4 S. Kabana,40 K. Kajimoto,42 K. Kang,43 J. Kapitan,11 M. Kaplan,8 D. Keane,19 A. Kechechyan,12 D. Kettler,48 V. Yu. Khodyrev,32 J. Kiryluk,22 A. Kisiel,29 S. R. Klein,22 A. G. Knospe,51 A. Kocoloski,23 D. D. Koetke,45 M. Kopytine,19 L. Kotchenda,26 V. Kouchpil,11 P. Kravtsov,26 V. I. Kravtsov,32 K. Krueger,1 M. Krus,11 C. Kuhn,17 L. Kumar,30 P. Kurnadi,6 M. A. C. Lamont,3 J. M. Landgraf,3 S. LaPointe,49 J. Lauret,3 A. Lebedev,3 R. Lednicky,13 C-H. Lee,34 M. J. LeVine,3 C. Li,38 Y. Li,43 G. Lin,51 X. Lin,50 S. J. Lindenbaum,27 M. A. Lisa,29 F. Liu,50 H. Liu,5 J. Liu,36 L. Liu,50 T. Ljubicic,3 W. J. Llope,36 R. S. Longacre,3 W. A. Love,3 Y. Lu,38 T. Ludlam,3 D. Lynn,3 G. L. Ma,39 Y. G. Ma,39 D. P. Mahapatra,14 R. Majka,51 O. I. Mall,5 L. K. Mangotra,18 R. Manweiler,45 S. Margetis,19 C. Markert,42 H. S. Matis,22 Yu. A. Matulenko,32 T. S. McShane,10 A. Meschanin,32 J. Millane,23 M. L. Miller,23 N. G. Minaev,32 S. Mioduszewski,41 A. Mischke,28 J. Mitchell,36 B. Mohanty,46 L. Molnar,33 D. A. Morozov,32 M. G. Munhoz,37 B. K. Nandi,15 C. Nattrass,51 T. K. Nayak,46 J. M. Nelson,2 C. Nepali,19 P. K. Netrakanti,33 M. J. Ng,4 L. V. Nogach,32 S. B. Nurushev,32 G. Odyniec,22 A. Ogawa,3 H. Okada,3 V. Okorokov,26 D. Olson,22 M. Pachr,11 B. S. Page,16 S. K. Pal,46 Y. Pandit,19 Y. Panebratsev,12 T. Pawlak,47 T. Peitzmann,28 V. Perevoztchikov,3 C. Perkins,4 W. Peryt,47 S. C. Phatak,14 M. Planinic,52 J. Pluta,47 N. Poljak,52 A. M. Poskanzer,22 B. V. K. S. Potukuchi,18 D. Prindle,48 C. Pruneau,49 N. K. Pruthi,30 J. Putschke,51 R. Raniwala,35 S. Raniwala,35 R. L. Ray,42 R. Reed,5 A. Ridiger,26 H. G. Ritter,22 J. B. Roberts,36 O. V. Rogachevskiy,12 J. L. Romero,5 A. Rose,22 C. Roy,40 L. Ruan,3 M. J. Russcher,28 V. Rykov,19 R. Sahoo,40 I. Sakrejda,22 T. Sakuma,23 S. Salur,22 J. Sandweiss,51 M. Sarsour,41 J. Schambach,42 R. P. Scharenberg,33 N. Schmitz,24 J. Seger,10 I. Selyuzhenkov,16 P. Seyboth,24 A. Shabetai,17 E. Shahaliev,12 M. Shao,38 M. Sharma,49 S. S. Shi,50 X-H. Shi,39 E. P. Sichtermann,22 F. Simon,24 R. N. Singaraju,46 M. J. Skoby,33 N. Smirnov,51 R. Snellings,28 P. Sorensen,3 J. Sowinski,16 H. M. Spinka,1 B. Srivastava,33 A. Stadnik,12 T. D. S. Stanislaus,45 D. Staszak,6 M. Strikhanov,26 B. Stringfellow,33 A. A. P. Suaide,37 M. C. Suarez,9 N. L. Subba,19 M. Sumbera,11 X. M. Sun,22 Y. Sun,38 Z. Sun,21 B. Surrow,23 T. J. M. Symons,22 A. Szanto de Toledo,37 J. Takahashi,7 A. H. Tang,3 Z. Tang,38 T. Tarnowsky,33 D. Thein,42 J. H. Thomas,22 J. Tian,39 A. R. Timmins,2 S. Timoshenko,26 Tlusty,11 M. Tokarev,12 V. N. Tram,22 A. L. Trattner,4 S. Trentalange,6 R. E. Tribble,41 O. D. Tsai,6 J. Ulery,33 T. Ullrich,3 D. G. Underwood,1 G. Van Buren,3 M. van Leeuwen,28 A. M. Vander Molen,25 J. A. Vanfossen, Jr.,19 R. Varma,15 G. M. S. Vasconcelos,7 I. M. Vasilevski,13 A. N. Vasiliev,32 F. Videbaek,3 S. E. Vigdor,16 Y. P. Viyogi,14 S. Vokal,12 S. A. Voloshin,49 M. Wada,42 W. T. Waggoner,10 F. Wang,33 G. Wang,6 J. S. Wang,21 Q. Wang,33 X. Wang,43 X. L. Wang,38 Y. Wang,43 J. C. Webb,45 G. D. Westfall,25 C. Whitten Jr.,6 H. Wieman,22 S. W. Wissink,16 R. Witt,44 Y. Wu,50 N. Xu,22 Q. H. Xu,22 Y. Xu,38 Z. Xu,3 P. Yepes,36 I-K. Yoo,34 Q. Yue,43 M. Zawisza,47 H. Zbroszczyk,47 W. Zhan,21 H. Zhang,3 S. Zhang,39 W. M. Zhang,19 Y. Zhang,38 Z. P. Zhang,38 Y. Zhao,38 C. Zhong,39 J. Zhou,36 R. Zoulkarneev,13 Y. Zoulkarneeva,13 and J. X. Zuo39 2 (STAR Collaboration) 1Argonne National Laboratory, Argonne, Illinois 60439, USA 2University of Birmingham, Birmingham, United Kingdom 3Brookhaven National Laboratory, Upton, New York 11973, USA 4University of California, Berkeley, California 94720, USA 5University of California, Davis, California 95616, USA 6University of California, Los Angeles, California 90095, USA 7Universidade Estadual de Campinas, Sao Paulo, Brazil 8Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 9University of Illinois at Chicago, Chicago, Illinois 60607, USA 10Creighton University, Omaha, Nebraska 68178, USA 11Nuclear Physics Institute AS CR, 250 68 Reˇz/Prague, Czech Republic ˇ 12Laboratory for High Energy (JINR), Dubna, Russia 13Particle Physics Laboratory (JINR), Dubna, Russia 14Institute of Physics, Bhubaneswar 751005, India 15Indian Institute of Technology, Mumbai, India 16Indiana University, Bloomington, Indiana 47408, USA 17Institut de Recherches Subatomiques, Strasbourg, France 18University of Jammu, Jammu 180001, India 19Kent State University, Kent, Ohio 44242, USA 20University of Kentucky, Lexington, Kentucky, 40506-0055, USA 21Institute of Modern Physics, Lanzhou, China 22Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 23Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA 24Max-Planck-Institut f¨ur Physik, Munich, Germany 25Michigan State University, East Lansing, Michigan 48824, USA 26Moscow Engineering Physics Institute, Moscow Russia 27City College of New York, New York City, New York 10031, USA 28NIKHEF and Utrecht University, Amsterdam, The Netherlands 29Ohio State University, Columbus, Ohio 43210, USA 30Panjab University, Chandigarh 160014, India 31Pennsylvania State University, University Park, Pennsylvania 16802, USA 32Institute of High Energy Physics, Protvino, Russia 33Purdue University, West Lafayette, Indiana 47907, USA 34Pusan National University, Pusan, Republic of Korea 35University of Rajasthan, Jaipur 302004, India 36Rice University, Houston, Texas 77251, USA 37Universidade de Sao Paulo, Sao Paulo, Brazil 38University of Science & Technology of China, Hefei 230026, China 39Shanghai Institute of Applied Physics, Shanghai 201800, China 40SUBATECH, Nantes, France 41Texas A&M University, College Station, Texas 77843, USA 42University of Texas, Austin, Texas 78712, USA 43Tsinghua University, Beijing 100084, China 44United States Naval Academy, Annapolis, MD 21402, USA 45Valparaiso University, Valparaiso, Indiana 46383, USA 46Variable Energy Cyclotron Centre, Kolkata 700064, India 47Warsaw University of Technology, Warsaw, Poland 48U
niversity of Washington, Seattle, Washington 98195, USA 49Wayne State University, Detroit, Michigan 48201, USA 50Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China 51Yale University, New Haven, Connecticut 06520, USA 52University of Zagreb, Zagreb, HR-10002, Croatia (Dated: April 13, 2009, version 30h) Identified charged particle spectra of π ±, K±, p and p at mid-rapidity (|y| < 0.1) measured by the dE/dx method in the STAR-TPC are reported for pp and d+Au collisions at √sNN = 200 GeV and for Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. Average transverse momenta, total particle production, particle yield ratios, strangeness and baryon production rates are investigated as a function of the collision system and centrality. The transverse momentum spectra are found to be flatter for heavy particles than for light particles in all collision systems; the effect is more prominent for more central collisions. The extracted average transverse momentum of each particle species follows a trend determined by the total charged particle multiplicity density. The Bjorken energy density estimate is at least several GeV/fm3 for a formation time less than 1 fm/c. A significantly 3 larger net-baryon density and a stronger increase of the net-baryon density with centrality are found in Au+Au collisions at 62.4 GeV than at the two higher energies. Antibaryon production relative to total particle multiplicity is found to be constant over centrality, but increases with the collision energy. Strangeness production relative to total particle multiplicity is similar at the three measured RHIC energies. Relative strangeness production increases quickly with centrality in peripheral Au+Au collisions, to a value about 50% above the pp value, and remains rather constant in more central collisions. Bulk freeze-out properties are extracted from thermal equilibrium model and hydrodynamics-motivated blast-wave model fits to the data. Resonance decays are found to have little effect on the extracted kinetic freeze-out parameters due to the transverse momentum range of our measurements. The extracted chemical freeze-out temperature is constant, independent of collision system or centrality; its value is close to the predicted phase-transition temperature, suggesting that chemical freeze-out happens in the vicinity of hadronization and the chemical freezeout temperature is universal despite the vastly different initial conditions in the collision systems. The extracted kinetic freeze-out temperature, while similar to the chemical freeze-out temperature in pp, d+Au, and peripheral Au+Au collisions, drops significantly with centrality in Au+Au collisions, whereas the extracted transverse radial flow velocity increases rapidly with centrality. There appears to be a prolonged period of particle elastic scatterings from chemical to kinetic freeze-out in central Au+Au collisions. The bulk properties extracted at chemical and kinetic freeze-out are observed to evolve smoothly over the measured energy range, collision systems, and collision centralities. PACS numbers: 25.75.Nq, 25.75.-q, 25.75.Dw, 24.85.+p Contents I. Introduction 3 II. Detector Setup and Data Samples 4 A. Detector Setup and Track Reconstruction 4 B. Event Selection and Track Quality Cuts 5 C. Centrality Measures 5 1. Centrality Definitions 5 2. Corrected Charged Particle Multiplicity 6 3. Glauber Model Calculations 8 III. Particle Identification by dE/dx 8 IV. Corrections and Backgrounds 10 A. Monte-Carlo Embedding Technique 10 B. Energy Loss Correction 12 C. Vertex Inefficiency and Fake Vertex 12 D. Tracking Efficiency 14 E. Proton Background Correction 15 F. Pion Background Correction 16 V. Systematic Uncertainties 17 A. On Transverse Momentum Spectra 17 B. On dN/dy 18 C. On Particle Ratios and hp⊥i 19 D. On Chemical Freeze-Out Parameters 19 E. On Kinetic Freeze-Out Parameters 20 VI. Results and Discussions 20 A. Transverse Momentum Spectra 22 B. Average Transverse Momenta 22 C. Total Particle Production 24 D. Bjorken Energy Density Estimate 28 E. Antiparticle-to-Particle Ratios 28 F. Baryon Production and Transport 29 G. Strangeness Production 31 VII. Freeze-Out Properties 34 A. Chemical Freeze-out Properties 34 B. Kinetic Freeze-out Properties 35 C. Excitation Functions 38 VIII. Summary 39 A. The Glauber Model 40 1. The Optical Glauber Model 42 2. The Monte-Carlo Glauber Model 42 3. Uncertainties 43 B. Resonance Effect on Blast-Wave Fit 43 1. Effect of Resonance Decays 43 2. Regeneration of Short-Lived Resonances 44 C. Invariant p⊥ Spectra Data Tables 46 Acknowledgments 46 References 46 I. INTRODUCTION Quantum Chromodynamics (QCD) predicts a phase transition at sufficiently high energy density from normal hadronic matter to a deconfined state of quarks and gluons, the Quark-Gluon Plasma (QGP) [1, 2, 3]. Such a phase transition may be achievable in ultra-relativistic heavy-ion collisions. Many QGP signatures have been proposed which include rare probes (e.g. direct photon and dilepton production, jet modification) as well as bulk probes (e.g. enhanced strangeness and antibaryon production, strong collective flow) [4]. While rare probes are more robust, they are relatively difficult to measure. On the other hand, signals of QGP that are related to the bulk of the collision are most probably disguised or 4 diluted by other processes like final state interaction. Simultaneous observations and systematic studies of multiple QGP signals in the bulk would, however, serve as strong evidence for QGP formation. These bulk properties include strangeness and baryon production rates and collective radial flow. These bulk observables can be studied via transverse momentum (p⊥) spectra of identified particles in heavy-ion collisions in comparison to nucleon-nucleon and nucleon-nucleus reference systems. This paper reports results on identified charged pions (π ±), charged kaons (K±), protons (p) and antiprotons (p) at low p⊥ at mid-rapidity [5]. The results are measured by the STAR experiment in pp and d+Au collisions at a nucleon-nucleon center-of-mass energy of √sNN = 200 GeV and in Au+Au collisions at √sNN = 62.4 GeV, 130 GeV and 200 GeV. The particles are identified by their specific ionization energy loss in the detector material – the dE/dx method. Transverse momentum spectra, average transverse momenta, total particle production, particle yield ratios, antibaryon and strangeness production rates are presented as a function of the event multiplicity for pp, d+Au and Au+Au collisions. The paper also presents freeze-out parameters extracted from thermal equilibrium model and hydrodynamics-motivated blast-wave model fits to the data. The paper summarizes low p⊥ results from STAR with dE/dx particle identification, including the previously published data [6]. The paper is organized as follows: Section II describes the STAR detector, followed by descriptions of event selection, track quality cuts, and centrality definitions. Section III presents the dE/dx method for particle identification at low p⊥. Section IV discusses the backgrounds and corrections applied at the event and track levels. Section V summarizes the systematic uncertainties of the measurements. Section VI presents results on identified particle p⊥ spectra, average hp⊥i, particle yields and ratios. Section VII discusses the systematics of bulk properties extracted from a statistical model and the hydrodynamics-motivated blast-wave model. Section VIII summarizes the paper. Appendix A describes the details of the Glauber model calculations used in this paper. Appendix B discusses in detail the effect of resonance decays on the extracted kinetic freeze-out parameters. Appendix C lists tabulated data of transverse momentum spectra. II. DETECTOR SETUP AND DATA SAMPLES A. Detector Setup and Track Reconstruction Details of the STAR experiment can be found in Ref. [7]. The main detector of the STAR experiment is the Time Projection Chamber (TPC) [8, 9]. The cylindrical axis of the TPC is aligned to the beam direction and is referred to as the z-direction. The TPC provides the full azimuthal coverage (0 ≤ φ
≤ 2π) and a pseudorapidity coverage of −1.8 < η < 1.8. Trigger selection of the experiment is obtained from the Zero Degree Calorimeters (ZDC) [10], the BeamBeam Counters (BBC) [11] and the Central Trigger Barrel (CTB) [12]. The ZDC’s are located at ±18 m along the z-direction from the TPC center and measure neutral energy. The scintillator-based BBC’s provide the principal relative luminosity measurement in pp data taking. The scintillator CTB surrounds the TPC and measures the charged particle multiplicity within |η| < 1. The coincidence of the signals from the ZDC’s and the BBC’s selects minimum bias (MB) events in pp and d+Au collisions. Our minimum bias pp events correspond to nonsingly diffractive (NSD) pp collisions, whose cross-section is measured to be 30.0 ± 3.5 mb [13]. The combination of the CTB and ZDC information provides the minimum bias trigger for Au+Au collisions. In addition, a central trigger is constructed by imposing an upper cut on the ZDCs’ signal with a modest minimum CTB cut to exclude contamination from very peripheral events; the central trigger corresponds to approximately 12% of the total cross-section. The trigger efficiencies are found to be approximately 86% and 95% in pp and d+Au, respectively, and essentially 100% in Au+Au collisions. The TPC is filled with P-10 gas (90% Argon and 10% Methane). Charged particles interact with the gas atoms while traversing the TPC gas volume and ionize the electrons out of the gas atoms. Drift electric field is provided along the z-direction between the TPC central membrane and both ends of the TPC by a negative high voltage on the central membrane. Ionization electrons drift in the electric field towards the TPC ends. The TPC ends are divided into twelve equal-size bisectors, and are equipped with read-out pads and front-end electronics. Multi-Wire Proportional Chambers (MWPC) are installed close to the end pads inside the TPC. The drifting electrons avalanche in the high fields at the MWPC anode wires. The positive ions created in the avalanche induce a temporary image charge on the pads measured by a preamplifier/shaper/waveform digitizer system [9, 14]. The original track positions (hits) are formed from the signals on each padrow (a row of read-out pads) by the hit reconstruction algorithm. Hits can be reconstructed to a small fraction of a pad width because the induced charge from an avalanche is shared over several adjacent pads. The TPC is located inside a magnet which provides a magnetic field along the z-direction for particle momentum measurements. Data are taken at a maximum magnetic field of 0.5 Tesla. Inhomogeneities are on the level of 5 × 10−3 Tesla and are incorporated in track reconstruction [15]. The direction of the magnetic field can be reversed to study systematic effects, which are found to be negligible for the bulk particles presented in this paper. Track reconstruction starts from the outermost hits in the TPC, projecting inward assuming an initial primary vertex position at the center of the TPC. Hits on the 5 padrows are searched about the projected positions, and track segments are formed. Particle track momentum is estimated from the curvature of the track segments and the magnetic field strength. The momentum information is in turn used to refine further track projections. Track segments can be connected over short gaps from missed padrow signals. Tracks are formed from track segments and are allowed to cross the TPC sector boundaries. The reconstructed tracks are called global tracks. The primary interaction vertex is fit from the global tracks with at least 10 hits. The distance of closest approach (dca) to the fit primary vertex is calculated for each global track. Iterations are made such that global tracks with dca > 3 cm are excluded from subsequent primary vertex fitting. Tracks with dca < 3 cm (from the final fit primary vertex position) and at least 10 hits are called primary tracks. The primary tracks are refit including the primary vertex to improve particle track momentum determination. The reconstructed transverse momentum resolution is measured to be σδp⊥ = 0.01+p⊥/(200 GeV/c) [16]. The effect of the momentum resolution is negligible on the measured low p⊥ particle spectra reported here, and is thus not corrected for. Only primary tracks are used in this analysis. B. Event Selection and Track Quality Cuts Data sets used in this paper are from pp collisions at 200 GeV from Run II, d+Au collisions at 200 GeV from Run III, and Au+Au collisions at 62.4 GeV from Run IV, at 130 GeV from Run I, and at 200 GeV from Run II. The pp and Au+Au data at 200 GeV from Run II have been published in Ref. [17], and the Au+Au data for K±, p and p at 130 GeV from Run I have been published in Refs. [18, 19, 20]. These data are incorporated in this paper to provide a systematic overview. The pion spectra from the 130 GeV Au+Au data are analyzed in this work. The data sets are summarized in Table I. The longitudinal, z position of the interaction point is determined on-line by the measured signal time difference in the two ZDC’s. A cut of the order of 50 cm on the z position of the interaction point from the TPC center is applied on-line for all data sets (except pp) in order to maximize the amount of useful data for physics analysis, since events with primary vertex far away from the TPC center have a significantly non-uniform acceptance. In off-line data analyses further cuts are applied on the z position of the reconstructed primary vertex, zvtx, to ensure nearly uniform detector acceptance and avoid multiplicity biases near the edges of the on-line cuts. These off-line cuts are listed in Table I. In addition, the x and y position of the primary vertex are required to be within ±3.5 cm of the beam since the beam pipe diameter is 3 inches. The use of primary tracks significantly reduces contributions from background processes and pileup events in pp data. Tracks can have a maximum of 45 hits. In the analysis at least 25 hits are required for each track to avoid track splitting effects. Singly charged particles must have a minimum p⊥ of 0.15 GeV/c to exit the TPC in the 0.5 Tesla magnetic field. In this analysis tracks are required to have p⊥ > 0.2 GeV/c. For the identified particle results in this paper, the rapidity region is restricted within |y| < 0.1 (i.e. mid-rapidity). The full 2π azimuthal coverage of the TPC is utilized. C. Centrality Measures 1. Centrality Definitions In Au+Au collisions, the measured (uncorrected) charged particle multiplicity density in the TPC within |η| < 0.5, dNraw ch /dη, is used for centrality selection. The primary tracks to be counted in the charged particle multiplicity are required to have at least 10 fit points (good primary tracks). The multiplicity distributions in Au+Au collisions at 62.4 GeV and 200 GeV are shown in Fig. 1 . Nine centrality bins are chosen, the same as in Ref. [17]; they correspond to the fraction of the measured total cross section from central to peripheral collisions of 0-5%, 5-10%, 10-20%, 20-30%, 30-40%, 40-50%, 50-60%, 60-70%, and 70-80%. The 80-100% centrality is not used in our analysis because of its significant trigger bias due to vertex inefficiency at low multiplicities and the contamination from electromagnetic interactions. (|η|<0.5) raw Nch 0 100 200 300 400 500 600 700 800 raw ch /dN evt ) dN evt (1/N -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 200 GeV (scaled ×5) 62.4 GeV FIG. 1: Uncorrected charged particle multiplicity distribution measured in the TPC in |η| < 0.5 for Au+Au collisions at 62.4 GeV and 200 GeV. The shaded regions indicate the centrality bins used in the analysis. The 200 GeV data are scaled by a factor 5 for clarity. In d+Au collisions centralities are selected based on the charged particle multiplicity measured in the East (Au-direction) Forward Time Projection Chamber (EFTPC) [21] within the pseudo-rapidity range of −3.8 < η < −2.8. To be counted, tracks are required to have at least 6 hits out of 11 maximum and a dca < 3 cm. Additionally the transverse momentum is re
quired not 6 TABLE I: Summary of data sets, primary vertex cuts, and the numbers of good events (after cuts) used in the analysis. Run Data set √sNN (GeV) Year Trigger Max. |zvtx| No. of events I Au+Au 130 2000 min. bias 25 cm 2.0 million I Au+Au 130 2000 central 25 cm 2.0 million II Au+Au 200 2001 min. bias 30 cm 2.0 million II pp 200 2002 min. bias 30 cm 3.9 million III d+Au 200 2003 min. bias 50 cm 8.8 million IV Au+Au 62.4 2004 min. bias 30 cm 6.4 million (-3.8<η<-2.8) raw Nch 0 10 20 30 40 50 60 70 80 90 100 raw ch /dN evt ) dN evt (1//N -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 (a) d+Au 200 GeV (|η|<0.5) raw Nch 0 10 20 30 40 50 60 raw ch /dN evt ) dN evt (1/N -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 Min. bias 0-20% 20-40% 40-100% (b) FIG. 2: (a) Uncorrected charged particle multiplicity distribution measured in the E-FTPC (Au-direction) within −3.8 < η < −2.8 in d+Au collisions at 200 GeV. The shaded regions indicate the centrality bins used in the analysis. (b) The TPC mid-rapidity multiplicity distributions (|η| < 0.5) for the corresponding E-FTPC selected centrality bins. to exceed 3 GeV/c because of the reduced momentum resolution and a significant background contamination at high p⊥ [21]. Figure 2(a) shows the measured (uncorrected) E-FTPC charged particle multiplicity. Three centrality classes are defined, as indicated by the shaded regions, representing 40-100%, 20-40% and 0-20% of the measured total cross section [22]. The mid-rapidity multiplicities measured in the TPC for the selected centrality bins are shown in Fig. 2(b). Positive correlation between the TPC multiplicity and the E-FTPC multiplicity is ev- (|η|<0.5) raw Nch 0 5 10 15 20 25 30 35 raw ch /dN evt ) dN evt (1/N -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 1 pp 200 GeV FIG. 3: Uncorrected charged particle multiplicity distribution measured in the TPC within |η| < 0.5 in pp collisions at 200 GeV. ident, although the correlation is not very strong due to the low multiplicities of d+Au collisions. The reason to use the FTPC multiplicity instead of the TPC mid-rapidity multiplicity for centrality selection is to avoid auto-correlation between centrality and the measurements of charged particles which are made within |y| < 0.1 in the TPC. The auto-correlation is not significant for Au+Au collisions due to their large multiplicities. The auto-correlation is significant for pp, and since the FTPC was not ready for data taking in the pp run only minimum bias data are presented for pp. For completeness, the uncorrected multiplicity distribution in minimum bias pp collisions is shown in Fig. 3. Table II summarizes the centralities for pp, d+Au, and Au+Au collisions. 2. Corrected Charged Particle Multiplicity The results in this paper are presented as a function of centrality. As an experimental measure of centrality, the corrected charged particle rapidity density (dNch/dy) is used. It is obtained from the identified charged particle spectra (π ±, K±, p and p) as the sum of the individual rapidity densities. The identified charged particle spectra are either from prior STAR publications [17, 18, 19, 20] or obtained by this work [5]. The charged particle rapidity 7 TABLE II: Summary of centralities in pp and d+Au collisions at 200 GeV and in Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. Our minimum bias pp data correspond to NSD events with total cross-section of 30.0 ± 3.5 mb. [13]. The centrality percentages in other systems are in terms of the measured total cross-sections. The uncorrected charged particle multiplicity dNraw ch /dη for d+Au is measured in the E-FTPC within −3.8 < η < −2.8, and for all other systems in the TPC within |η| < 0.5. The corrected charged particle multiplicity dNch/dη (and the corrected negatively charged particle multiplicity dNh− /dη for the 130 GeV Au+Au data) are from the TPC within |η| < 0.5. The multiplicity rapidity density dN/dy are from the rapidity slice of |y| < 0.1. The 200 GeV pp and Au+Au data are from Ref. [17]; the 130 GeV data are from Ref. [23] and this work; and the 200 GeV d+Au and 62.4 GeV Au+Au data are from this work. The Monte-Carlo Glauber model is used in the calculation of the impact parameter (b), the number of participant nucleons (Npart), the number of binary nucleon-nucleon collisions (Ncoll), and the overlap area between the colliding nuclei in the transverse plane (S⊥). The nucleon-nucleon cross-sections used in the calculations are 36±2 mb, 39±2 mb, 41±2 mb for 62.4 GeV, 130 GeV, and 200 GeV, respectively. The Glauber model results for d+Au are from Ref. [24], and for all other systems from this work. The quoted errors are total statistical and systematic uncertainties added in quadrature. Centrality dNraw ch /dη dNraw ch /dη dNch/dη dNh− /dη dNch/dy b (fm) b (fm) Npart Ncoll S⊥ (fm2 ) range mean range mean pp 200 GeV pp min. bias – 2.4 2.98 ± 0.34 3.40 ± 0.23 – – 2 1 4.1 ± 0.7 d+Au 200 GeV d+Au [24] min. bias – 10.2 10.2 ± 0.68 11.3 ± 0.7 8.31 ± 0.37 7.51 ± 0.39 40-100% 0-9 6.2 6.23 ± 0.34 6.98 ± 0.44 5.14 ± 0.44 4.21 ± 0.49 20-40% 10-16 12.6 14.1 ± 1.0 14.9 ± 0.9 11.2 ± 1.1 10.6 ± 0.8 0-20% ≥17 17.6 19.9 ± 1.6 20.9 ± 1.3 15.7 ± 1.2 15.1 ± 1.3 Au+Au 200 GeV Au+Au (σpp = 41 mb) 70-80% 14-29 22.5 22 ± 2 26.5 ± 1.8 12.3-13.2 12.8 ± 0.3 15.7 ± 2.6 15.0 ± 3.2 17.8 ± 2.2 60-70% 30-55 43.1 45 ± 3 52.1 ± 3.5 11.4-12.3 11.9 ± 0.3 28.8 ± 3.7 32.4 ± 5.5 27.2 ± 2.5 50-60% 56-93 74.8 78 ± 6 90.2 ± 6.0 10.5-11.4 11.0 ± 0.3 49.3 ± 4.7 66.8 ± 9.0 38.8 ± 2.7 40-50% 94-145 120 126 ± 9 146 ± 10 9.33-10.5 9.90 ± 0.23 78.3 ± 5.3 127 ± 13 52.1 ± 2.7 30-40% 146-216 181 195 ± 14 222 ± 15 8.10-9.33 8.73 ± 0.19 117.1 ± 5.2 221 ± 17 67.5 ± 2.9 20-30% 217-311 264 287 ± 20 337 ± 23 6.61-8.10 7.37 ± 0.16 167.6 ± 5.4 365 ± 24 86.1 ± 3.1 10-20% 312-430 370 421 ± 30 484 ± 33 4.66-6.61 5.70 ± 0.14 234.3 ± 4.6 577 ± 36 109.8 ± 3.4 5-10% 431-509 470 558 ± 40 648 ± 44 3.31-4.66 4.03 ± 0.13 298.6 ± 4.1 805 ± 50 133.0 ± 3.5 0-5% ≥510 559 691 ± 49 811 ± 56 0 -3.31 2.21 ± 0.07 350.6 ± 2.4 1012 ± 59 153.9 ± 4.3 Au+Au 130 GeV Au+Au (σpp = 39 mb) 58-85% 11-57 30.8 17.9 ± 1.3 39.5 ± 4.0 11.1-13.4 12.3 ± 0.4 22.6 ± 5.0 24.4 ± 7.0 21.9 ± 3.6 45-58% 57-105 80.3 47.3 ± 3.3 105 ± 8 9.77-11.1 10.5 ± 0.3 61.0 ± 7.8 88 ± 16 43.4 ± 3.8 34-45% 105-163 133 78.9 ± 5.5 177 ± 11 8.50-9.77 9.15 ± 0.28 100.9 ± 8.4 175 ± 22 60.2 ± 3.7 26-34% 163-217 190 115 ± 8 257 ± 18 7.43-8.50 7.99 ± 0.25 141.9 ± 8.4 280 ± 26 75.6 ± 3.9 18-26% 217-286 251 154 ± 11 348 ± 24 6.19-7.43 6.82 ± 0.21 187.7 ± 7.5 411 ± 31 91.9 ± 3.8 11-18% 286-368 327 196 ± 14 460 ± 34 4.83-6.19 5.55 ± 0.18 237.8 ± 6.8 568 ± 39 109.7 ± 3.7 6-11% 368-417 392 236 ± 17 562 ± 35 3.58-4.83 4.23 ± 0.16 289.0 ± 5.4 739 ± 49 127.8 ± 3.7 0-6% ≥417 462 290 ± 20 695 ± 45 0 -3.58 2.39 ± 0.09 344.3 ± 3.1 945 ± 58 149.5 ± 4.3 Au+Au 62.4 GeV Au+Au (σpp = 36 mb) 70-80% 9-19 12.4 13.9 ± 1.1 17.7 ± 1.3 12.3-13.1 12.7 ± 0.3 15.3 ± 2.4 14.1 ± 2.8 16.1 ± 2.0 60-70% 20-37 26.8 29.1 ± 2.2 35.8 ± 2.8 11.4-12.3 11.8 ± 0.3 27.8 ± 3.7 30.0 ± 5.2 24.8 ± 2.4 50-60% 38-64 49.1 53.1 ± 4.2 65.0 ± 5.0 10.4-11.4 10.9 ± 0.2 47.9 ± 4.7 61.2 ± 8.2 35.8 ± 2.6 40-50% 65-101 81.0 87.2 ± 7.1 107 ± 8 9.27-10.4 9.83 ± 0.23 76.3 ± 5.2 115 ± 12 48.7 ± 2.7 30-40% 102-153 125.2 135 ± 11 166 ± 11 8.05-9.27 8.67 ± 0.19 114.3 ± 5.1 199 ± 16 63.6 ± 2.8 20-30% 154-221 184.8 202 ± 17 249 ± 16 6.56-8.05 7.32 ± 0.17 164.1 ± 5.4 325 ± 23 81.6 ± 3.1 10-20% 222-312 263.6 292 ± 25 359 ± 24 4.63-6.56 5.67 ± 0.14 229.8 ± 4.6 511 ± 34 104.6 ± 3.3 5-10% 313-372 340.5 385 ± 33 476 ± 30 3.29-4.63 4.00 ± 0.13 293.9 ± 4.2 710 ± 47 127.2 ± 3.6 0-5% ≥373 411.8 472 ± 41 582 ± 38 0 -3.29 2.20 ± 0.07 346.5 ± 2.8 891 ± 57 147.5 ± 4.3 densities are listed in Table II for various systems and centralities. The systematic uncertainties on dNch/dy are discussed in Section V B. Another commonly used centrality measure is the charged particle pseudo-rapidity density, either uncorrected (dNraw ch /dη) or cor
rected (dNch/dη) for detector losses and tracking efficiency. These quantities are also listed in Table II for reference. The correction is done using reconstruction efficiency of pions obtained from embedding Monte Carlo (see Section IV D). This is because the efficiencies at high p⊥ are the same for different particle species and at low p⊥ charged particles are dominated by pions. The pseudorapidity multiplicity density data for 130 GeV are from Ref. [25], for pp and Au+Au at 200 GeV from Ref. [17], and for d+Au at 200 GeV and Au+Au at 62.4 GeV from this work. 8 3. Glauber Model Calculations While the charged hadron multiplicity is a viable experimental way to characterize centrality, it is sometimes desirable to use other variables directly connected to the collision geometry. Those variables include the number of participant nucleons (Npart), the number of nucleonnucleon binary collisions (Ncoll), and the ratio of the charged pion rapidity density to the transverse overlap area of the colliding nuclei ( dNπ/dy S⊥ ). Many models have studied particle production mechanisms based on these centrality variables. For example, the two-component model [26, 27, 28], characterizing particle production by a linear combination of Npart and Ncoll, can describe the multiplicity density well, allowing the extraction of the relative fractions of the two components. The gluon saturation model [29, 30, 31, 32, 33] predicts a suppressed multiplicity in heavy-ion collisions relative to the Ncollscaled pp collision multiplicity, with an increased hp⊥i for the produced particles. The relevant, and perhaps only scale in such a gluon-saturation picture is dNπ/dy S⊥ [29]. Unfortunately, Npart, Ncoll and the transverse overlap area S⊥ cannot be measured directly from collider experiments, so they have to be extracted from the measured multiplicity distributions via models, such as the Glauber model [34, 35]. The essential ingredient is to match the calculated cross-section versus impact parameter (dσ/db) to the measured cross-section versus charged multiplicity (dσ/dNch), exploiting the fact that the average multiplicity should monotonically increase with decreasing impact parameter, b. The matching relates the measured Nch to b (and thus Npart and Ncoll). Two different schemes are used to implement the Glauber model, the optical calculation and the MonteCarlo (MC) calculation. The details of the optical and MC Glauber calculations are described in Appendix A. In this work the MC Glauber calculation is used except when otherwise noted. The Npart, Ncoll, and S⊥ for Au+Au collisions from the MC Glauber model calculation are listed in Table II. For pp collisions the overlap area S⊥ is simply taken as the pp cross-section, σpp. For d+Au collisions the Npart and Ncoll are calculated using the realistic wavefunction for the deuteron in Ref. [24]. Figure 4(a) shows the ratio of S⊥ to (Npart/2)2/3 as a function of (Npart/2)2/3 . The overlap area S⊥ scales with (Npart/2)2/3 to a good approximation, and the scaling factor is the proton-proton cross-section used in the Glauber calculation, σpp = 36 mb and 41 mb for 62.4 GeV and 200 GeV, respectively. Figure 4(b) shows the ratio of the charged pion multiplicity to the transverse overlap area dNπ/dy S⊥ as a function of Ncoll Npart/2 , the average number of binary collisions per participant nucleon pair. As seen from the figure, the two quantities have monotonical correspondence and have little dependence on beam energy (i.e. on the value of σpp). 2/3 /2) part (N 0 5 10 15 20 25 30 35 ] 2 [fm 2/3 /2) part / (N S 3 3.5 4 4.5 5 5.5 6 Au+Au 62.4 GeV Au+Au 200 GeV pp MB 200 GeV (a) /2) part Ncoll/(N 0 1 2 3 4 5 6 7 ] -2 [fm /dy)/S π (dN 0 1 2 3 4 5 Au+Au 62.4 GeV Au+Au 200 GeV pp MB 200 GeV (b) FIG. 4: (a) The ratio of the transverse overlap area S⊥ to (Npart/2)2/3 versus (Npart/2)2/3 . (b) The ratio of the charged pion multiplicity to the transverse overlap area dNπ /dy S⊥ versus Ncoll/Npart. Errors shown are total errors, dominated by systematic uncertainties. The systematic uncertainties are correlated between Npart, Ncoll, and S⊥, and are largely canceled in the plotted ratio quantities. III. PARTICLE IDENTIFICATION BY dE/dx Charged particles, while traversing the TPC gas volume, interact with the gas atoms and lose energy by ionizing electrons out of the gas atoms. This specific ionization energy loss, called the dE/dx, is a function of the particle momentum magnitude. This property is used for particle identification. This paper focuses on particle identification in the low p⊥ region. This section describes the low p⊥ dE/dx particle identification method in detail. Extension of particle identification to high p⊥ is possible by the Time of Flight (TOF) patch [36, 37] and by using the relativistic rise of the specific ionization energy loss (rdE/dx) [16]. The details of the TOF and rdE/dx methods are out of the scope of this paper. The electron ionization process has large fluctuations; the measured dE/dx sample for a given track length follows the Landau distribution. The Landau tail results in a large fluctuation in the average dE/dx. To reduce fluctuation, a truncated mean, hdE/dxi, is used to character- 9 ize the ionization energy loss of charged particles. In this analysis, the truncated mean hdE/dxi is calculated from the lowest 70% of the measured dE/dx values of the hits for each track. The resolution of the obtained hdE/dxi depends on the track length and particle momentum. For a minimum ionizing pion at momentum p = 0.5 GeV/c with long track length (45 hits), the resolution is measured to be 8-9% in central Au+Au collisions. The resolution is better in pp, d+Au, and peripheral Au+Au collisions due to less cluster overlapping. p [GeV/c] 0.2 0.4 0.6 0.8 1 1.2 [keV/cm] 10 π e K p (a) p [GeV/c] 0.2 0.4 0.6 0.8 1 1.2 K z -2 -1.5 -1 -0.5 0 0.5 1 1.5 π e K p (b) FIG. 5: (color online) (a) Truncated hdE/dxi of specific ionization energy loss of π −, e−, K−, p as a function of p⊥ for particles in |η| < 0.1 measured in 200 GeV minimum bias pp collisions by the STAR-TPC. The Gaussian centroids for π −, e −, K− and p fit to the kaon zK distributions are shown with circles. (b) The zK variable for kaon versus p⊥ in 200 GeV minimum bias pp collisions. Particles are restricted in |yK| < 0.1 where the kaon mass is used in the rapidity calculation. In this narrow rapidity (or pseudo-rapidity) slice, p⊥ is approximately equal to pmag. The ionization energy loss by charged particles in material is given by the Bethe-Bloch formula [38] and for thin material by the more precise Bichsel formula [39]. At low momentum, ionization energy loss is approximately inversely proportional to the particle velocity squared. With the measured particle momentum and hdE/dxi, the particle type can be determined by comparing the measurements against the Bethe-Bloch expectation. Figure 5(a) shows the measured hdE/dxi versus momentum magnitude for particles in |η| < 0.1. Various bands, corresponding to different mass particles, are clearly separated at low p⊥. At modest p⊥, the bands start to overlap: e ± and K± merge at ∼ 0.5 GeV/c, K± and π ± merge at ∼ 0.75 GeV/c, and p (p) and π ± merge at ∼ 1.2 GeV/c. However, particles can still be statistically identified by a fitting procedure to deconvolute the overlapped distribution into several components. The separation of the dE/dx bands depends on the pseudorapidity region and decreases toward higher rapidities. To obtain maximal separation we only concentrate on the mid-rapidity region of |y| < 0.1. Since the hdE/dxi distribution for a fixed particle type is not Gaussian [40], a new variable is useful in order to have a proper deconvolution into Gaussians. It is shown [40] that a better Gaussian variable, for a given particle type, is the z-variable, defined as zi = ln hdE/dxi hdE/dxi BB i ! , (1) where hdE/dxi BB i is the Bethe-Bloch (Bichsel [39]) expectation of hdE/dxi for the given particle type i (i = π, K, p). In this analysis, hdE/dxi BB i is parameterized as hdE/dxi BB i = Ai 1 + m2 i p 2 mag ,
(2) where mi is the particle’s rest mass and pmag is the particle momentum magnitude. This parameterization is found to describe the data well, with the normalization factor Ai determined from data. The expected value of zi for the particle in study is around 0. The zK variable is shown for K− in Fig. 5(b), where the kaon band is situated around 0. The zi distribution is constructed for a given particle type in a given p⊥ bin within |y| < 0.1. Figure 6 shows the zπ and zK distributions, each for two p⊥ bins. The distributions show a multi-Gaussian structure. To extract the raw particle yield for a given particle type, a multi-Gaussian fit is applied to the zi distribution as superimposed in Fig. 6. The parameters of the multiGaussian fit are the centroids, widths, and amplitudes for π ±, e ±, K±, p and p. The positive and negative particle zi-distributions are fit simultaneously. The particle and antiparticle centroids and widths are kept the same. The centroid of the particle type in study is not fixed at zero, but treated as a free parameter because the parameterization by Eq. (2) is only approximate. For the large p⊥ bins where the hdE/dxi bands merge, the Gaussian widths for all three particle species are kept the same. The fit centroids of π −, e −, K−, and p, where K− is the particle type in study, are superimposed on Fig. 5(a) as a function of p⊥. The kaon zK fit centroid is very close to zero, affirming the good description of hdE/dxi BB K by Eq. (2) at low p⊥. The particle yield extracted from the fit to the corresponding z distribution is the raw yield. The fit yields for the other particle peaks cannot be used, because the 10 zπ -0.5 0 0.5 1 1.5 2 ] -1 [(GeV/c) π dz dy dp π 2 3N d evt N 1 -4 10 -3 10 -2 10 -1 10 1 10 Combined fit pion kaon electron 0.40

0.5 GeV/c. In order to extract the kaon yield at relatively large p⊥, electron contributions are interpolated to the dE/dx overlapping p⊥ range and are then fixed. The uncertainties in the estimation of electron contaminations are the main source of systematic uncertainties on the extracted kaon yields at large p⊥, as discussed in Section V. IV. CORRECTIONS AND BACKGROUNDS A. Monte-Carlo Embedding Technique The correction factors are obtained by the multi-step embedding MC technique. First, simulated tracks are blended into real events at the raw data level. Real data events to be used in the embedding are sampled over the entire data-taking period in order to have proper representation of the whole data set used in the analysis. MC tracks are simulated with primary vertex position taken from the real events. The MC track kinematics are taken from flat distributions in η and p⊥. The flat p⊥ distribution is used in order to have similar statistics in different p⊥ bins. The number of embedded MC tracks is of the order of 5% of the measured multiplicity in real events. The tracks are propagated through the full simulation of the STAR detector and geometry using GEANT with a realistic simulation of the STAR-TPC response. The simulation starts with the initial ionization of the TPC gas by charged particles, followed by electron transport and multiplication in the drift field, and finally the induced 11 signal on the TPC read-out pads and the response of the read-out electronics. All physical processes (hadronic interaction, decay, multiple scattering, etc.) are turned on in the GEANT simulation. The obtained raw data pixel information for the simulated particles are added on to the existing information of the real data. Detector effects such as the saturation of ADC channels are taken into account. The format of the resulting combined events is identical to that of the real raw data events. Second, the mixed events are treated just as real data and are processed through the full reconstruction chain. Clusters and hits are formed from the pixel information; tracks are reconstructed from the hits. Third, an association map is created between the input MC tracks and the reconstructed tracks of the mixed event. The association is made by matching hits by proximity 1 . For each MC hit from GEANT, a search for reconstructed hits from the embedded event is performed with a window of ±6 mm in x, y, and z [25]. The window size is chosen based on the hit resolution and the typical occupancy of the TPC in central Au+Au collisions. If a reconstructed hit is found in the search window, the MC hit is marked as matched. The MC track is considered to be reconstructed if more than 10 of its hits are matched to a single reconstructed track in the embedded event. Multiple associations are allowed, but the probability is small to have a single MC track matched with two or more reconstructed tracks or vice versa. From the multiple associations, the effects of track splitting (two reconstructed tracks matched to one MC track) and track merging (two MC tracks matched to a single reconstructed track) can be studied. The reconstruction effi- ciency is obtained by the ratio of the number of matched MC tracks to the number of input MC tracks. The reconstruction efficiency contains the net effect of tracking efficiency, detector acceptance, decays, and interaction losses. The most critical quality assurance is to make sure that the MC simulation reproduces the characteristics of the real data. This is carried out by comparing various distributions from real data and from embedding MC. • Figure 7 shows the longitudinal and transverse hit residuals for matched MC tracks from embedding and for real data tracks. The hit residuals are compared as a function of the dip angle (the angle between the particle momentum and the z-direction), the crossing angle (the angle between the particle momentum and the TPC pad-row direction [8, 9]) and the hit z position. Good agreement is found as seen from Fig. 7. The observed differences are small relative to the typical TPC occupancy and do not affect the obtained reconstruction efficiency. 1 Another possible matching algorithm is the identity truth method, where the track identity information is propagated to the reconstructed hits. Cross angle [degree] -15 -10 -5 0 5 10 15 Trans. resolution [cm] 0 0.05 0.1 Cross angle [degree] Au+Au 62 GeV data Au+Au 62 GeV embedding z [cm] -100 -50 0 50 100 z [cm] Au+Au 62 GeV data Au+Au 62 GeV embedding Cross angle [degree] -15 -10 -5 0 5 10 15 [cm] -0.04 -0.02 -0 0.02 0.04 Cross angle [degree] Au+Au 62 GeV data Au+Au 62 GeV embedding z [cm] -100 -50 0 50 100 z [cm] Au+Au 62 GeV data Au+Au 62 GeV embedding tan(dip angle) -0.4 -0.2 0 0.2 0.4 Long. resolution [cm] 0 0.05 0.1 0.15 0.2 tan(dip angle) Au+Au 62 GeV data Au+Au 62 GeV embedding z [cm] -100 -50 0 50 100 z [cm] Au+Au 62 GeV data Au+Au 62 GeV embedding tan(dip angle) -0.4 -0.2 0 0.2 0.4 [cm] -0.04 -0.02 -0 0.02 0.04 tan(dip angle) Au+Au 62 GeV data Au+Au 62 GeV embedding z [cm] -100 -50 0 50 100 z [cm] Au+Au 62 GeV data Au+Au 62 GeV embedding FIG. 7: Hit resolution and mean hit residual as a function of the track crossing angle at the hit position, the track dip angle, and the hit z coordinate. The data are an enriched K+ sample (via dE/dx cut) within |y| < 1 and 0.4 < p⊥ < 0.5 GeV/c in 62.4 GeV Au+Au collisions. Errors shown are statistical only. • Figure 8 shows the dca distributions of kaons reconstructed from matched MC kaon tracks and kaon candidates from real data. Kaon candidates are selected from real data by applying a tight dE/dx cut of ±0.5σ around the kaon Bethe-Bloch curve. Kaons are used because they contain minimal weak decay contributions and other background so that their dca distributions give a good assessment of the quality of the embedding data. Good agreement is found between embedding MC and real data. • Figure 9 shows a comparison of the number of 12 [cm] dca 0 1 2 3 0 0.5 1 1.5 pp 200 GeV : 0.3

0.2 GeV/c, but falls steeply at lower p⊥ because particles below p⊥ = 0.15 GeV/c cannot traverse the entire TPC due to their large track curvature inside the solenoidal magnetic field. The efficiency for protons and antiprotons is flat above p⊥ ∼ 0.35 GeV/c. At lower p⊥, the efficiency drops steeply because of the large multiple scattering effect due to the large (anti)proton mass. The kaon efficiency shown in Figs. 13 and 14 increases smoothly with p⊥ and already includes decay loss (which decreases with increasing p⊥). The significantly smaller kaon efficiency at small momentum than that of pions is caused by the large loss of kaons due to decays. In pp and d+Au collisions, the difference between the efficiencies for the different multiplicity bins is negligible because the multiplicities are low and the different occupancies have no effect on the track reconstruction per- 15 [GeV/c] MC p 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Efficiency 0 0.2 0.4 0.6 0.8 1 [GeV/c] MC p (a) pp 200 GeV MB – π – K p (GeV/c) MC p 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Efficiency 0.2 0.4 0.6 0.8 1 (b) d+Au 200 GeV MB – π – K p FIG. 13: Efficiency (product of tracking efficiency and detector acceptance) of π −, K−, and p in pp (a) and d+Au collisions (b) at 200 GeV as a function of input MC p⊥. Errors shown are binomial errors. The curves are parameterizations to the efficiency data and are used for corrections in the analysis. [GeV/c] MC p 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Efficiency 0.2 0.4 0.6 0.8 1 (a) Au+Au 62 GeV 70-80% – π – K p [GeV/c] MC p 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Efficiency 0.2 0.4 0.6 0.8 1 (b) Au+Au 62 GeV 0-5% – π – K p FIG. 14: Efficiency (product of tracking efficiency and detector acceptance) of π −, K−, and p in 70-80% peripheral Au+Au (a) and 0-5% central Au+Au collisions (b) at 62.4 GeV as a function of input MC p⊥. Errors shown are binomial errors. The curves are parameterizations to the efficiency data and are used for corrections in the analysis. formance. In Au+Au collisions, the particle multiplicity (hence the TPC occupancy) is high, resulting in the different reconstruction efficiency magnitudes in peripheral and central Au+Au collisions as seen in Fig. 14. The change in the efficiency from peripheral to central collisions at 62.4 GeV is smooth and is of the order of 15-20%. However, this is still a relatively small variation; the 5% embedded multiplicity used in the embedding MC simulation, which biases the embedded events towards higher multiplicity and TPC occupancy, has negligible effect on the calculated reconstruction efficiency for each centrality bin. The curves superimposed in Figs. 13 and 14 are parameterizations to the efficiencies. Table IV lists the fit parameters for 200 GeV minimum bias d+Au data and five centrality bins of 62.4 GeV Au+Au data. The fit parameters for π −, K−, p and p are tabulated. The fit parameters for π + and π − are similar, and also for K+ and K−. These parameterizations are used in the analysis for efficiency corrections. E. Proton Background Correction The proton sample contains background protons knocked out from the beam pipe and the detector materials by interactions of produced hadrons in these materials [43]. Most of these protons have large dca and are not reconstructed as primary particles. However, some of these background protons have small dca and are therefore included in the primary track sample and a correction is needed. Figure 15 shows the dca distributions of protons and antiprotons for two selected p⊥ bins in 200 GeV d+Au (upper panels) and 62.4 GeV central Au+Au collisions (lower panels), respectively. The protons and antiprotons are selected by a dE/dx cut of |zp| < 0.3 where zp is given by Eq. (1). The long, nearly flat dca tail in the 16 TABLE IV: Parameterizations to π −, K−, p and p efficiencies for 200 GeV minimum bias d+Au data and five centrality bins of 62.4 GeV Au+Au data. d+Au Au+Au min bias 70-80% 50-60% 30-40% 10-20% 0-5% π −: P0 exp[−(P1/p⊥) P2 ] P0 0.856 0.840 0.818 0.809 0.781 0.759 P1 0.075 0.129 0.111 0.109 0.097 0.070 P2 1.668 4.661 3.631 3.224 2.310 1.373 K−: P0 exp[−(P1/p⊥) P2 ] + P3p⊥ P0 0.527 0.608 0.585 0.503 0.494 0.450 P1 0.241 0.238 0.234 0.231 0.229 0.229 P2 3.496 2.425 3.034 3.968 3.492 3.925 P3 0.160 0.099 0.085 0.152 0.139 0.149 p¯: (P0 exp[−(P1/p⊥) P2 ] + P3p⊥) exp[(P4/p⊥) P5 ] P0 0.830 0.317 0.233 0.227 0.245 0.246 P1 0.295 0.303 0.303 0.300 0.305 0.301 P2 7.005 19.473 13.480 11.183 15.567 13.054 P3 −0.029 −0.004 0.028 0.041 0.026 0.039 P4 0 fixed 10.156 4.160 2.031 1.895 0.889 P5 0 fixed 0.006 0.104 0.153 0.107 0.160 p: (P0 exp[−(P1/p⊥) P2 ] + P3p⊥) exp[(P4/p⊥) P5 ] P0 0.921 0.189 0.201 0.193 0.187 0.221 P1 0.291 0.306 0.310 0.303 0.308 0.307 P2 7.819 10.643 16.825 9.565 12.826 14.488 P3 −0.057 0.023 0.026 0.041 0.042 0.033 P4 0 fixed 15.212 9.331 3.585 3.380 1.944 P5 0 fixed 0.131 0.127 0.194 0.194 0.181 proton distribution comes mainly from knock-out background protons. The effect is large at low p⊥ and significantly diminished at high p⊥ (note the logarithm scale for the high-p⊥ data). Antiprotons do not have knockout background; the flat dca tail is absent from their dca distributions. In order to correct for the knock-out background protons, the dca dependence at dca < 3 cm is needed for the knock-out protons. Based on MC simulation studies, we found the following functional form to describe the background protons well [20]: pbkgd(dca) ∝ [1 − exp(−dca/d0)]α . (5) Assuming that the shape of the background subtracted proton dca distribution is identical to that for the antiproton dca distribution, the proton data can be fit by p(dca) = p(dca)/rp/p + A · pbkgd(dca) , (6) where the magnitude of the background protons A, the parameter d0, the exponent α, and the antiproton-toproton ratio rp/p are free parameters. This assumption is, however, not strictly valid because the weak decay contributions to the proton and antiproton samples are in principle different, and the dca distribution of the weak decay products differs from that of the primordial protons and antiprotons. However, the measured Λ¯/Λ ratio is close to the p/p ratio [44] and the difference in dca distributions between protons and antiprotons arising from weak decay contaminations is small. The effect of slightly different proton and antiproton dca distributions on the extracted background proton fraction is estimated and is within the systematic uncertainty discussed in Section V. The dca distributions of protons and antiprotons are fit with Eq. (6) in each p⊥ and centrality bin. The dca distributions up to 10 cm are included in the fit for the Au+Au data. The proton dca distributions in d+Au collisions, however, have a peculiar dip at dca ≈ 4 cm as seen in Fig. 15. We think this dip is related to effects of the beam pipe (whose diameter is 3 inches) and a specific algorithm of the vertex finder in low multiplicity collisions; however, its exact cause is still under investigation. Due to the dip in the d+Au data, we fit the dca distributions up to 10 cm but exclude the region 3.2 < dca < 5 cm from the fit. The fit results are shown in Fig. 15. The dashed curve is the fit proton background. The dotted curve is the p distribution scaled up by the fit p/p ratio. The solid histogram is the fit of Eq. (6) to the proton distribution. The fit qualities are good. It is found that the fit power exponent α is larger than one, indicating that the background protons die off faster than the simple 1 − exp(−dca/d0) form at small dca. The α value is large at high p⊥; there is practically no background at high p⊥ at small dca. Table V lists the fraction of knock-out background protons out of the total measured proton sample within dca < 3 cm as a function of p⊥ in minimum bias d+Au and three selected centrality bins of Au+Au data. The fraction of knock-out background protons depends on a number of factors, including the amount of detector material, analysis cuts, the total particle multiplicity produced in the collisions and their kinetic energies. Since the ratio of
proton multiplicity to total particle multiplicity varies somewhat with centrality, and the particle kinematics change with centrality, the background fraction varies slightly with centrality. For pp data [17] and Au+Au data at 130 GeV [20] and 200 GeV [17], the background protons are corrected in a similar way. The fraction of background protons are similar in all collision systems. F. Pion Background Correction The pion spectra are corrected for feed-downs from weak decays, muon contamination, and background pions produced in the detector materials. The corrections are obtained from MC simulations of HIJING events, with the STAR geometry and a realistic description of the detector response. The simulated events are reconstructed in the same way as for real data. The weak-decay daughter pions are mainly from K0 S and Λ and are identified by the parent particle information accessible from the simulation. The pion decay muons can be mis-identified as primordial pions because of the similar masses of muon and pion. This contamination is obtained from MC by identifying the decay, which is also accessible from the 17 dca [cm] 0 2 4 6 8 10 ] -1 dN/d(dca) [cm 0 0.002 0.004 0.006 d+Au MB, 0.40 < p < 0.45 GeV/c p p fitted p p scaled -dca/0.79 5.0 bkgd: 0.0036 1-e /ndf = 1.41 2 χ dca [cm] 0 2 4 6 ] -1 dN/d(dca) [cm -4 10 -3 10 -2 10 d+Au MB, 0.70 < p < 0.75 GeV/c p p fitted p p scaled -dca/0.47 9.0 bkgd: 0.0004 1-e /ndf = 1.49 2 χ dca [cm] 0 2 4 6 8 10 ] -1 dN/d(dca) [cm 0 0.05 0.1 0.15 0.2 Au+Au 0-5%, 0.40 < p < 0.45 GeV/c p p fitted p p scaled -dca/1.30 2.8 bkgd: 0.094 1-e /ndf = 1.13 2 χ dca [cm] 0 2 4 6 ] -1 dN/d(dca) [cm -3 10 -2 10 -1 10 1 Au+Au 0-5%, 0.70 < p < 0.75 GeV/c p p fitted p p scaled -dca/0.58 29.1 bkgd: 0.012 1-e /ndf = 1.06 2 χ FIG. 15: The dca distributions of protons and antiprotons for 0.40 < p⊥ < 0.45 GeV/c and 0.70 < p⊥ < 0.75 GeV/c in 200 GeV minimum bias d+Au (upper panels) and 62.4 GeV 0-5% central Au+Au collisions (lower panels). Errors shown are statistical only. The dashed curve is the fit proton background; the dotted histogram is the p distribution scaled up by the fit p/p ratio; and the solid histogram is the fit p distribution by Eq. (6). The range 3.2 < dca < 5 cm is excluded from the fit for the d+Au data. Note the logarithm scale of the right panels. TABLE V: Fraction of proton background out of total measured proton sample as a function of p⊥. Minimum bias d+Au collisions at 200 GeV and three centrality bins of Au+Au collisions at 62.4 GeV are listed. The errors are systematic uncertainties. p⊥ d+Au 200 GeV Au+Au 62.4 GeV (GeV/c) min. bias 70-80% 30-40% 0-5% 0.425 0.49 ± 0.07 0.32 ± 0.09 0.36 ± 0.08 0.36 ± 0.08 0.475 0.47 ± 0.04 0.29 ± 0.06 0.29 ± 0.06 0.29 ± 0.05 0.525 0.41 ± 0.04 0.26 ± 0.05 0.22 ± 0.04 0.23 ± 0.04 0.575 0.36 ± 0.04 0.18 ± 0.05 0.15 ± 0.03 0.16 ± 0.03 0.625 0.28 ± 0.04 0.12 ± 0.05 0.12 ± 0.03 0.11 ± 0.02 0.675 0.23 ± 0.04 0.09 ± 0.05 0.08 ± 0.02 0.07 ± 0.02 0.725 0.17 ± 0.04 0.06 ± 0.05 0.05 ± 0.02 0.04 ± 0.01 0.775 0.12 ± 0.05 0.05 ± 0.05 0.04 ± 0.02 0.03 ± 0.01 0.825 0.10 ± 0.05 0.03 ± 0.03 0.02 ± 0.01 0.02 ± 0.01 0.875 0.06 ± 0.04 0.03 ± 0.03 0.02 ± 0.01 0.02 ± 0.01 0.925 0.06 ± 0.04 0.02 ± 0.02 0.01 ± 0.01 0.01 ± 0.01 0.975 0.04 ± 0.04 0.02 ± 0.02 0.01 ± 0.01 0.01 ± 0.01 simulation. The obtained weak-decay pion background and muon contamination are shown in Fig. 16 as a function of p⊥. The total background rate, which is dominated by these two sources, is also shown. The pion background fraction is independent of event multiplicity in 200 GeV pp and d+Au collisions; therefore, a single correction is applied. In 62.4 GeV Au+Au collisions the multiplicity dependence of the pion background is weak (within 1.5% over the entire centrality range); a single, averaged correction is applied to all centralities, similar to the approach in Ref. [17]. V. SYSTEMATIC UNCERTAINTIES A. On Transverse Momentum Spectra The point-to-point systematic uncertainties on the spectra are estimated by varying event and track selection and analysis cuts and by assessing sample purity 18 p [GeV/c] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 background [%] – π 0 2 4 6 8 10 12 14 16 background – Total π – Weak decay π Muon contamination FIG. 16: Pion background fraction from weak decays (Λ, K0 S) and µ ± contamination as a function of p⊥ in minimum bias d+Au collisions at 200 GeV. Errors shown are statistical only. from the dE/dx measurement. In addition, the Gaussian fit ranges are varied to estimate the systematic uncertainty on the extracted raw spectra. The estimated uncertainties are less than 4% for π ±, p and p. Those for K± are less than 12% for p⊥ bins with significant overlap in dE/dx with e ± or π ±, and less than 4% for other bins. These point-to-point systematic errors are similar for pp, d+Au, and Au+Au collisions. The point-to-point systematic errors are combined with statistical errors in quadrature in the plotted spectra in Figs. 18, 19, 20 and 21. The combined errors are treated as random errors and are included in the fitting of the spectra. For proton spectra, an additional systematic error is estimated due to background subtraction. The estimated uncertainty at p⊥ = 0.45-0.50 GeV/c is about 8% and drops rapidly with p⊥ [20, 45] (see Table V). The p⊥ dependence of background contribution varies somewhat with centrality, presumably due to the combined effect of the rapid change in the proton p⊥ spectral shape with centrality and little change in the pion’s. The proton background uncertainties for pp and d+Au collisions are similar. The systematic uncertainties on the pion spectra due to background correction are negligible. A correlated overall systematic uncertainty of 5% is estimated for all spectra and is dominated by uncertainties in the MC determination of reconstruction efficiencies. This systematic uncertainty is estimated by varying parameters in the MC simulation. B. On dN/dy The particle yield measured at mid-rapidity (|y| < 0.1) for each identified particle spectrum is calculated from the measured p⊥ range and extrapolated to the unmeasured regions with various parameterizations. For kaons and protons the extrapolation is done by the hydrodynamics-motivated blast-wave model fit (deTABLE VI: Fraction of measured and extrapolated yield for negatively charged particles for selected collision systems and centralities. For extrapolation, Bose-Einstein fit is used for pions and blast-wave fit is used for kaons and (anti)protons. measured extrapolated dN/dy system dN/dy low p⊥ high p⊥ π −, measured range p⊥=0.2-0.7 GeV/c d+Au min. bias 59% 30% 11% Au+Au 70-80% 58% 32% 10% Au+Au 30-40% 58% 28% 14% Au+Au 0-5% 58% 28% 14% K−, measured range p⊥=0.2-0.75 GeV/c d+Au min. bias 60% 12% 28% K, measured range p⊥=0.25-0.75 GeV/c Au+Au 70-80% 58% 21% 21% Au+Au 30-40% 56% 15% 29% Au+Au 0-5% 54% 13% 33% p, measured range p⊥=0.4-1.10 GeV/c d+Au min. bias 53% 21% 26% p, measured range p⊥=0.35-1.15 GeV/c Au+Au 70-80% 65% 21% 14% Au+Au 30-40% 64% 12% 24% Au+Au 0-5% 60% 9% 31% scribed in section VII). Our default blast-wave fit does not include resonance decays (the effect of which is studied in detail in Appendix B). The fit is done to all six spectra of π ±, K±, p and p simultaneously. However, because the low p⊥ region of the pion spectra are affected by resonance decays, the p⊥ < 0.5 GeV/c part of the pion spectra is excluded from the blast-wave fit. Instead, the Bose-Einstein distribution, dN m⊥dm⊥ ∝ 1 /[exp(m⊥/TBE) − 1] (7) is found to describe the pion spectra well and is employed to extrapolate the pion spectra, with TBE a fit parameter. The point-to-point systematic errors on the spectra are included in the fits. Table VI shows the fractional yields of dN/dy extrapolated to the unmeasured p⊥ regions. The systematic uncertainties on the extrapolated yields are estimated by comparing the extrapolation to those using other fit functions. Those fit functions are: p⊥−exponential : dN p⊥dp⊥ ∝ exp(−p⊥/Tp⊥ ) , p⊥−Gaussian
: dN p⊥dp⊥ ∝ exp(−p 2 ⊥/T 2 p⊥ ) , p 3 ⊥−exponential : dN p⊥dp⊥ ∝ exp(−p 3 ⊥/T 3 p⊥ ) , m⊥−exponential : dN m⊥dm⊥ ∝ exp(−m⊥/Tm⊥ ) , Boltzmann : dN m⊥dm⊥ ∝ mT exp(−m⊥/TB) . (8) where Tp⊥ , Tm⊥ , and TB are fit parameters. The fit functions used for pion dN/dy systematic uncertainty assessment are the blast-wave function and the p⊥-exponential. Those used for kaons are the m⊥-exponential and the Boltzmann function. Those used for proton and antiproton are the p⊥-Gaussian and p 3 ⊥-exponential; also used 19 for Au+Au 20-80% centrality bins and for d+Au collisions are the Boltzmann function, the m⊥-exponential, and the p⊥-exponential. The systematic uncertainties on the extrapolated total particle yields are dominated by the uncertainties in the extrapolation, which are estimated to be of the order of 15% of the extrapolated part of the integrated yields for pions and kaons, and 15-40% for antiprotons and protons depending on centrality. The 5% overall MC uncertainty is added in quadrature. For protons, the p⊥-dependent systematic uncertainty on background subtraction leads to an overall systematic uncertainty in the yields. This systematic uncertainty is estimated and included in quadrature in the total systematic uncertainties on dN/dy. Identified particle spectra in pp and d+Au collisions at 200 GeV and Au+Au collisions at 62.4 GeV are measured at relatively high p⊥ by the TOF detector in STAR [46, 47]. In the overlap region in p⊥, the TOF measurements and the TPC measurements reported here are consistent within systematic uncertainties. The TOF measurement is a good systematic check on our extrapolation. As an example, Fig. 17 shows the measured antiproton spectra by dE/dx in d+Au and central Au+Au collisions and their various parameterizations, together with the TOF measurements. The TOF measurements are well within the range of the extrapolations. Blast-wave fits are also performed including the large p⊥ ranges from TOF [46, 47] and the spectra obtained by the extended particle identification method (rdE/dx) [16]. The blast-wave fit parameters thus obtained are consistent with our results within the systematic uncertainties. To keep consistency and fair comparisons of the various datasets, only the TPC measurements are studied here, since TOF was only installed as a prototype test for a full TOF system and was absent in many collision systems reported here. The total charged particle density dNch/dy, calculated from the sum of the individual dN/dy yields of π ±, K±, p and p, is used as one of the centrality measures in this paper. The systematic uncertainties on dNch/dy are calculated assuming that the extrapolation uncertainties are completely correlated between particles and antiparticles and completely uncorrelated between different particle species. In addition, the efficiency uncertainty is common for all particle species, and the proton background uncertainty is uncorrelated with the rest. C. On Particle Ratios and hp⊥i Systematic uncertainties on particle yield ratios come from those on the extrapolated total yields, estimated as above. The efficiency uncertainties are canceled in the ratios. The extrapolation uncertainties are canceled to a large degree in the antiparticle-to-particle ratios; a common systematic uncertainty of 2%, 3%, and 5% is assigned to π −/π+, K−/K+, and p/p, respectively [17]. The extrapolation uncertainties are treated as uncorre- 0 0.5 1 1.5 2 2.5 3 -4 10 -3 10 -2 10 -1 10 1 (a) p: d+Au 200 GeV, min-bias dE/dx Blast-Wave p Gaussian p Exponential TOF 0 0.5 1 1.5 2 2.5 3 -3 10 -2 10 -1 10 1 10 (b) p: Au+Au 62.4 GeV, 0-5% dE/dx Blast-Wave p Gaussian Exponential 3 p TOF p [GeV/c] ] -2 dy) [(GeV/c) dp p π N / (2 2 d FIG. 17: Mid-rapidity identified antiproton spectra in 200 GeV minimum bias d+Au (a) and 62.4 GeV central Au+Au collisions (b) measured by dE/dx together with those by TOF [46, 47]. The dE/dx data are from |y| < 0.1 and the TOF data are from |y| < 0.5. The curves are various fits to the dE/dx data for extrapolation. The quadratic sum of statistical errors and point-to-point systematic errors are plotted, but are smaller than the point size. lated in the unlike particle ratios (K−/π−, p/π−, p/π−, etc.). The uncertainty due to proton background substraction is added in quadrature for the ratios involved with the proton yield. The average transverse momentum, hp⊥i, is extracted from the measured spectra and the extrapolations (blastwave model fits for kaons and protons and Bose-Einstein function for pions as described above). Systematic uncertainties on hp⊥i are also estimated by using the various functional forms mentioned before for extrapolation of the spectra. For protons an additional systematic uncertainty on hp⊥i due to the p⊥-dependent proton background subtraction is estimated and included in quadrature in the total systematic uncertainties. D. On Chemical Freeze-Out Parameters Chemical freeze-out parameters (chemical freeze-out temperature Tchem, baryon and strangeness chemical po- 20 tentials µB and µS, and strangeness suppression factor γS) are extracted from the measured particle ratios obtained from the six particle spectra within the framework of a statistical model. The systematic uncertainties on the particle ratios are included in the statistical model fit and are treated as independent. These uncertainties propagate to the systematic uncertainties on the chemical freeze-out parameters. Our measured protons are inclusive of all protons from primordial Σ+ and Λ (and Σ0 -decay Λ) decays, and likewise for the antiparticles. To assess the systematic uncertainties on the fit chemical freeze-out parameters, we vary the detection probability of weak-decay (anti)protons from 100% to 50%. The chemical freeze-out temperature thus obtained is larger by about 8 MeV and is included in the systematic uncertainty estimate. The effects on baryon and strangeness chemical potentials are negligible. Due to the decay kinematics, Λ’s from Ξ and Ω decays mostly follow the parent direction [44], and the decay protons from most of those decay Λ’s are reconstructed as primordial protons in the STAR TPC; likewise for the antiparticles. In our statistical model fit, we assume 50% of the (anti)protons from multi-step decays are included in our measured primary (anti)proton samples. To assess the systematic uncertainty due to the multi-step decay products, we include either all the multistep decay (anti)protons or none of them in the statistical model fit. We found that this systematic uncertainty is small. The other source of systematic uncertainty is due to the relatively limited set of particle ratios used in this analysis. While the Tchem, µB and µS should be well constrained because of the high statistics data for pions, kaons, and (anti)protons, the ad-hoc strangeness suppression factor γS is not well constrained because the single-strangeness K± are the only strangeness species used in this work. STAR has measured a variety of strange and multi-strange particles, including K∗±, K0 S , Λ and Λ, Λ1520, Ξ and Ξ, and Ω and Ω at 130 GeV [44, 48, 49, 50] and 200 GeV [51, 52, 53]. The chemical freezeout parameters have also been studied by particle ratios including these particles [50]. It is found that the extracted chemical freeze-out temperature and baryon and strangeness chemical potentials are similar to those obtained from this work using the limited set of particle ratios. However, the γS parameter differs: in central Au+Au collisions, γS ∼ 0.9 from this work and ∼ 1.0 from the fit including the extended list of strange and multi-strange particles [50]. This difference gives a reasonable estimate of the systematic uncertainty on γS. E. On Kinetic Freeze-Out Parameters The kinetic freeze-out parameters are extracted from the simultaneous blast-wave parameterization of the measured particle spectra. The kinetic freeze-out temperature Tkin, the average transverse radial flow velocity hβi, and the flow velocity profile exponent n are treated as free para
meters. The point-to-point systematic errors on the spectra are included in the blast-wave fit. The p⊥-dependent systematic uncertainty due to proton background correction is taken into account in evaluating the systematic uncertainties of the blast-wave parameters. The measured pions contain large contributions from resonance decays; the contributions vary with the pion p⊥. Our default blast-wave fit does not include resonance decays. In order to reduce the systematic uncertainty due to resonance decays, the low p⊥ part (p⊥ < 0.5 GeV/c) of the pion spectra is excluded from the blast-wave fit. The remaining systematic uncertainty is estimated by varying the p⊥ range of the pion spectra included in the blastwave fit. The resonance decay effect on the blast-wave fit is also thoroughly studied in Appendix B. Comparisons between the blast-wave parameters obtained including or excluding resonance decays also give a good estimate of the systematic uncertainties. Due to the large mass of (anti)protons and kaons, the (anti)proton and kaon spectra constrain the transverse flow velocity well. Thus the systematic uncertainties on the kinetic freeze-out parameters are also assessed by excluding the K± spectra, the p spectrum, or the p spectrum from the blast-wave fit. While the spectra are mainly determined by Tkin and hβi, the shape of the flow velocity profile also has some effect on the spectra, due to the non-linearity in the dependence of the spectral shape on the flow velocity. However, the effect is fairly weak, as indicated by the large fitting errors on the velocity profile exponent n for some of the spectra. Nevertheless, to assess the systematic uncertainty from this effect, we fit the spectra by fixing n to unity. The fit qualities are significantly degraded for some of the spectra. However, we use the changes in the fit parameters as our conservative estimates of the systematic uncertainties due to the flow velocity profile used. We note that the blast-wave model assumes a simple picture of local particle sources of a common temperature in a transverse radial velocity field to describe the flattening of particle transverse spectra. The extracted kinetic freeze-out parameters are within the framework of this picture. However, it is possible that other effects may also contribute to the spectra flattening: semi-hard scatterings may even be the main contributer in pp collisions [54]; the possible effect of statistical global energy and momentum conservation on particle spectra is recently studied in Ref. [55]. Such effects are not included in our systematic uncertainties on the extracted values of the kinetic freeze-out parameters. VI. RESULTS AND DISCUSSIONS In this section, results on identified π ±, K±, p and p in d+Au collisions at 200 GeV and Au+Au collisions at 62.4 GeV [5] are presented and discussed. The results 21 0 0.2 0.4 0.6 -2 10 -1 10 1 10 2 10 (a) d+Au 200 GeV + π – π 0 0.2 0.4 0.6 0.8 -2 10 -1 10 1 10 2 10 (b) d+Au 200 GeV + K- K 0 0.2 0.4 0.6 0.8 1 1.2 -2 10 -1 10 1 10 2 10 (c) d+Au 200 GeV p p p [GeV/c] ] -2 [(GeV/c) dy dp p N 2 d π 2 1 FIG. 18: Mid-rapidity (|y| < 0.1) identified particle spectra in d+Au collisions at 200 GeV. The p and p spectra are inclusive, including weak decay products. Spectra are plotted for three centrality bins and for minimum bias events. Spectra from top to bottom are for 0-20% scaled by 4, 20-40% scaled by 2, minimum bias not scaled, and 40-100% scaled by 1/2. Errors plotted are statistical and point-to-point systematic errors added in quadrature, but are smaller than the point size. The curves are the blast-wave model fits to the minimum bias data; the normalizations of the curves are fixed by the corresponding negative particle spectra. 0 0.2 0.4 0.6 -1 10 1 10 2 10 3 10 (a) Au+Au 62.4 GeV + π – π 0 0.2 0.4 0.6 0.8 -1 10 1 10 2 10 3 10 (b) Au+Au 62.4 GeV + K – K 0 0.5 1 -1 10 1 10 2 10 3 10 (c) Au+Au 62.4 GeV p 0 0.5 1 -1 10 1 10 2 10 3 10 (d) Au+Au 62.4 GeV p p [GeV/c] ] -2 [(GeV/c) dy dp p N 2 d π 2 1 FIG. 19: Mid-rapidity (|y| < 0.1) identified particle spectra in Au+Au collisions at 62.4 GeV. The p and p spectra are inclusive, including weak decay products. Spectra are plotted for nine centrality bins, from top to bottom, 0-5%, 5-10%, 10-20%, 20-30%, 30-40%, 40-50%, 50-60%, 60-70%, and 70-80%. Errors plotted are statistical and point-to-point systematic errors added in quadrature, but are smaller than the point size. The curves are the blast-wave model fits to the spectra; the normalizations of the curves in (a,b) are fixed by the corresponding negative particle spectra. are measured at mid-rapidity in the range |y| < 0.1. The charged pion spectra in Au+Au collisions at 130 GeV are also presented. The results are discussed together with previously published identified π ±, K±, p and p results in pp and Au+Au collisions at 200 GeV [17], and charged kaons [18] and (anti)protons results [20] at 130 GeV. The identified particle spectra are presented first, followed by the average transverse momenta hp⊥i, the integrated particle multiplicity densities dN/dy and ratios, and baryon and strangeness production rates. The 22 0 0.2 0.4 0.6 0.8 1 10 2 10 Au+Au 130 GeV + π – π p [GeV/c] ] -2 [(GeV/c) dy dp p N 2 d π 2 1 FIG. 20: Mid-rapidity (|y| < 0.1) identified pion spectra in Au+Au collisions at 130 GeV. Spectra are plotted for eight centrality bins, from top to bottom, 0-6%, 6-11%, 11-18%, 18- 26%, 26-34%, 34-45%, 45-58%, and 58-85%. Errors plotted are statistical and point-to-point systematic errors added in quadrature, but they are smaller than the data point size. The curves are the Bose-Einstein fits to the spectra; the normalizations of the curves are fixed by the corresponding negative particle spectra. hp⊥i and dN/dy are extracted from the measured spectra and the extrapolations from the blast-wave model fits for kaons and protons and the Bose-Einstein function for pions. In order to have the same procedure to obtain dN/dy and hp⊥i, the identified particle spectra from 130 GeV Au+Au collisions are fit by the blast-wave model parameterization in this work. The extracted hp⊥i and dN/dy are listed in Table VII and Table VIII, respectively. The quoted errors are the quadratic sum of statistical and systematic uncertainties and are dominated by the latter. Since the systematic uncertainties on particle ratios cannot be readily obtained from the individual particle dN/dy yields, Table IX lists particle ratios together with the total uncertainties. A. Transverse Momentum Spectra Figure 18 shows the centrality dependent and the minimum bias π ±, K±, p and ¯p spectra in d+Au collisions at 200 GeV. The minimum bias spectra are obtained from the cross-section weighted sum of the corresponding spectra in each centrality bin. The minimum bias d+Au spectra are in good agreement with the previously published results [46]. Spectra from different centralities are similar. Figure 19 shows the centrality dependence of the π ±, K±, p and ¯p spectra measured in Au+Au collisions at 62.4 GeV. Pion spectral shapes are similar in all centrality bins. Kaon and (anti)proton spectra show a signifi- cant flattening with increasing centrality with the effect being stronger for proton. Figure 20 shows the centrality dependent pion spectra measured in Au+Au collisions at 130 GeV. All spectra are parallel indicating no significant centrality dependence of the shape. The kaon spectra at 130 GeV are published in Ref. [18], and the proton and antiproton spectra are published in Ref. [19]. Spectra results from pp and Au+Au collisions at 200 GeV are published in Ref. [17]. Spectra shapes from 62.4 GeV, 130 GeV, and 200 GeV Au+Au collisions are all similar. Hardening of the spectra is more pronounced with increasing centrality and increasing particle mass at all three energies. Figure 21 compares pion, kaon, and antiproton spectra in pp, d+Au, and Au+Au collisions. The pp, d+Au, and peripheral Au+Au spectra are similar in shape. The central Au+Au spectra of kaons and (anti)protons are significantly flatter. B. Average Transverse Momenta The spectra shape can
be quantified by the average transverse momentum, hp⊥i. In Fig. 22, the evolution of hp⊥i is shown as a function of the charged particle multiplicity. The pion hp⊥i increases slightly with centrality in Au+Au collisions. For kaons, protons and antiprotons the hp⊥i increases significantly with centrality. No obvious centrality dependence is observed for d+Au collisions. One interesting observation is that the hp⊥i in central d+Au collisions is larger than that in peripheral Au+Au collisions. This can be due to jets, k⊥ broadening, and multiple scattering [56]. These effects can be stronger in d+Au collisions than in peripheral Au+Au collisions, because nucleons in the deuteron suffer multiple collisions traversing the incoming Au nucleus in central d+Au collisions while peripheral Au+Au collisions are close to simple superposition of multiple pp collisions. In fact, the hp⊥i in peripheral Au+Au collisions is similar to that in pp. On the other hand, the hp⊥i in central d+Au collisions is smaller than that in central Au+Au collisions. Central d+Au collisions likely have larger effects from initial state multiple scattering and k⊥ broadening. Although jet contribution is larger in central Au+Au than in d+Au, it is likely softened due to jet energy loss in central Au+Au collisions. Consequently jet contribution to the flattening of the low p⊥ spectra in Au+Au collisions may not 23 0 0.2 0.4 0.6 0.8 1 1.2 -3 10 -2 10 -1 10 1 10 2 10 3 10 (a) pp 200 GeV – π – K p 0 0.2 0.4 0.6 0.8 1 1.2 -3 -2 -1 10 1 10 2 10 3 10 (b) d+Au 200 GeV – π – K p 0 0.2 0.4 0.6 0.8 1 1.2 -3 -2 -1 1 10 2 10 3 10 (c) Au+Au 62.4 GeV – π – K p filled: 0-5% open: 70-80% p [GeV/c] ] -2 [(GeV/c) dy dp p N 2 d π 2 1 FIG. 21: Comparisons of π −, K−, and p transverse momentum spectra for (a) minimum bias pp collisions at 200 GeV, (b) minimum bias d+Au collisions at 200 GeV, and (c) Au+Au collisions at 62.4 GeV. Two centralities are shown: 0-5% central collisions in black filled symbols and 70-80% peripheral collisions in open symbols. Errors are statistical and point-to-point systematic errors added in quadrature. /dy ch dN 1 10 2 10 3 10 > [GeV/c]

[GeV/c]

= 0.38+0.33 (dN /dy)/S π

= 0.38+0.16 (dN /dy)/S π

= 0.29+0.07 (dN (b) FIG. 22: (color online) Average transverse momenta as a function of dNch/dy (a) and qdNπ /dy S⊥ (b) for Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. The minimum bias pp data are also shown. The d+Au data are shown in panel (a). Errors shown are systematic errors and statistical errors added in quadrature. be much larger than that in d+Au collisions. The larger hp⊥i in central Au+Au collisions cannot be only due to the effects already present in d+Au collisions, as randomwalk models argue [56], but also be due to other effects including transverse radial flow, due to thermodynamic pressure, and remaining contributions from (semi-)hard scatterings. Transverse radial flow suggested by these data will be discussed in more detail in Sec. VII. For Au+Au collisions, hp⊥i increases significantly with increasing centrality. The trends are similar at 62.4 GeV, 130 GeV, and 200 GeV, and hp⊥i qualitatively agree with each other at the same dNch/dy. This suggests that the kinetic freeze-out properties in Au+Au collisions are rather energy independent for the measured collision energies. In the Color Glass Condensate (gluon saturation) picture, small x gluons overlap and recombine, reducing the total number of gluons and increasing their transverse energy [29, 30]. These gluons hadronize into mostly soft hadrons. Thus, a lower particle multiplicity and larger hp⊥i is predicted. In the gluon saturation picture, the only relevant scale is dNπ/dy S⊥ , and the hp⊥i is predicted to scale with qdNπ/dy S⊥ [29, 30]. In Fig. 22(b), the hp⊥i 24 is shown as a function of qdNπ/dy S⊥ for minimum bias pp and for Au+Au collisions of the various centralities. A linear dependence of the hp⊥i on qdNπ/dy S⊥ is observed for all three particle species, as shown by the lines in Fig. 22. It is interesting to note that the slope, characterizing the rate of increase in the hp⊥i, is a factor 2 larger for p than for kaons which is in turn a factor 2 larger than for pions. The intercepts of the linear fits for p and kaons are the same, but are larger than that for pions. C. Total Particle Production The total particle multiplicity reflects the total entropy generated in the collision system. There has been renewed interest in total particle production as its centrality dependence could distinguish between different models of particle production [57]. Models based on the assumption of final-state gluon saturation advocate a decrease of the charged particle multiplicities per participant nucleon with increasing centrality. For example, the EKRT model [58] parameterizes the multiplicity rapidity density as dNch dη b=0 = C 2 3 1.16 Npart 2 0.92 ( √ s) 0.40 . (9) Models based on initial state gluon saturation (e.g. the color glass condensate model [59, 60]) or pQCD inspired models (e.g. the HIJING [42, 61] or the soft/hard scattering model used in Ref. [29]) predict an increase of the rapidity density per participant nucleon with centrality. In both the HIJING and the soft/hard model, particle production arises from two major contributions: (a) a soft component scaling with the number of participants Npart, and (b) a hard component from mini-jet production, which is directly proportional to the number of binary collisions Ncoll and the average inclusive jet crosssection. Reference [29] expresses these two components as dNch/dη = (1 − xhard) npp Npart 2 + xhardnppNcoll (10) where xhard is the fraction of hard collisions. The basic assumption here is that the average particle multiplicity produced per hard process in heavy-ion collisions is identical to that in pp collisions. In Eq. (10), npp is the charged particle pseudo-rapidity density in NSD pp interactions. We have measured npp in pp collisions only at 200 GeV. In order to apply the two-component model to data at other energies, we use a parameterization from pp¯ measurements [62, 63, 64, 65] by npp = (2.5±1.0)−(0.25±0.19) ln(s)+(0.023±0.008) ln2 (s) (11) where s is the squared center-of-mass energy in GeV2 . The parameterized value of npp = 2.43 at 200 GeV differs from our measurement in pp collisions because of the numerical difference between our measured NSD crosssection of 30.0 ± 3.5 mb [13] and the measurement in Ref. [66] of 35 ± 1 mb. In the following, we call Eq. (9) and (10) the EKRT and K-N parameterizations, respectively, and use them to study the discrimination power of our data against the two opposing models of particle production. Unfortunately, neither Npart nor Ncoll can be directly measured in the experiment. They can only be derived by calculating the nuclear overlap integral with the help of the Glauber model. However, two different implementations of the Glauber calculation, the optical and the MC Glauber calculations, lead to different values of Npart and Ncoll with rather large uncertainties for peripheral collisions (for details see Appendix A). Figure 23 shows the pseudo-rapidity multiplicity density per participant pair, dNch/dη Npart/2 , versus the number of participants Npart for Au+Au collisions at 62.4 and 200 GeV, where we have used Npart and Ncoll from the optical Glauber calculation in the left panel and the MC Glauber calculation in the right panel. The dNch/dη data are from Table II. In both panels, the vertical error bars represent the quadratic sum of the systematic uncertainties on dNch/dη and Npart. The latter dominates the uncertainties for peripheral collisions. As seen in Fig. 23(a) (using the optical Glauber calculation), we observe no significant change in charged hadron production as a function of centrality within the large uncertainties (mainly from the optical Glauber calculations). Superimposed for comparison are the EKRT and K-N parameterizations in the dashed and solid curves, respectively. The EKRT parameterization is obtained from the best fit to the data by Eq.(9), treating C as the single fit parameter. The K-N parameterization is obtained from the best fit to the data by Eq.(10), treating npp as fixed from Eq.(11) and xhard as the single fit parameter. Neither our data nor the EKRT parameterization seems to approach the parameterized npp by Eq.(11) in the limit of Npart = 2. The K-N parameterization recovers npp for Npart = 2 by construction of the model. Both models do a modest job in describing the data. When using the MC Glauber model to evaluate Npart and Ncoll as done in Fig. 23(b), our data clearly exhibit a centrality dependence rising from the most peripheral to the most central collisions, by about (50 ± 20)% and (40 ± 20)% for 62.4 GeV and 200 GeV, respectively. The data are fit by Eq. (9) treating C as the single fit parameter. The obtained EKRT parameterizations, shown in the dashed curves, clearly fail to describe our data due to the opposite centrality dependence. The fit χ 2/ndf is printed on the plot and is fairly large, especially considering that the systematic uncertainties are included in the fit as random errors. On the other hand, shown in the solid curves are the K-N parameterizations obtained from fitting Eq. (10) to the data fixing npp by Eq.(11) and treating xhard as the single fit parameter. As can be seen, the K-N parameterization fits the data 25 TABLE VII: Extrapolated average transverse momenta, hp⊥i in GeV/c, of identified particles for various collision systems and centralities. Quoted errors are the quadratic sum of statistical and systematic uncertainties, and are dominated by the latter. System Centrality π − π + K− K+ p p pp 200 GeV min. bias 0.348 ± 0.018 0.348 ± 0.018 0.517 ± 0.030 0.517 ± 0.030 0.683 ± 0.041 0.686 ± 0.041 min. bias 0.367 ± 0.027 0.369 ± 0.027 0.599 ± 0.068 0.599 ± 0.068 0.847 ± 0.090 0.847 ± 0.093 d+Au 40-100% 0.359 ± 0.024 0.364 ± 0.025 0.582 ± 0.071 0.582 ± 0.071 0.816 ± 0.085 0.817 ± 0.087 200 GeV 20-40% 0.363 ± 0.031 0.370 ± 0.031 0.623 ± 0.085 0.623 ± 0.085 0.896 ± 0.112 0.895 ± 0.116 0-20% 0.378 ± 0.028 0.378 ± 0.028 0.607 ± 0.061 0.608 ± 0.061 0.855 ± 0.081 0.855 ± 0.085 70-80% 0.363 ± 0.018 0.367 ± 0.018 0.550 ± 0.035 0.553 ± 0.035 0.746 ± 0.049 0.749 ± 0.049 60-70% 0.377 ± 0.019 0.
377 ± 0.019 0.583 ± 0.033 0.583 ± 0.033 0.814 ± 0.047 0.817 ± 0.047 50-60% 0.389 ± 0.020 0.389 ± 0.020 0.609 ± 0.036 0.608 ± 0.036 0.863 ± 0.052 0.864 ± 0.052 Au+Au 40-50% 0.395 ± 0.020 0.395 ± 0.020 0.619 ± 0.037 0.619 ± 0.037 0.895 ± 0.055 0.897 ± 0.055 30-40% 0.402 ± 0.021 0.404 ± 0.021 0.643 ± 0.042 0.643 ± 0.042 0.939 ± 0.062 0.939 ± 0.062 200 GeV 20-30% 0.408 ± 0.021 0.411 ± 0.021 0.668 ± 0.047 0.668 ± 0.047 0.989 ± 0.071 0.989 ± 0.071 10-20% 0.416 ± 0.021 0.421 ± 0.021 0.680 ± 0.055 0.681 ± 0.055 1.017 ± 0.082 1.017 ± 0.082 5-10% 0.418 ± 0.021 0.422 ± 0.021 0.704 ± 0.064 0.703 ± 0.064 1.070 ± 0.098 1.071 ± 0.098 0-5% 0.422 ± 0.022 0.427 ± 0.022 0.719 ± 0.074 0.720 ± 0.074 1.103 ± 0.114 1.104 ± 0.110 58-85% 0.355 ± 0.036 0.351 ± 0.035 0.559 ± 0.020 0.560 ± 0.020 0.745 ± 0.030 0.745 ± 0.030 45-58% 0.366 ± 0.020 0.360 ± 0.020 0.576 ± 0.030 0.571 ± 0.030 0.808 ± 0.054 0.808 ± 0.054 34-45% 0.375 ± 0.014 0.375 ± 0.014 0.598 ± 0.048 0.604 ± 0.048 0.869 ± 0.053 0.871 ± 0.053 Au+Au 26-34% 0.382 ± 0.020 0.383 ± 0.020 0.628 ± 0.049 0.633 ± 0.049 0.925 ± 0.066 0.926 ± 0.066 130 GeV 18-26% 0.386 ± 0.020 0.388 ± 0.020 0.644 ± 0.046 0.640 ± 0.046 0.942 ± 0.067 0.944 ± 0.067 11-18% 0.391 ± 0.023 0.395 ± 0.023 0.650 ± 0.036 0.649 ± 0.036 0.949 ± 0.085 0.949 ± 0.085 6-11% 0.390 ± 0.011 0.393 ± 0.011 0.640 ± 0.034 0.642 ± 0.034 0.965 ± 0.078 0.966 ± 0.078 0-6% 0.404 ± 0.013 0.404 ± 0.013 0.667 ± 0.030 0.666 ± 0.030 1.002 ± 0.087 1.003 ± 0.087 70-80% 0.357 ± 0.021 0.356 ± 0.021 0.529 ± 0.023 0.531 ± 0.023 0.702 ± 0.044 0.706 ± 0.045 60-70% 0.372 ± 0.019 0.364 ± 0.019 0.542 ± 0.015 0.542 ± 0.015 0.728 ± 0.028 0.729 ± 0.031 50-60% 0.381 ± 0.018 0.379 ± 0.018 0.560 ± 0.022 0.560 ± 0.022 0.759 ± 0.042 0.761 ± 0.046 Au+Au 40-50% 0.385 ± 0.017 0.385 ± 0.017 0.584 ± 0.020 0.583 ± 0.020 0.812 ± 0.042 0.814 ± 0.049 30-40% 0.395 ± 0.015 0.394 ± 0.015 0.607 ± 0.021 0.607 ± 0.021 0.864 ± 0.053 0.864 ± 0.061 62.4 GeV 20-30% 0.400 ± 0.012 0.403 ± 0.013 0.629 ± 0.023 0.629 ± 0.023 0.913 ± 0.060 0.910 ± 0.070 10-20% 0.402 ± 0.014 0.402 ± 0.014 0.636 ± 0.029 0.636 ± 0.029 0.928 ± 0.031 0.925 ± 0.050 5-10% 0.404 ± 0.010 0.407 ± 0.011 0.644 ± 0.027 0.643 ± 0.027 0.950 ± 0.040 0.948 ± 0.059 0-5% 0.403 ± 0.011 0.406 ± 0.011 0.645 ± 0.029 0.646 ± 0.029 0.959 ± 0.060 0.956 ± 0.075 Optical Glauber Npart 0 100 200 300 η /d ch ) dN part (2/N 0 2 4 6 (a) /ndf=0.73 2 EKRT 200 : C=0.83±0.03, χ /ndf=0.72 2 EKRT 62.4: C=0.91±0.03, χ /ndf 2 npp xhard χ K-N 200 : 2.43, 0.14±0.01, 1.38 K-N 62.4: 2.01, 0.10±0.01, 0.41 MC Glauber Npart 100 200 300 400 (b) /ndf=3.07 2 EKRT 200 : C=0.75±0.02, χ /ndf=3.15 2 EKRT 62.4: C=0.81±0.03, χ /ndf 2 npp xhard χ K-N 200 : 2.43, 0.13±0.01, 0.12 K-N 62.4: 2.01, 0.08±0.01, 0.03 FIG. 23: (color online) The pseudo-rapidity multiplicity density per participant nucleon pair dNch/dη Npart/2 versus the number of participants Npart, with Npart calculated from the optical Glauber model (a) and from the MC Glauber model (b). Data are presented for Au+Au collisions at 62.4 GeV (black dots) and 200 GeV (red squares). The vertical errors are total uncertainties including uncertainties on Npart. The uncertainties on Npart (horizontal error bars) are smaller than the data point size. The solid curves are the K-N fit by Eq. (10) where xhard is a fit parameter and npp is fixed from Eq. (11). The dashed curves are the EKRT fit by Eq. (9) where C is a fit parameter. 26 TABLE VIII: Integrated multiplicity rapidity density, dN/dy, of identified particles and net-protons for various collision systems and centralities. Quoted errors are the quadratic sum of statistical and systematic uncertainties, and are dominated by the latter. System Centrality π − π + K− K+ p p p − p pp 200 GeV min. bias 1.42 ± 0.11 1.44 ± 0.11 0.145 ± 0.013 0.150 ± 0.013 0.113 ± 0.010 0.138 ± 0.012 0.025 ± 0.004 min. bias 4.63 ± 0.31 4.62 ± 0.31 0.582 ± 0.052 0.595 ± 0.054 0.412 ± 0.053 0.500 ± 0.069 0.088 ± 0.029 d+Au 40-100% 2.89 ± 0.20 2.87 ± 0.21 0.348 ± 0.032 0.356 ± 0.033 0.236 ± 0.030 0.281 ± 0.039 0.045 ± 0.018 200 GeV 20-40% 6.06 ± 0.41 6.01 ± 0.41 0.783 ± 0.085 0.803 ± 0.087 0.569 ± 0.082 0.72 ± 0.11 0.154 ± 0.050 0-20% 8.42 ± 0.57 8.49 ± 0.58 1.09 ± 0.09 1.11 ± 0.10 0.793 ± 0.087 0.95 ± 0.11 0.159 ± 0.049 70-80% 10.9 ± 0.8 10.8 ± 0.8 1.38 ± 0.13 1.41 ± 0.13 0.915 ± 0.081 1.09 ± 0.10 0.170 ± 0.030 60-70% 21.1 ± 1.6 21.1 ± 1.6 2.89 ± 0.26 2.98 ± 0.27 1.84 ± 0.16 2.20 ± 0.20 0.361 ± 0.061 50-60% 36.3 ± 2.8 36.2 ± 2.7 5.19 ± 0.47 5.40 ± 0.49 3.16 ± 0.29 3.88 ± 0.35 0.72 ± 0.11 Au+Au 40-50% 58.9 ± 4.5 58.7 ± 4.5 8.37 ± 0.78 8.69 ± 0.81 4.93 ± 0.46 6.17 ± 0.57 1.24 ± 0.18 30-40% 89.6 ± 6.8 89.2 ± 6.8 13.2 ± 1.3 13.6 ± 1.3 7.46 ± 0.72 9.30 ± 0.89 1.85 ± 0.30 200 GeV 20-30% 136 ± 10 135 ± 10 19.7 ± 2.0 20.5 ± 2.0 11.2 ± 1.1 14.4 ± 1.4 3.22 ± 0.51 10-20% 196 ± 15 194 ± 15 28.7 ± 3.1 30.0 ± 3.2 15.7 ± 1.7 20.1 ± 2.2 4.42 ± 0.77 5-10% 261 ± 20 257 ± 20 39.8 ± 4.6 40.8 ± 4.7 21.4 ± 2.5 28.2 ± 3.3 6.8 ± 1.3 0- 5% 327 ± 25 322 ± 25 49.5 ± 6.2 51.3 ± 6.5 26.7 ± 3.4 34.7 ± 4.4 8.0 ± 1.8 58-85% 16.0 ± 2.1 16.0 ± 1.9 2.23 ± 0.14 2.31 ± 0.15 1.31 ± 0.09 1.65 ± 0.11 0.347 ± 0.040 45-58% 42.4 ± 3.5 42.2 ± 3.5 5.81 ± 0.41 6.83 ± 0.48 3.33 ± 0.30 4.38 ± 0.39 1.05 ± 0.14 34-45% 70.9 ± 4.9 71.8 ± 5.0 10.1 ± 0.9 11.2 ± 1.0 5.51 ± 0.45 7.35 ± 0.60 1.85 ± 0.20 Au+Au 26-34% 104 ± 8 103 ± 8 15.0 ± 1.3 16.4 ± 1.4 8.02 ± 0.81 10.9 ± 1.1 2.91 ± 0.35 130 GeV 18-26% 140 ± 11 140 ± 11 20.5 ± 1.8 22.3 ± 1.9 10.5 ± 1.0 14.4 ± 1.3 3.94 ± 0.41 11-18% 187 ± 16 186 ± 16 26.6 ± 1.9 29.0 ± 2.1 12.8 ± 1.6 17.9 ± 2.2 5.09 ± 0.70 6-11% 228 ± 16 228 ± 16 33.1 ± 2.4 35.6 ± 2.6 15.7 ± 1.6 21.9 ± 2.3 6.25 ± 0.75 0-6% 280 ± 20 278 ± 20 42.7 ± 2.8 46.3 ± 3.0 20.0 ± 2.2 28.2 ± 3.1 8.24 ± 0.93 70-80% 7.43 ± 0.62 7.34 ± 0.62 0.813 ± 0.055 0.868 ± 0.058 0.464 ± 0.047 0.745 ± 0.086 0.280 ± 0.050 60-70% 14.7 ± 1.3 14.8 ± 1.3 1.74 ± 0.12 1.95 ± 0.13 0.960 ± 0.059 1.60 ± 0.12 0.639 ± 0.078 50-60% 26.8 ± 2.4 26.5 ± 2.3 3.31 ± 0.23 3.64 ± 0.25 1.68 ± 0.12 2.98 ± 0.22 1.30 ± 0.11 Au+Au 40-50% 43.7 ± 3.5 43.2 ± 3.5 5.68 ± 0.39 6.62 ± 0.46 2.77 ± 0.19 5.07 ± 0.36 2.30 ± 0.19 30-40% 67.4 ± 5.2 66.5 ± 5.1 8.89 ± 0.62 10.4 ± 0.7 4.27 ± 0.35 8.08 ± 0.67 3.81 ± 0.33 62.4 GeV 20-30% 101 ± 7 98.9 ± 6.9 14.0 ± 1.0 15.9 ± 1.1 6.39 ± 0.55 12.2 ± 1.1 5.86 ± 0.52 10-20% 146 ± 11 144 ± 11 19.8 ± 1.4 23.0 ± 1.6 8.77 ± 0.78 17.8 ± 1.6 9.07 ± 0.85 5-10% 192 ± 13 191 ± 13 27.2 ± 1.9 31.2 ± 2.2 11.4 ± 1.1 23.8 ± 2.4 12.4 ± 1.3 0-5% 237 ± 17 233 ± 17 32.4 ± 2.3 37.6 ± 2.7 13.6 ± 1.7 29.0 ± 3.8 15.4 ± 2.1 27 TABLE IX: Particle dN/dy ratios for various collision systems and centralities. Quoted errors are the quadratic sum of statistical and systematic uncertainties, and are dominated by the latter (except some of the antiparticle-to-particle ratios). System Centrality π −/π+ K−/K+ p/p K−/π− p/π− K+/π+ p/π+ pp 200 GeV min. bias 0.988 ± 0.043 0.967 ± 0.040 0.819 ± 0.047 0.102 ± 0.008 0.080 ± 0.006 0.104 ± 0.008 0.096 ± 0.008 min. bias 1.003 ± 0.031 0.979 ± 0.036 0.824 ± 0.061 0.126 ± 0.011 0.089 ± 0.011 0.129 ± 0.011 0.108 ± 0.015 d+Au 40-100% 1.008 ± 0.042 0.977 ± 0.037 0.841 ± 0.067 0.120 ± 0.011 0.082 ± 0.010 0.124 ± 0.012 0.098 ± 0.014 200 GeV 20-40% 1.007 ± 0.035 0.976 ± 0.041 0.787 ± 0.064 0.129 ± 0.014 0.094 ± 0.013 0.134 ± 0.014 0.120 ± 0.018 0-20% 0.993 ± 0.035 0.982 ± 0.036 0.833 ± 0.058 0.130 ± 0.011 0.094 ± 0.010 0.131 ± 0.011 0.112 ± 0.013 70-80% 1.003 ± 0.044 0.981 ± 0.049 0.843 ± 0.048 0.127 ± 0.010 0.084 ± 0.007 0.130 ± 0.011 0.100 ± 0.008 60-70% 1.003 ± 0.043 0.971 ± 0.040 0.836 ± 0.047 0.137 ± 0.011 0.087 ± 0.007 0.141 ± 0.011 0.104 ± 0.008 50-60% 1.002 ± 0.044 0.961 ± 0.040 0.815 ± 0.047 0.143 ± 0.011 0.087 ± 0.007 0.149 ± 0.012 0.107 ± 0.009 Au+Au 40-50% 1.003 ± 0.044 0.963 ± 0.039 0.799 ± 0.046 0.1
42 ± 0.012 0.084 ± 0.007 0.148 ± 0.012 0.105 ± 0.009 30-40% 1.005 ± 0.045 0.969 ± 0.040 0.801 ± 0.047 0.147 ± 0.013 0.083 ± 0.007 0.152 ± 0.013 0.104 ± 0.009 200 GeV 20-30% 1.008 ± 0.046 0.961 ± 0.039 0.777 ± 0.047 0.145 ± 0.013 0.082 ± 0.008 0.152 ± 0.014 0.107 ± 0.010 10-20% 1.012 ± 0.049 0.959 ± 0.041 0.780 ± 0.048 0.147 ± 0.015 0.080 ± 0.008 0.155 ± 0.016 0.104 ± 0.011 5-10% 1.014 ± 0.050 0.975 ± 0.046 0.759 ± 0.051 0.153 ± 0.017 0.082 ± 0.009 0.159 ± 0.017 0.110 ± 0.012 0-5% 1.015 ± 0.051 0.965 ± 0.048 0.769 ± 0.055 0.151 ± 0.018 0.082 ± 0.010 0.159 ± 0.019 0.108 ± 0.013 58-85% 0.996 ± 0.066 0.963 ± 0.050 0.790 ± 0.043 0.140 ± 0.018 0.082 ± 0.010 0.144 ± 0.016 0.103 ± 0.012 45-58% 1.004 ± 0.040 0.850 ± 0.047 0.760 ± 0.043 0.137 ± 0.011 0.078 ± 0.008 0.162 ± 0.013 0.104 ± 0.010 34-45% 0.988 ± 0.037 0.900 ± 0.044 0.749 ± 0.040 0.142 ± 0.013 0.078 ± 0.006 0.156 ± 0.014 0.102 ± 0.008 Au+Au 26-34% 1.003 ± 0.039 0.912 ± 0.045 0.734 ± 0.039 0.145 ± 0.014 0.077 ± 0.008 0.159 ± 0.015 0.106 ± 0.011 130 GeV 18-26% 1.002 ± 0.037 0.920 ± 0.045 0.727 ± 0.038 0.146 ± 0.014 0.075 ± 0.007 0.159 ± 0.015 0.103 ± 0.010 11-18% 1.003 ± 0.037 0.915 ± 0.046 0.716 ± 0.039 0.142 ± 0.012 0.069 ± 0.009 0.156 ± 0.013 0.096 ± 0.013 6-11% 1.003 ± 0.043 0.929 ± 0.045 0.715 ± 0.039 0.145 ± 0.010 0.069 ± 0.007 0.156 ± 0.011 0.096 ± 0.010 0-6% 1.008 ± 0.029 0.923 ± 0.037 0.708 ± 0.036 0.153 ± 0.010 0.071 ± 0.008 0.167 ± 0.011 0.101 ± 0.011 70-80% 1.012 ± 0.031 0.936 ± 0.036 0.623 ± 0.047 0.109 ± 0.009 0.063 ± 0.007 0.118 ± 0.010 0.101 ± 0.013 60-70% 0.990 ± 0.031 0.894 ± 0.037 0.600 ± 0.039 0.119 ± 0.010 0.065 ± 0.005 0.132 ± 0.011 0.108 ± 0.010 50-60% 1.011 ± 0.032 0.907 ± 0.038 0.563 ± 0.031 0.123 ± 0.011 0.063 ± 0.006 0.137 ± 0.012 0.113 ± 0.010 Au+Au 40-50% 1.012 ± 0.032 0.858 ± 0.036 0.546 ± 0.030 0.130 ± 0.010 0.063 ± 0.005 0.153 ± 0.012 0.117 ± 0.009 30-40% 1.014 ± 0.033 0.854 ± 0.036 0.529 ± 0.028 0.132 ± 0.010 0.063 ± 0.006 0.156 ± 0.012 0.121 ± 0.011 62.4 GeV 20-30% 1.023 ± 0.034 0.883 ± 0.036 0.522 ± 0.027 0.138 ± 0.010 0.063 ± 0.005 0.160 ± 0.011 0.124 ± 0.011 10-20% 1.013 ± 0.033 0.862 ± 0.037 0.492 ± 0.026 0.136 ± 0.010 0.060 ± 0.006 0.160 ± 0.012 0.124 ± 0.012 5-10% 1.007 ± 0.033 0.870 ± 0.036 0.481 ± 0.026 0.141 ± 0.010 0.060 ± 0.006 0.164 ± 0.011 0.125 ± 0.012 0-5% 1.018 ± 0.033 0.860 ± 0.035 0.469 ± 0.026 0.137 ± 0.010 0.057 ± 0.007 0.162 ± 0.012 0.125 ± 0.016 better. We obtain the fit fraction of hard collisions to be xhard = (7.8 ± 1.3)% and (12.8 ± 1.3)% for Au+Au collisions at 62.4 GeV and 200 GeV, respectively. We may evaluate the fraction of produced particles originating from hard collisions, within the framework of the K-N two-component model, as Fhard = xhard npp Ncoll dNch/dη , (12) yielding Fhard = (30 ± 5)% and (46 ± 5)% for the top 5% central Au+Au collisions at 62.4 GeV and 200 GeV, respectively. In our K-N two-component model study, we have used the charged particle multiplicity from NSD pp interactions in Eq. 11 and the Glauber model results calculated with the total pp cross-section. This is because singly diffractive nucleon-nucleon interactions also contribute to the total charged particle multiplicities in Au+Au collisions. If we use instead the Glauber data of σpp = 36 mb from Table II for 200 GeV, we obtain xhard = (15 ± 2)%. It should be noted that the K-N two-component model assumes the same average particle multiplicity per hard process in pp and Au+Au collisions. This assumption is likely invalid because jet-medium interactions induce a larger average multiplicity per hard process in Au+Au collisions with a softer energy distribution [67]. The size of this effect is dependent on centrality. This relative increase in particle multiplicity from hard processes would result in an overestimate of the fraction of hard component, especially for pp collisions. A two-component model study based on the multiplicity dependence of transverse rapidity spectra from pp collisions, assuming most of the charged particles are pions, has revealed a significantly smaller fraction of hard component [54]. It remains an open question how realistic the simple K-N two-component model is for heavy-ion collisions. An improved two-component model would be to use the total transverse energy instead of the total particle multiplicity as the total transverse energy likely remains the same with jet modification processes. However, such a model would need as input the total transverse energy in inelastic pp collisions which is not well measured. It is worth noting that the normalized pseudo-rapidity density dNch/dη Npart/2 in the EKRT parameterization has only the overall scale C as a free parameter. The centrality dependence is fixed by N0.92 part . In the K-N parameteriza- 28 tion, on the other hand, the overall scale is fixed by npp, while the centrality dependence changes with the free parameter xhard. However, the npp value is obtained from parameterization to elementary collision data, and thus is designed to describe the overall scale of the heavyion data. As shown in Fig. 23, due to the uncertainties from the Glauber calculations, we cannot explicitly rule out either of the models. However, recent developments in analyzing the small systems (Cu+Cu) indicate that MC Glauber model is preferred, albeit with its own caveats as mentioned before. This in turn favors the twocomponent model and initial state gluon saturation [68] over the EKRT model. D. Bjorken Energy Density Estimate The central rapidity region is approximately boost invariant [17]. Under boost invariance, the energy density of the central rapidity region in the collision zone at formation time τ can be estimated by the Bjorken energy density [2]: ǫBj = dE⊥ dy 1 S⊥τ , (13) where E⊥ is the total transverse energy and S⊥ is the transverse overlap area of the colliding nuclei. Since we do not measure transverse energy, but only charged particle transverse momenta, we use the approximation dhE⊥i dy ≈ 3 2 hm⊥i dN dy π± + 2 hm⊥i dN dy K±,p,p¯ . (14) Here, we calculate hm⊥i = p hp⊥i 2 + m2 from the π ±, K±, p, and ¯p average transverse momenta presented in this work and in Refs. [17, 18, 19, 20]. The factors 3/2 and 2 compensate for the neutral particles. Isospin effects are estimated to be less than 2% and are neglected. Propagation of systematic uncertainties is done in the same way as for the total dNch/dy discussed in Section V B, i.e. the extrapolation uncertainties are correlated between particle and antiparticle and uncorrelated between different particle species, and the overall reconstruction efficiency is correlated for all particle species. The uncertainties on the hp⊥i are not included because they come from extrapolation of the spectra, similar to those on the dNch/dy, and are already applied to the dNch/dy. Figure 24 shows the product of the Bjorken energy density and the formation time as a function of Npart. For the top 5% central collisions, ǫBj · τ = 3.7±0.3 GeV/fm2 at collision energy 62.4 GeV, 4.4 ± 0.3 GeV/fm2 at 130 GeV (not shown), and 5.2±0.4 GeV/fm2 at 200 GeV. Our 130 GeV value is in good agreement with the value ǫBj · τ = 4.6 GeV/fm2 quoted in Ref. [69] for the most central 2% inelastic collisions. These estimated Bjorken energy densities are at least several GeV/fm3 with a formation time τ < 1 fm/c. They well exceed the phase transition energy density of 1 GeV/fm3 predicted by Lattice QCD [3]. Npart 0 50 100 150 200 250 300 350 400 ] 2 [GeV/fm τ× BJ ∈ 0 1 2 3 4 5 6 Au+Au 200 GeV Au+Au 62.4 GeV FIG. 24: Estimate of the product of the Bjorken energy density and the formation time (ǫBj ·τ ) as a function of centrality Npart. Errors shown are the quadratic sum of statistical and systematic uncertainties. At the top SPS energy, the formation time is traditionally taken as τ = 1 fm/c resulting in ǫBj = 3.2 GeV/fm3 for central Pb+Pb collisions [70]. At RHIC, the choice of τ is still a matter of debate. While Ref. [71] uses τ = 0.6 fm/c for their hydr
odynamic model (√sNN = 200 GeV), Ref. [72] uses τ = 0.2 fm/c, evaluated from the energy loss of high-p⊥ π 0 in √sNN = 130 GeV Au+Au collisions. Because of these uncertainties in τ, the Bjorken energy density estimate should be taken with caution, in addition to the assumptions of Bjorken longitudinal boost invariance and formation of a thermalized central region at an initial time τ. It should be noted that due to final state interactions, measured (final) total transverse energies are expected to be less than initial ones [73]. E. Antiparticle-to-Particle Ratios Relative particle production can be studied by particle ratios of the integrated dN/dy yields. Figure 25 shows the antiparticle-to-particle ratios (π −/π+, K−/K+, and p/p) as a function of the charged particle multiplicity in pp, d+Au at 200 GeV and Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. The 200 GeV and some of the 130 GeV data have been presented before [17, 45, 49]. The π −/π+ ratio is approximately 1 for all measured collision systems and collision energies. The ratios are independent of multiplicity and centrality. Similar behavior has been observed at lower collision energies as well. The K−/K+ ratios are close to 1 in pp, d+Au and Au+Au collisions at 200 GeV. The ratio decreases slightly from 200 GeV to 62.4 GeV Au+Au data. This may be due to the increasing net baryon density in the 29 collision zone which leads to differences in associated production of kaons. There appears to be a decreasing trend with centrality in the 62.4 GeV data, presumably due to a significant increase in the net baryon density. The p/p ratio appears to be independent of multiplicity in pp and d+Au collisions at 200 GeV. The ratio in peripheral Au+Au at 200 GeV is similar to that in pp and d+Au collisions at the same energy. A slight decrease is observed with increasing centrality in Au+Au collisions at 200 GeV and 130 GeV. The ratio is significantly lower at 62.4 GeV and shows a considerable drop with increasing centrality. The drop of the p/p ratio with increasing centrality is consistent with larger baryon stopping in central collisions. Figure 26 shows the K−/K+ ratio versus the p/p ratio, together with results from other energies [74, 75, 76, 77, 78, 79]. Both ratios are affected by the net baryon content; they show a strong correlation as seen in Fig. 26. This can be simply understood in the chemical equilibrium model where particle ratios are governed by only a few parameters. This aspect will be discussed in section VII. It is worth to note that at low energies, the absorption of antiprotons in the baryon-rich environment plays a vital role. F. Baryon Production and Transport The antiproton is the lightest antibaryon. Most high mass antibaryons decay into antiprotons. The p/π− ratio, therefore, characterizes well antibaryon production relative to total particle multiplicity. As mentioned earlier, the inclusive p yield reported here is the sum of the primordial p yield and the weak-decay contributions. Because all decay (anti)protons are measured in the data sample, the weak-decay contribution can be estimated as 0.64 ·(Λ+Σ 0 +Ξ+Ω + )+ 0.52 ·Σ − . With the assumption of isospin symmetry with n ≈ p and Σ 0 ≈ Σ + ≈ Σ − , one may estimate the total antibaryon rapidity density to be approximately twice the measured antiproton rapidity density [19], and the total net-baryon density to be approximately twice the total net-proton density. The assumption of isospin symmetry is fairly good for Au+Au collisions, and should be good for pp collisions at high energy because of the efficient charge exchange reactions to convert between protons and neutrons [80]. Figure 27 shows the p/π− ratio as a function of event multiplicity in pp, d+Au and Au+Au collisions. The ratio at 200 GeV is found to be independent of centrality and is the same for pp, d+Au, and Au+Au collisions within the experimental uncertainties. The values of the p/π− ratio at 62.4 GeV are lower than those at 200 GeV at all centralities, indicating the significant effect of collision energy on the production of heavy particles even at these high energies. Although the net-baryon density increases with centrality, especially at 62.4 GeV with narrower rapidity gap between the beams, the p/π− ratio does not seem to be affected much by the net-baryon /dy ch dN 10 2 10 3 10 + π/ – π 0.9 0.95 1 1.05 1.1 1.15 pp 200 GeV MB d+Au 200 GeV d+Au 200 GeV MB Au+Au 200 GeV Au+Au 130 GeV Au+Au 62.4 GeV /dy ch dN 10 2 10 3 10 + -/K K 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 pp 200 GeV MB d+Au 200 GeV d+Au 200 GeV MB Au+Au 200 GeV Au+Au 130 GeV Au+Au 62.4 GeV /dy ch dN 10 2 10 3 10 /p p 0.4 0.5 0.6 0.7 0.8 0.9 1 pp 200 GeV MB d+Au 200 GeV MB d+Au 200 GeV Au+Au 200 GeV Au+Au 130 GeV Au+Au 62.4 GeV FIG. 25: Antiparticle-to-particle ratios as a function of dNch/dy for pp and d+Au collisions at 200 GeV and Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. Errors shown are the quadratic sum of statistical and systematic uncertainties. density, suggesting that antibaryon absorption is not a significant effect at these energies. At the lower AGS and SPS energies the p/π− has a much stronger decreasing trend with increasing centrality [81]; baryon stopping and the effect of net-baryon density are much stronger at low energies. It has been argued that production of antibaryons, due to their large masses, is sensitive to energy den- 30 p/p -4 10 -3 10 -2 10 -1 10 1 + -/K K -1 10 1 STAR: pp 200 GeV STAR: d+Au 200 GeV STAR: 200 GeV STAR: 130 GeV STAR: 62.4 GeV BRAHMS: 200 GeV NA44: 17 GeV NA49: E scan E866: 5 GeV 0.21 = (p/p) + /KK 0 0.2 0.4 0.6 0.8 1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 FIG. 26: (color online) Ratio of charged kaons versus that of antiprotons to protons at various energies. Errors shown are the quadratic sum of statistical and systematic uncertainties. The line is a power-law fit to the data except the AGS data point (the inverse solid triangle) and the two lowest energy SPS data points (solid squares) which have significant baryon absorption effect. The insert is a linear plot. /dy ch dN 10 2 10 3 10 ratios + π and p/ – π/p 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 + p/π – /p π pp 200 GeV MB d+Au 200 GeV MB d+Au 200 GeV + p/π – /p π Au+Au 62.4 GeV Au+Au 130 GeV Au+Au 200 GeV FIG. 27: (color online) The p/π+ and p/π− ratios as a function of the charged particle multiplicity in pp, d+Au and Au+Au collisions. Errors shown are the quadratic sum of statistical and systematic uncertainties. sity. An increased antibaryon production relative to total entropy with increasing centrality at the same collision energy could indicate formation of high energy density, or QGP in central collisions. On the hadronic level, at high pion density, multiple-pion fusion into baryonantibaryon pairs could contribute significantly to the antibaryon yield [82]. Such an increase with centrality is not observed in data, but could be canceled by the effect of positive net-baryon density, resulting in antibaryon absorption. On the other hand, antibaryon production does increase with the collision energy. However, this cannot be taken as evidence of QGP formation as antibaryon production is very sensitive to the available energy for production due to their large mass. Indeed, antibaryon production in elementary collisions is found to be a sensitive function of the collision energy. Figure 27 also shows the p/π+ ratio as a function of the charged particle multiplicity. The p/π+ ratio is found to be constant over centrality at 130 GeV and 200 GeV, and shows an increasing trend with centrality at 62.4 GeV. The p/π+ ratio is found to be the same in pp, d+Au, and Au+Au collisions at 200 GeV within our experimental uncertainties. Unlike antibaryons, baryons come from two sources: pair production together with antibaryons and transport from the initial colliding nuclei at beam rapidities. The latter can be obtained from the difference between baryon and antibaryon yields. Figure 27 indicates a finite net-baryon number is present at mid-rapidity in all collisions. A finite baryon number has been
transported over ∼ 3-5.4 units of rapidity in these collisions. How baryons are transported over many units of rapidity has been a long-standing theoretical issue [83, 84, 85]. Baryon transport occurs very early in the collision and affects the subsequent evolution of the collision system. Further understanding of baryon transport can shed more light on the evolution of heavy-ion collisions. Npart 1 10 2 10 /dy p p- ) dN part (2/N 0 0.02 0.04 0.06 0.08 0.1 0.12 Au+Au 62.4 GeV Au+Au 130 GeV Au+Au 200 GeV pp MB 200 GeV FIG. 28: The ratio of mid-rapidity net-protons to half of the number of participants versus the number of participants in pp collisions at 200 GeV and in Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. Errors shown are the quadratic sum of statistical and systematic uncertainties. Figure 28 shows the ratio of the number of net-protons (p−p) to half the number of participant nucleons, i.e. the approximate probability of each incoming nucleon to be transported to mid-rapidity, as a function of Npart. The probability is non-zero even in pp collisions at 200 GeV. Compared to pp, the probability is larger in central heavy-ion collisions at the same energy by a factor ∼ 2. 31 The probability of baryon transport to mid-rapidity is larger in the lower 62.4 GeV collisions, due to the smaller beam rapidity. Our data demonstrate that baryon-antibaryon pair production and baryon stopping are two independent processes: The baryon-antibaryon pair production rate does not depend on the collision centrality and increases with the collision energy, whereas the baryon stopping increases with the collision centrality and decreases with the collision energy. The net-baryon density due to baryon stopping may have an effect on the final observed yield of antibaryons because of absorption. However, this effect does not seem to be significant at our measured energies. beam δy = y 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 /dy p p- ) dN part (2/N -1 10 AGS E802 SPS NA49 RHIC STAR RHIC BRAHMS 0.99 exp(-0.60 δy) FIG. 29: The ratio of mid-rapidity inclusive net-protons to half of the number of participants in central heavy-ion collisions as a function of the rapidity shift. The AGS data is taken from Refs. [75, 86], SPS data from Refs. [87, 88, 89], and BRAHMS data from Ref. [90]. The published SPS data have already been corrected for weak-decays, the size of which is of the order 20-25% [88], so we have added 25% to the published net-proton yields to obtain the inclusive ones. Errors shown are total statistical and systematic uncertainties. The dashed line is an exponential fit to the data. Proton and antiproton production has been measured in heavy-ion collisions at lower energies. Figure 29 shows the ratio of mid-rapidity inclusive net-proton density to half of the number of participants in central Au+Au collisions as a function of the beam rapidity (i.e. the rapidity shift suffered by those net-protons). The measured NA49 data have been corrected for weak-decays, which is dominated by weak-decay protons, the size of which is of the order 20-25% [88]. In order to obtain the inclusive net-proton yield, we multiplied the measured NA49 data by a factor 1.25. All other data are inclusive measurements already including weak-decay products. The ratio (or the approximate probability of each nucleon to be transported to mid-rapidity) drops rapidly with increasing rapidity shift. The dashed line is an exponential fit to the data, yielding dNp−p/dy Npart/2 = 0.99 exp(−0.60δy). One may view the net-proton density versus rapidity shift, obtained from central collisions at different energies, as a “measure” of the rapidity distribution of netprotons in central Au+Au collisions at the top RHIC energy. Since the net-protons shown in Fig. 29 contain equal contributions from the two colliding nuclei, the netproton rapidity distribution in Au+Au collisions at the top RHIC energy is the data points in Fig. 29 multiplied by a factor varying between 1/2 and 1. At small δy ∼ 0 the net-proton density should be close to 1/2 of those shown in Fig. 29, and at large δy (i.e. nearly mid-rapidity) the factor should be close to 1. Assuming an exponential variation in this factor between 1/2 and 1, i.e. a net-proton rapidity distribution of dNp−p/dy Npart/2 = 2 δy/5.36−1 × 0.99 exp(−0.60δy) = 0.50 exp(−0.47δy) in 200 GeV Au+Au collisions (where 5.36 is the beam rapidity for 100 GeV beams), we estimate a rapidity shift of hδyi = 1/0.47 ≈ 2.1. It is interesting to note that the integral of the above rapidity distribution between 0 and 5.36 comes out to be rather close to unity as required by proper normalization. Clearly the exponential form we used is a simplification. BRAHMS has measured the rapidity distribution of net-protons in the range 0 < y < 3 in central Au+Au collisions at 200 GeV, and used a more sophisticated functional form to estimate the average rapidity shift to be approximately 2.06 ± 0.16 [90]. G. Strangeness Production Strangeness has a special place in heavy-ion physics. Enhanced production of strangeness has long been predicted as a prominent signature of QGP formation. In a hadron gas strangeness has to be produced via strange hadron pairs which require a large energy, while in QGP it can be produced via a strange quark-antiquark pair, which is energetically favored [91, 92, 93]. Elementary pp collisions, where QGP formation is unlikely, are important as a reference: an enhanced strangeness production in heavy-ion collisions relative to pp could signal QGP formation. However, other processes can also enhance strangeness production as shown by many studies [94, 95]. Although not a sufficient signature for QGP formation, strangeness enhancement is a necessary condition which QGP formation requires. Strangeness production and the K/π ratios have been intensively studied in heavy-ion collisions at the AGS [76, 96, 97, 98] and the SPS [77, 99, 100, 101, 102, 103, 104, 105], and in elementary interactions of pp [106, 107] and pp [108, 109], prior to RHIC [17, 18, 110]. Figure 30(a) compiles the K/π ratios in pp collisions and central heavy-ion collisions as a function of the collision energy √sNN . The 200 GeV pp and Au+Au data are from Ref. [17], and the Au+Au data at 62.4 GeV and 130 GeV are from this work. The K/π ratio was already studied in Ref. [18], but there the pion yield was not measured but estimated from negatively charged hadrons, kaons, and antiprotons. In this work the measured pion 32 yield is used to obtain the K/π ratio. The other data in Fig. 30 are taken from Refs. [106, 107, 108, 109] for pp collisions and Refs. [17, 76, 77, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105] for central heavy-ion collisions, as also compiled in Ref. [18]. [GeV] NN s 1 10 2 10 3 10 π K/ 0 0.05 0.1 0.15 0.2 0.25 0.3 – /π – /π + Filled: K + Open: K AGS Au+Au SPS Pb+Pb STAR Au+Au ISR pp STAR pp 0.68 -2.26) NN 0.051 ln( s /NDF=27/9 2 χ (a) [GeV] NN s 1 10 2 10 3 10 – /K + K 1 10 AGS Au+Au SPS Pb+Pb STAR Au+Au 1.69 -1.24) NN ln( s +21.9) NN ln( s 1.02 /NDF=20/9 2 χ (b) FIG. 30: (a) The K+/π+ and K−/π− ratios as a function of the collision energy in pp [106, 107, 108, 109] and central heavy-ion collisions. (b) The K+/K− ratio as a function of the collision energy in central heavy-ion collisions. The heavy-ion data not covered in this work are taken from Refs. [17, 76, 77, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105]. The error bars on the heavy-ion data are the quadratic sum of statistical and systematic uncertainties, and are statistical only on the elementary collision data. The curves going through the heavy-ion K−/π− and K+/K− data are phenomenological fits. The curves going through the heavy-ion K+/π+ data are the product of the fit curves. See text for details. One obvious feature in Fig. 30(a) is that the K−/π− ratio in heavy-ion collisions steadily increases with √sNN , while K+/π+ sharply increases at low energies. The addition of the K+/π+ measurements at RHIC energies clearly demonstrates that K+/π+ drops at high energies. A maximum K+/π+ value is reached at about √sNN ≈ 10 Ge
V. This behavior of K+/π+ can be partially attributed to the net-baryon density which changes signifi- cantly with √sNN , as noted previously [111, 112, 113]. It is instructive to consider the two possible kaon production mechanisms: pair production of K and K which is sensitive to √sNN , and associated production of K (K) with a hyperon (antihyperon) which is sensitive to the baryon (antibaryon) density2 . The excess of K over K is due to the finite net-baryon density. To visualize the relative contributions from these two mechanisms, Fig. 30(b) shows the ratio of K+/K− as function of √sNN in central heavy-ion collisions. The ratio sharply drops with energy, demonstrating the transition from associated production of K+ dominant at low energies to the dominance of equal production of K+ and K− via either pair production of K+K− or associated production of K+ (K−) with hyperon (antihyperon) at high energies. The K+/K− dependence on √sNN is relatively smooth, and can be fit reasonably well by the functional form shown in the figure. On the other hand, the rate of symmetric production of K+ and K− increases with √sNN as seen in the K−/π− ratio in Fig. 30(a). We fit the K−/π− ratio by the functional form shown in the figure as the solid curve. The curve describes the data points well except at low √sNN , where the K−/π− ratio can be better described by a linear increase in log(√sNN ) as shown by the dashed line. The product of the curve in Fig. 30(b) and the solid curve (dashed line) in Fig. 30(a) yields the dotted (dash-dotted) curve in Fig. 30(a). It suggests that the smooth dropping of K+/K− with √sNN in Fig. 30(b) and the seemingly smooth increase of K−/π− with √sNN can generate a maximum in K+/π+ at √sNN ∼ 10 GeV. In fact, model studies [112, 113] have indeed shown a maximum in the K+/π+ excitation function. However, the maximum peak from model studies is broad and smooth, not as sharp as Fig. 30(a) shows. NA49 has first observed the sharp maximum peak structure in the K+/π+ ratio [77], and referred to it as the “horn”. They attribute the horn to a phase-transition between hadrons and the QGP, because ordinary physics (involving production rate and baryon density) does not seem to explain the data. The smooth dependence of the K+/K− ratio on √sNN indicates that the horn is not K+/π+ specific, but is also present in the K−/π− ratio as can be seen in Fig. 30(a). In order to shed light on the horn, more precise measurements are needed for which the RHIC energy scan program should help. Figure 30(a) indicates that the enhancement in K−/π− from elementary pp to central heavy-ion collisions is about 50% and is similar at the SPS and RHIC, while that in K+/π+ is larger at lower energies due to the large net-baryon density in heavy-ion collisions. The increase in K/π ratios from pp to central heavy-ion collisions has been argued as due to canonical suppression of strangeness production in small-volume pp collisions [114, 115, 116, 117]. Although the increase in the K/π ratios from pp to central heavy-ion collisions cannot be readily taken as evidence for QGP formation, it is in- 2 These mechanisms also apply at the quark level. 33 teresting to study how and where the increase happens as a function of centrality. Figure 31 shows the K−/π− ratio as a function of the charged hadron multiplicity in pp, d+Au, and Au+Au collisions at RHIC energies. The K+/π+ ratio shows similar dependence on centrality. The K−/π− ratio appears to increase approximately linearly with log(dNch/dy). /dy ch dN 10 2 10 3 10 – π/ – K 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 pp 200 GeV MB d+Au 200 GeV MB d+Au 200 GeV Au+Au 62.4 GeV Au+Au 130 GeV Au+Au 200 GeV FIG. 31: The K−/π− ratio as a function of the charged particle rapidity density in pp, d+Au and Au+Au collisions at RHIC. Errors shown are the quadratic sum of statistical and systematic uncertainties. Npart 10 2 10 – π/ – K 0 0.05 0.1 0.15 0.2 STAR Au+Au 200 GeV STAR Au+Au 130 GeV STAR Au+Au 62.4 GeV E866 Au+Au 4.7 GeV E859 Si+Al 5.4 GeV NA49 Pb+Pb 17.3 GeV NA49 Pb+Pb energy scan NA49 S+S 20 GeV NA49 C+C/Si+Si 17.3 GeV FIG. 32: (color online) The K−/π− ratio as a function of the number of participants Npart in heavy-ion collisions at the AGS [76, 97], the SPS [77, 100, 101, 102, 103, 104, 105], and RHIC. Errors shown are the quadratic sum of statistical and systematic uncertainties for the RHIC data, and only statistical for the AGS and SPS data. Experiments at the AGS and SPS have also studied the centrality dependence of kaon production in heavyion collisions. Figure 32 shows those results as a function of the number of participants, Npart, together with our results at RHIC. The K−/π− ratio increases with Npart within the same collision system3 . The increase happens rather quickly at RHIC, restricted to very peripheral collisions; little variation with centrality is found from medium-central to central collisions. At lower energies, the K−/π− ratio increases steadily with Npart. However at the same value of Npart, the ratio differs in different systems at similar energies as shown in Refs. [76, 101], indicating that Npart is not an appropriate variable to describe K−/π−. This has been noted and emphasized before [76, 101]. ] -2 /dy)/S [fm π (dN 0 2 4 – π/ – K 0 0.05 0.1 0.15 STAR Au+Au 200 GeV STAR Au+Au 130 GeV STAR Au+Au 62.4 GeV NA49 Pb+Pb 17.3 GeV NA49 Pb+Pb energy scan NA49 S+S 20 GeV NA49 C+C/Si+Si 17.3 GeV E866 Au+Au 4.7 GeV E859 Si+Al 5.4 GeV FIG. 33: (color online) The K−/π− ratio as a function of dNπ/dy S⊥ in heavy-ion collisions at the AGS [76, 97], the SPS [77, 100, 101, 102, 103, 104, 105], and RHIC. Errors shown are the quadratic sum of statistical and systematic uncertainties for the RHIC data, and statistical only for the AGS and SPS data. Neither charged hadron multiplicity nor the number of participants can satisfactorily describe the systematics of the K−/π− ratio. It is desirable to search for a quantity that better describes the systematics. We first note that strangeness production may be enhanced due to the fast and energetically favorable process of gluon-gluon fusion into strange quark-antiquark pairs, and therefore may be sensitive to the initial gluon density. Indeed, it has been argued that particle production at RHIC (and perhaps at SPS) is dominated by the gluon saturation region [118, 119]. At high energies, the only relevant quantity in the gluon saturation picture is dNπ/dy S⊥ , which is approximately proportional to the number of nucleon-nucleon collisions per participant as mentioned earlier. Motivated by these considerations, Fig. 33 shows the K−/π− ratio as a function of dNπ/dy S⊥ . It is interesting to note that the K−/π− ratio linearly increases with dNπ/dy S⊥ in the AGS and SPS energy regime. The 3 Systematic uncertainties on the K/π ratio are largely correlated. The 130 GeV data may miss a very peripheral but crucial data point. 34 RHIC data show a different behavior: the K−/π− ratio increases from pp to peripheral Au+Au collisions, but quickly saturates in medium central to central collisions. In the gluon saturation picture, it is possible that the initial gluon density is saturated at RHIC energies [119]. As the saturation scale becomes large, the difference between kaon and pion masses becomes less important, resulting in a roughly constant K−/π−. Gluon saturation may already be relevant in central Pb+Pb collisions at the top SPS energy [119]. Gluon saturation should be irrelevant at AGS energies, as gluons can be distinguished longitudinally and quark contribution to particle production is significant. However, the fact that Si+Al and Au+Au data are on top of each other in Fig. 33 indicates that dNπ/dy S⊥ may be the relevant quantity for K−/π− at the AGS, although the interpretation may be different from that at high energies. VII. FREEZE-OUT PROPERTIES In this section, particle ratios are used in the context of a thermal equilibrium model [120, 121, 122, 123] to extract ch
emical freeze-out properties. The extracted blastwave model fit parameters are investigated to learn about the kinetic freeze-out properties. The systematics of the chemical and kinetic freeze-out properties extracted from data within the model frameworks are studied, and implications of these results in terms of the system created in heavy-ion collisions are discussed. A. Chemical Freeze-out Properties In the chemical equilibrium model, particle abundance in a thermal system of volume V is governed by only a few parameters, Ni/V = gi (2π) 3 γ Si S Z 1 exp Ei−µBBi−µS Si Tchem ± 1 d 3 p , (15) where Ni is the abundance of particle species i, gi is the spin degeneracy, Bi and Si are the baryon number and strangeness number, respectively, Ei is the particle energy, and the integral is over the whole momentum space. The model parameters are the chemical freezeout temperature (the temperature of the system), Tchem, the baryon and strangeness chemical potentials, µB and µS, respectively, and the ad-hoc strangeness suppression factor, γS. The measured particle abundance ratios are fit by the chemical equilibrium model. The ratios included in the fit are: π −/π+, K−/K+, p/p, K−/π−, p/π−. The fit is performed for each collision system and each multiplicity or centrality class. The extracted chemical freeze-out parameters are summarized in Table X. The 200 GeV pp and Au+Au results are from Ref. [17]. Figure 34(a) shows the extracted baryon and strangeness chemical potentials as a function of the charged particle multiplicity in pp and d+Au at 200 GeV, and Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. The baryon chemical potential increases with centrality in heavy-ion collisions, especially at 62.4 GeV. This is already indicated by the p/p ratio in Fig. 25. The strangeness chemical potential is small and close to zero. It is mainly reflected in the K/π and K−/K+ ratios. As already shown in Fig. 26, the K−/K+ ratio is correlated with the p/p ratio by a universal curve. In the chemical equilibrium picture without considering resonance decays, these ratios are simply equal to K−/K+ = exp[(−2µB/3 + 2µS)/Tchem] and p/p = exp(−2µB/Tchem), respectively. Weak decays and resonance decays complicate the situation, but the effects of decays are small for the K−/K+ and p/p ratios. A power-law fit to all data points in Fig. 26 (except the AGS data point and the two lowest SPS data points) yields K−/K+ ∝ (p/p) 0.21. This gives µS/µB ≈ 0.12 in the chemical equilibrium picture. We show in Fig. 34(b) the ratio of the extracted µS to µB. A fit to a constant indeed shows µS/µB = 0.110±0.019. Analyses of chemical freeze-out parameters in heavy-ion collisions at other energies indicate a similar relationship [124]. The strong correlation between µS and µB should not come as a surprise, as the (anti)hyperons couple these two parameters naturally. However, the same relationship holding for different energies is not expected a priori. Figure 35 shows the extracted strangeness suppression factor γS as a function of the charged particle multiplicity. The γS in pp, d+Au, and peripheral Au+Au collisions is significantly smaller than unity, suggesting that strangeness production is strongly suppressed in these collisions. The γS factor increases with centrality, reaching a value in central Au+Au collisions that is not much smaller than unity. This suggests that strangeness production in central collisions is no longer strongly suppressed; strangeness is nearly chemically equilibrated with the light flavors. The extracted chemical freeze-out temperature is shown in Fig. 36. A striking feature is that the chemical freeze-out temperature is independent of collision system or centrality. In each system investigated the extracted chemical freeze-out temperature is Tchem ≈ 156 MeV which is close to the Lattice QCD calculation of the cross-over temperature between the deconfined phase and the hadronic phase for three flavors (154 ± 8 MeV) [125]. On the other hand, the initial conditions in Au+Au collisions of different centralities (and at different energies) are very different. In other words, systems starting off with different initial conditions always evolve toward a ‘universal’ condition at chemical freeze-out, independent of the initial conditions [17]. The proximity of the fit Tchem and the predicted phase-transition temperature strongly suggests that chemical freeze-out happens at the phase-transition boundary, or hadronization. Indeed, hadronization should be universal. 35 /dy ch dN 10 2 10 3 10 [MeV] B,S µ -20 0 20 40 60 80 100 Au+Au 62.4 GeV Au+Au 130 GeV Au+Au 200 GeV pp 200 GeV MB d+Au 200 GeV MB d+Au 200 GeV : black B µ : red S µ (a) /dy ch dN 10 2 10 3 10 B µ / S µ -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 pp 200 GeV MB d+Au 200 GeV MB d+Au 200 GeV Au+Au 62.4 GeV Au+Au 130 GeV Au+Au 200 GeV (b) 0.110 ± 0.019 FIG. 34: (color online) (a) Baryon (µB) and strangeness (µS) chemical potentials extracted from chemical equilibrium model fits to pp and d+Au data at 200 GeV, and Au+Au data at 62.4 GeV, 130 GeV, and 200 GeV. (b) Ratio µS/µB of the extracted chemical potentials. Errors shown are the total statistical and systematic errors. The 200 GeV pp and Au+Au fit results are taken from Ref. [17]. /dy ch dN 10 2 10 3 10 S γ 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 pp 200 GeV MB d+Au 200 GeV MB d+Au 200 GeV Au+Au 200 GeV Au+Au 130 GeV Au+Au 62.4 GeV FIG. 35: Strangeness suppression factor extracted from chemical equilibrium model fit to pp and d+Au data at 200 GeV, and Au+Au data at 62.4 GeV, 130 GeV, and 200 GeV. Errors shown are the total statistical and systematic uncertainties. The 200 GeV pp and Au+Au fit results are taken from Ref. [17]. The success of the chemical equilibrium model in describing the data should not be readily taken as a proof of chemical equilibrium of each individual collision [126]. In pp (and other elementary) collisions the compositions of most particles are described well by the chemical equilibrium model but with the ad-hoc strangeness suppression factor significantly smaller than unity. This has been argued as due, in part, to canonical suppression from conservation of strangeness in small volumes [114, 115, 126]. Canonical suppression appears to explain elementary e +e − data, while additional suppression seems needed to account for strangeness production in pp collisions. The apparent success of the chemical equilibrium model in describing elementary collisions, despite the strangeness suppression factor, in all likelihood suggests that particle production in these collisions is a statistical process, and the chemical temperature is a parameter governing the statistical production processes [126]. On the other hand, the stringent constrains of conservation laws are largely lifted in heavy-ion collisions as they only need to be satisfied globally over a large volume. As a result particle ensembles can be treated in a grand canonical framework. The chemical equilibrium model can describe the abundances of all stable hadrons. The ad-hoc strangeness suppression factor extracted from central heavy-ion collisions is close to unity, implying that strangeness is as equally equilibrated as light quarks. Moreover, many experimental results indicate that the medium created at RHIC is strongly interacting [6], which will naturally lead to thermalization. Thus the success of the chemical equilibrium model may indeed suggest that the individual Au+Au collisions are largely thermalized. B. Kinetic Freeze-out Properties The measured p⊥ spectral shape flattens significantly with increasing particle mass in central Au+Au collisions. This suggests the presence of a collective transverse radial flow field, although other physics mechanisms such as (semi-)hard scatterings also contribute. As shown in Figs. 18 and 19, the spectra are well described by the hydrodynamics-motivated blast-wave model [127, 128, 129, 130, 131, 132, 133]. The blastwave model makes the simple assumption that particles are locally thermalized at a kinetic freeze-out temperature and are moving with a common
collective transverse radial flow velocity field. The common flow velocity field results in a larger transverse momentum of heavier particles, leading to the change in the observed spectral shape with increasing particle mass. Assuming a hard-sphere uniform density particle source with a kinetic freeze-out temperature Tkin and a transverse radial flow velocity β, the particle transverse 36 TABLE X: Chemical and kinetic freeze-out properties in pp and d+Au collisions at 200 GeV, and Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. Quoted errors are the total statistical and systematic uncertainties. The 200 GeV pp and Au+Au data are taken from Ref. [17]. System Centrality Tchem (MeV) µB (MeV) µS (MeV) γS χ 2 /ndf Tkin (MeV) hβi n χ2 /ndf pp 200 GeV min. bias 157.5 ± 3.6 8.9 ± 3.8 2.3 ± 3.6 0.56 ± 0.04 0.81 127 ± 13 0.244 ± 0.081 4.3 ± 1.7 1.18 min. bias 164+11 −8 16.5 ± 6.5 3.3 ± 3.6 0.69 ± 0.07 0.013 112 ± 26 0.407 ± 0.033 1.9 ± 0.9 0.89 d+Au 40-100% 159+10 −7 14.4 ± 6.7 2.5 ± 3.6 0.66 ± 0.07 0.051 112 ± 24 0.377 ± 0.031 2.2 ± 1.3 1.55 200 GeV 20-40% 168+14 −10 21.0 ± 7.6 4.2 ± 4.1 0.71 ± 0.08 0.068 107 ± 33 0.428 ± 0.067 1.9 ± 0.9 1.32 0-20% 167+12 −7 15.8 ± 6.3 3.2 ± 3.6 0.71 ± 0.07 0.069 116 ± 21 0.420 ± 0.030 1.6 ± 0.7 0.72 70-80% 157.9 ± 3.9 14.1 ± 4.2 2.8 ± 2.6 0.70 ± 0.06 0.51 129 ± 14 0.358 ± 0.084 1.50 ± 0.28 0.70 60-70% 158.7 ± 4.1 15.3 ± 4.2 2.3 ± 2.6 0.76 ± 0.06 0.51 118 ± 13 0.405 ± 0.071 1.57 ± 0.11 0.42 50-60% 158.8 ± 4.1 17.7 ± 4.2 2.1 ± 2.6 0.81 ± 0.07 0.35 115 ± 12 0.456 ± 0.071 1.16 ± 0.08 0.45 Au-Au 40-50% 155.8 ± 4.0 18.9 ± 4.2 2.7 ± 2.6 0.80 ± 0.07 0.17 108 ± 12 0.499 ± 0.071 0.98 ± 0.06 0.48 30-40% 156.5 ± 4.2 18.6 ± 4.2 3.1 ± 2.6 0.83 ± 0.07 0.04 109 ± 11 0.514 ± 0.061 0.90 ± 0.05 0.45 200 GeV 20-30% 156.7 ± 4.8 21.3 ± 4.2 3.2 ± 2.6 0.82 ± 0.08 0.03 102 ± 11 0.539 ± 0.061 0.90 ± 0.04 0.37 10-20% 155.1 ± 4.8 21.0 ± 4.2 3.0 ± 2.6 0.83 ± 0.09 0.02 99 ± 12 0.560 ± 0.061 0.80 ± 0.03 0.36 5-10% 156.5 ± 5.3 22.8 ± 4.5 4.9 ± 2.6 0.86 ± 0.10 0.02 91 ± 12 0.577 ± 0.051 0.86 ± 0.02 0.51 0-5% 159.3 ± 5.8 21.9 ± 4.5 3.9 ± 2.6 0.86 ± 0.11 0.03 89 ± 12 0.592 ± 0.051 0.82 ± 0.02 0.25 58-85% 159+11 −7 19.9 ± 4.9 3.0 ± 4.3 0.78 ± 0.11 0.004 136 ± 32 0.400 ± 0.027 0.0 ± 10.1 0.96 45-58% 158+10 −6 26.2 ± 5.2 −5.9 ± 4.6 0.82 ± 0.08 0.015 113 ± 16 0.465 ± 0.010 0.6 ± 0.5 0.78 34-45% 158+9 −5 25.8 ± 4.8 −1.0 ± 4.1 0.83 ± 0.09 0.153 103 ± 11 0.502 ± 0.013 0.8 ± 0.3 1.01 Au+Au 26-34% 158+10 −6 27.1 ± 4.9 0.6 ± 4.1 0.84 ± 0.09 0.006 103 ± 16 0.526 ± 0.017 0.8 ± 0.3 0.81 130 GeV 18-26% 156+10 −6 27.4 ± 4.7 1.5 ± 4.0 0.85 ± 0.09 0.005 103 ± 15 0.531 ± 0.017 0.8 ± 0.2 0.81 11-18% 153+9 −6 27.9 ± 4.8 1.5 ± 4.0 0.83 ± 0.08 0.012 106 ± 20 0.538 ± 0.023 0.7 ± 0.4 0.52 6-11% 153+9 −5 27.7 ± 4.7 2.7 ± 3.8 0.84 ± 0.07 0.005 93 ± 12 0.558 ± 0.019 0.7 ± 0.3 0.70 0-6% 154+10 −6 29.0 ± 4.6 2.4 ± 3.3 0.89 ± 0.07 0.136 96 ± 8 0.567 ± 0.020 0.7 ± 0.3 0.67 70-80% 154+8 −6 37.7 ± 6.5 6.6 ± 3.5 0.62 ± 0.06 0.244 130 ± 15 0.306 ± 0.065 2.1 ± 1.8 0.93 60-70% 156+8 −5 42.5 ± 5.8 4.0 ± 3.6 0.69 ± 0.07 0.178 130 ± 15 0.389 ± 0.019 0.4 ± 0.9 0.55 50-60% 155+8 −5 47.0 ± 5.1 6.7 ± 3.5 0.71 ± 0.07 0.197 129 ± 16 0.426 ± 0.021 0.0 ± 9.8 0.59 Au+Au 40-50% 156+9 −5 51.3 ± 5.2 3.2 ± 3.6 0.78 ± 0.07 0.237 120 ± 13 0.459 ± 0.009 0.6 ± 0.5 0.54 30-40% 157+9 −5 54.2 ± 5.2 3.6 ± 3.6 0.79 ± 0.07 0.275 113 ± 12 0.494 ± 0.008 0.6 ± 0.4 0.45 62.4 GeV 20-30% 157+9 −5 54.5 ± 5.2 6.6 ± 3.4 0.82 ± 0.07 0.715 105 ± 10 0.517 ± 0.020 0.8 ± 0.3 0.52 10-20% 156+9 −5 59.4 ± 5.4 6.2 ± 3.5 0.82 ± 0.07 0.261 105 ± 14 0.535 ± 0.017 0.6 ± 0.4 0.52 5-10% 155+9 −5 61.0 ± 5.7 7.4 ± 3.5 0.85 ± 0.07 0.066 100 ± 12 0.546 ± 0.019 0.7 ± 0.3 0.77 0-5% 154+10 −7 62.7 ± 6.0 7.1 ± 3.5 0.82 ± 0.07 0.480 99 ± 10 0.554 ± 0.018 0.6 ± 0.4 0.75 momentum spectral shape is given by [127] dN p⊥dp⊥ ∝ Z R 0 rdr m⊥I0 p⊥ sinh ρ Tkin K1 m⊥ cosh ρ Tkin , (16) where ρ = tanh−1 β, and I0 and K1 are the modified Bessel functions. We use a flow velocity profile of the form β = βS (r/R) n , (17) where βS is the surface velocity and r/R is the relative radial position in the thermal source. The choice of the value of R bears no effect in the model. Six particle spectra (π ±, K±, p and p) of a given centrality bin are fit simultaneously with the blast-wave model. The free parameters are: the kinetic freeze-out temperature, Tkin, the average transverse flow velocity, hβi = 2 2+n βS, and the exponent of the assumed flow velocity profile, n. The low momentum part of the pion spectra (p⊥ < 0.5 GeV/c) are excluded from the fit, due to significant contributions from resonance decays. The blast-wave fit results for Au+Au collisions are listed in Table X. The χ 2/ndf is smaller than unity because the point-to-point systematic errors, which are included in the fit and dominate over statistical ones, are estimated on the conservative side and might not be completely random. If the χ 2/ndf is scaled such that the minimum is unity, then somewhat smaller statistical errors on the fit parameters are obtained. Figure 36 shows the extracted kinetic freeze-out temperature as a function of the event multiplicity for pp and d+Au collisions at 200 GeV and for Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV, together with the chemical freeze-out temperature. As opposed to Tchem, the kinetic freeze-out temperature Tkin shows a notable decreasing trend with centrality in Au+Au collisions. The Tkin values from pp and d+Au collisions are similar to those in peripheral Au+Au, although the systematic uncertainties are large. Figure 37 shows the extracted average transverse radial flow velocity hβi as a function of the event multiplicity. The hβi increases dramatically with increasing centrality 37 /dy ch dN 10 2 10 3 10 T [GeV] 0.05 0.1 0.15 0.2 pp 200 GeV MB d+Au 200 GeV MB d+Au 200 GeV Au+Au 62.4 GeV Au+Au 130 GeV Au+Au 200 GeV ch T Tkin FIG. 36: (color online) Chemical and kinetic freeze-out temperatures as a function of the charged hadron multiplicity. Errors shown are the total statistical and systematic uncertainties. The 200 GeV pp and Au+Au data are taken from Ref. [17]. /dy ch dN 10 2 10 3 10 > β < 0.1 0.2 0.3 0.4 0.5 0.6 0.7 pp 200 GeV MB d+Au 200 GeV MB d+Au 200 GeV Au+Au 62.4 GeV Au+Au 130 GeV Au+Au 200 GeV FIG. 37: (color online) Average transverse radial flow velocity extracted from blast-wave model fit to pp and d+Au at 200 GeV, and to Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV as a function of the charged hadron multiplicity. Errors shown are the total statistical and systematic uncertainties. The 200 GeV pp and Au+Au data are taken from Ref. [17]. in Au+Au collisions. The effect of the hβi increase on the transverse spectra is significantly stronger than the counter effect of the Tkin drop. The combination of the π, K, p and p spectra favor an increase of hβi with centrality rather than a similar increase in Tkin. In order to have the same base for comparison, the pp and d+Au data are also fit by the blast-wave model. The fit results are listed in Table X and shown as a function of the event multiplicity in Figs. 36 and 37 together with the Au+Au results. The model is found to give a fairly good description of the measured π ±, K±, p and p spectra. Surprisingly, the fit average flow velocities from pp and d+Au collisions are not small, and certainly not zero as one would naively expect. This should not be taken as a proof that there is collective flow in pp and d+Au collisions, because hard scatterings and jet production, generating relatively more high-p⊥ hadrons, can mimic collective flow and give rise to the extracted finite hβi [54]. In d+Au collisions, there is an additional effect of initial state scattering, which broadens the transverse momentum of the colliding constituents and hence the produced hadrons in the final state. Meanwhile, statistical global energy and momentum conservation can deplete large momentum par
ticles shown in recent studies [55], and the effect can be large in low multiplicity collisions. In the same framework, large initial energy fluctuation available for mid-rapidity particle production tends to harden the transverse spectrum [51, 134]. The interplay, as well as the relevance of statistical global energy and momentum conservation in high energy collisions, needs further quantitative studies. In Au+Au collisions the contribution from hard (and semi-hard) scatterings is larger than in pp collisions because hard scatterings scale with the number of binary nucleon-nucleon collisions while soft processes scale with the number of participant nucleons. From the two-component model study in Section VI C, the hardscattering contribution in pp collisions at 200 GeV is 13%, while in the top 5% central Au+Au collisions it is 46%, a factor of 3.5 times that in pp. From the blastwave model with a linear flow velocity profile, the increase in average hp⊥i or hm⊥i due to radial flow velocity hβi is approximately proportional to hβi 3 . Assuming the apparent finite flow velocity extracted from pp data, hβipp = 0.24 ± 0.08, is solely due to the energy excess of produced particles from hard processes over soft processes, and assuming the particle production from hard processes is identical in pp and central Au+Au collisions, then the hard processes in central Au+Au collisions would generate an apparent flow velocity of 3.5 1/3 hβipp = 0.36. However, the extracted flow velocity from the blast-wave model for central Au+Au collisions is significantly larger, hβiAA = 0.59±0.05. One may take the additional excess in central Au+Au collisions as the effect of collective transverse radial flow, and estimate the collective flow velocity in central Au+Au collisions by hβiflow ∼ 3 q hβi 3 AA − 3.5hβi 3 pp = 0.54 ± 0.08. As discussed in section VI C, the Kharzeev-Nardi twocomponent model likely overestimates the fraction of the hard component in pp collisions. However, using the hard-component fraction obtained from Ref. [54], with the same assumptions as stated above, the estimate of the collective flow velocity in central Au+Au collisions is not significantly altered. We note, however, that the preceding estimate is simplistic. The full understanding of the effects on transverse spectra from radial flow, (semi- )hard scatterings, interactions between (semi-)hard scatterings and the medium [67, 135, 136], and the interplay between these effects will need rigorous study which is outside the scope of this paper. It should be understood that the extracted values of the radial flow velocity in this 38 paper is under the framework of the Blast-wave model. Despite the different physical processes, the extracted Tkin and hβi evolve smoothly from pp to central heavyion collisions. In pp and peripheral Au+Au collisions, the kinetic freeze-out temperature is close to the chemical freeze-out temperature. As the multiplicity increases the Tkin decreases and the hβi increases. This trend continues through d+Au and Au+Au collisions. The extracted kinetic freeze-out temperature and the radial flow velocity are similar for Au+Au collisions at the three measured energies. As shown by Figs. 36 and 37, the magnitudes of the freeze-out parameters extracted from Au+Au collisions seem to be correlated only with the charged particle multiplicity, dNch/dy. This may suggest that the expansion rates, both before and after chemical freeze-out, are determined by the total event multiplicity, or the initial energy density as expressed through the energy density estimate in Eq. (13). In other words, a higher initial energy density results in a larger expansion rate and longer expansion time, yielding a larger flow velocity and lower kinetic freeze-out temperature. The blast-wave fit so far treated all particles as primordial, ignoring resonance decays which are contained in the measured inclusive spectra. To assess the effect of resonance decays on the extracted kinetic freeze-out parameters, we extended the blast-wave model to include resonance decays as described in detail in Appendix B. We found that the thus extracted kinetic freeze-out parameters agree with those obtained without including resonances within systematic uncertainties. This is because the resonance decay contributions are relatively p⊥- independent within the p⊥ ranges of our measurements. In addition, our study including short-lived resonances lends support to the picture of regeneration of short-lived resonances [48, 51, 137, 138] during a relatively long time span from chemical to kinetic freeze-out. C. Excitation Functions The thermal model has been very successful in describing heavy-ion collisions and elementary particle collisions over a wide range of collision energies. Heavy-ion data from many energies have also been successfully fit by the blast-wave model. We compile results from some of these previous investigations [120, 121, 122, 123, 126, 139, 140, 141, 142, 143], together with RHIC data to study the excitation functions of the extracted chemical and kinetic freeze-out parameters. We note that the thermal model studies in Refs. [120, 121, 122] do not include γS as a free parameter; strangeness is treated as equilibrated with light flavors, i.e. γS = 1. Figure 38 shows the baryon chemical potential extracted from chemical equilibrium model fits to central heavy-ion (Au+Au/Pb+Pb) data at various energies. The extracted µB falls monotonically from low to high energies. There are fewer net-baryons at mid-rapidity at higher energy because fewer baryons can transport over the larger rapidity gap. [GeV] SNN 1 10 2 10 [MeV] B µ 2 10 3 10 Becattini et al. Andronic et al. SIS AGS SPS STAR FIG. 38: Baryon chemical potential extracted for central heavy-ion collisions as a function of the collision energy. STAR 62.4 GeV and 130 GeV data are from this work; the 200 GeV data are from Ref. [17]. Other data are from SIS [140, 141], AGS [120, 122, 126, 142], SPS [121, 122, 126, 139, 142] and compilation by Refs. [143, 144]. Errors shown are the total statistical and systematic errors. [GeV] SNN 1 10 2 10 [MeV] kin , T ch T 0 20 40 60 80 100 120 140 160 180 200 220 240 Tch STAR pp EOS kin T elem. Becattini et al. Tch Becattini et al. Tch Andronic et al. Tch Tch SIS Tkin SIS Tch AGS Tkin AGS Tch SPS Tkin SPS Tch STAR Tkin STAR FIG. 39: (color online) The extracted chemical (open symbols) and kinetic (filled symbols) freeze-out temperatures for central heavy-ion collisions as a function of the collision energy. The STAR 62.4 GeV and 130 GeV data are from this work; the STAR 200 GeV data are from Ref. [17]. The other kinetic freeze-out results are from FOPI [145], EOS [146], E866 [147], and NA49 [148]. The other chemical freezeout data are from SIS [140, 141], AGS [120, 122, 126, 142], SPS [121, 122, 126, 139, 142] and compilation by Refs. [143, 144]. Errors shown are the total statistical and systematic errors. Figure 39 shows the evolution of the extracted chemical (open symbols) and kinetic (filled symbols) freeze-out temperature as a function of the collision energy in central heavy-ion collisions. The extracted Tchem rapidly rises at SIS and AGS energy range and saturates at 39 [GeV] SNN 1 10 2 10 >β< 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 FOPI EOS E866 NA49 STAR FIG. 40: Average transverse radial flow velocity extracted from the blast-wave model for central heavy-ion collisions as a function of the collision energy. The STAR 62.4 GeV and 130 GeV data are from this work, and the STAR 200 GeV pp and Au+Au data from Ref. [17]. The other data are from FOPI [145], EOS [146], E866 [147], and NA49 [148]. Errors shown are the total statistical and systematic errors. [MeV] B µ 0 200 400 600 800 [MeV] ch T 0 50 100 150 200 Andronic et al. SIS AGS SPS STAR STAR pp FIG. 41: (color online) Phase diagram plot of chemical freezeout temperature versus baryon chemical potential extracted from chemical equilibrium models. Low energy data are taken from Refs. [120, 121, 122, 126, 139, 140, 141, 142] and compilations in Refs. [143, 144]. Errors shown are the total statistical and systematic errors. SP
S and RHIC energies. In other words, central heavyion collisions at high energies can be characterized by a unique, energy independent chemical freeze-out temperature. The value of Tchem is close to the phase transition temperature predicted by Lattice QCD. This suggests the collision system at high energies decouples chemically at the phase boundary. On the other hand, the extracted kinetic freeze-out temperature rises at SIS and AGS energies, and decreases at higher energies, especially at RHIC energies. At low energies, the extracted Tkin is similar to Tchem. This suggests that kinetic freeze-out happens relatively quickly after or concurrently with chemical freeze-out. The two measured temperatures begin to separate at a collision energy around √sNN = 10 GeV, above which Tkin decreases with increasing energy, while Tchem remains relatively constant. This suggests a prolonging of the period between chemical and kinetic freeze-outs, during which the particles scatter elastically, building up additional collective motion in the system while it undergoes further expansion and cooling. Figure 40 shows the evolution of the extracted average flow velocity as a function of the collision energy. The extracted hβi steeply increases from SIS to AGS energies, and continues to increase at a lower rate at higher energies. Collective flow is an integral of all collective flow contributions over the entire evolution of the collision system. Part of it comes from the early stage of the collisions before chemical freeze-out, built up by the high pressure in the core of the collision zone. After chemical freeze-out, particles continue to interact elastically in central collisions, building up further transverse radial flow. This late-stage transverse expansion cools down the system and results in a lower kinetic freeze-out temperature in central collisions as discussed above. One should note that the extracted average flow velocity can be generated by different underlying physics at very low (SIS, AGS) and high (SPS, RHIC) incident energies. It is valuable to study collective radial flow at chemical freeze-out, as it comes from the early stage of the collision and hence is more sensitive to the initial condition than the final measured radial flow. The radial flow at chemical freeze-out may be assessed by analyzing p⊥ spectra of particles with small hadronic interaction cross sections; some rare particles like φ, Ξ, and Ω must develop most of their flow early (perhaps pre-hadronization) because their interaction cross sections are much lower than for the common π, K, p and p. It is found that the extracted radial flow for these rare particles is substantial in central heavy-ion collisions at RHIC, perhaps suggesting strong partonic flow in these collisions [50, 149]. Figure 41 shows the chemical freeze-out temperature versus baryon chemical potential extracted from chemical equilibrium model fits to central Au+Au data. Low energy data points (SIS, AGS, SPS) are from the chemical equilibrium model fits [122, 139, 140, 141, 143, 144] and references therein. At RHIC energies the chemical freeze-out points appear to be in the vicinity of the hadron-QGP phase-transition (hadronization) predicted by lattice gauge theory [150, 151]. VIII. SUMMARY Charged particles of π ±, K±, p and p are identified by the specific ionization energy loss (dE/dx) method in STAR at low transverse momenta and mid-rapidity (|y| < 0.1) in pp and d+Au collisions at √sNN = 200 GeV and in Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV. Transverse momentum spectra of the identi- fied particles are reported. Spectra of heavy particles are 40 flatter than those of light particles in all collision systems. This effect becomes more prominent in more central Au+Au collisions. In pp and d+Au collisions processes such as semi-hard scattering and k⊥ broadening should play an important role. In central Au+Au collisions the flattening of the spectra is likely dominated by collective transverse radial flow, developed due to the large pressure buildup in the early stage of heavy-ion collisions. The transverse momentum spectra are extrapolated to the unmeasured regions by the hydrodynamics-motivated blast-wave model parameterization for kaons, protons and antiprotons and by the Bose-Einstein function for pions. The total integrated particle yields are reported. The Bjorken energy density estimated from the total transverse energy is at least several GeV/fm3 at a formation time of less than 1 fm/c. The extrapolated hp⊥i increases with particle mass in each collision system, and increases with centrality for each particle species. The hp⊥i systematics are similar for the three measured energies at RHIC, and appear to be strongly correlated with the total particle multiplicity density or the ratio of the multiplicity density over the transverse overlap area of the colliding nuclei. Ratios of the integrated particle yields are presented and discussed. While rather independent of centrality for 130 GeV and 200 GeV, the p/p ratio drops significantly with centrality in 62.4 GeV Au+Au collisions. This indicates a more significant net-baryon content at mid-rapidity in Au+Au collisions at 62.4 GeV. On the other hand, antibaryon production relative to the total particle multiplicity, while lower at the lower energy, is independent of centrality for all three collision energies at RHIC, despite the increasing net-baryon density at the low 62.4 GeV energy. Strangeness production relative to the total particle multiplicity is similar at the different RHIC energies. The effect of collision energy on the production rate is significantly smaller on strangeness production than on antibaryon production. Relative strangeness production increases quickly with centrality in peripheral Au+Au collisions, and remains the same above medium-central collisions at RHIC. The increase in relative strangeness production in central Au+Au collisions from pp is approximately 50%. The particle yield ratios are fit in the framework of the thermal equilibrium model. The extracted chemical freeze-out temperature is the same in pp, d+Au, and Au+Au collisions at all measured energies at RHIC, and shows little centrality dependence in Au+Au collisions. The extracted value of chemical freeze-out temperature is close to the Lattice QCD predicted phase transition temperature between hadronic matter and the QuarkGluon Plasma, suggesting that chemical freeze-out happens in the vicinity of the phase boundary shortly after hadronization. The extracted strangeness suppression factor is substantially below unity in pp, d+Au, and peripheral Au+Au collisions; strangeness production is significantly suppressed in these collisions. The strangeness suppression factor in medium-central to central Au+Au collisions is not much below unity; the strangeness and light flavor are nearly equilibrated, which may suggest a fundamental change from peripheral to central collisions. The extracted kinetic freeze-out temperature from the blast-wave fit to the transverse momentum spectra, on the other hand, decreases from pp and d+Au to central Au+Au collisions. At the same time, the extracted collective flow velocity increases significantly with increasing centrality. While the apparent finite flow velocity fit in pp and d+Au collisions may be due to semi-hard scatterings and jets, the extracted large flow velocity in central Au+Au collisions is likely dominated by collective transverse radial flow. The significant difference between the extracted chemical and kinetic freeze-out temperature suggests the presence of an elastic rescattering phase between the two freeze-outs. The variations of the extracted freeze-out properties are smooth from pp and d+Au to Au+Au collisions and over the measured energies for the Au+Au collision system; the trends seem to be tied to the event multiplicity. Resonance decays are found to have little effect on the extracted kinetic freezeout parameters due to the fact that the resonance decay products have similar kinematics as the primordial particles in our measured transverse momentum ranges. The study incl
uding different contributions from short-lived resonances lends support to the regeneration picture of those resonances with a long time span from chemical to kinetic freeze-out. The identified particle spectra at RHIC energies and the equilibrium model studies presented here suggest that the collision systems chemically decouple at a universal temperature, independent of the vastly different initial conditions at different centralities. The apparent different collective flow strengths in the final state of non-peripheral heavy-ion collisions likely are dominated by transverse radial flow and stem out of the different amount of pressure build-up at the initial stage. Part of the collective flow in central collisions appears to be built up after chemical freeze-out, during which the collision zone undergoes further expansion and cooling through particle elastic scatterings, resulting in a lower kinetic decoupling temperature in more central collisions. APPENDIX A: THE GLAUBER MODEL To describe heavy-ion collisions, geometric quantities are often used, such as the number of participant nucleons (Npart), the number of nucleon-nucleon binary collisions (Ncoll), and the transverse overlap area of the colliding nuclei (S⊥). Unfortunately these quantities cannot be 41 measured directly from experiments 4 . Their values can only be derived by mapping the measured data, such as the dN/dNch distribution, to the corresponding distribution obtained from phenomenological calculations, thus relating Npart, Ncoll, and S⊥ to the measured dN/dNch distribution. These types of calculations are generally called Glauber model calculations and come in two implementation schemes, the optical and the Monte-Carlo Glauber calculations. The optical model is based on an analytic consideration of continuously overlapping nuclei [29, 152, 153, 154]. The MC approach is based on a computer simulation of billiard ball-like colliding nucleons [68, 155, 156, 157, 158, 159]. Figure 42 shows the differential cross-sections versus b of minimum bias Au+Au collisions at 200 GeV calculated by the optical and MC Glauber models. As seen from the figure, the differential cross-sections agree between the two calculations except at large impact parameters, or in very peripheral collisions. The disagreement in very peripheral collisions is understood because the optical approach loses its validity in these collisions. Due to this disagreement, the integrated total cross-sections differ between the optical and MC calculations, by about 5%. b [fm] 0 5 10 15 20 /db [barn/fm] σ d 0 0.2 0.4 0.6 0.8 Optical Glauber MC Glauber FIG. 42: Differential cross-sections obtained from the optical and MC Glauber calculations for Au+Au collisions at 200 GeV. Statistical errors are smaller than the point size. To relate Glauber calculations to experimental measurements, one first obtains the impact parameter range corresponding to the measured centrality bin using the differential cross-section, such as the ones shown in Fig. 42. The average Npart and Ncoll values are then calculated in the Glauber model for the impact parameter range. Table XI lists the Npart and Ncoll values obtained from the optical Glauber calculations for our 4 An exception is that in fixed target experiments the number of participants can be experimentally measured by zero degree calorimeters. multiplicity classes in 62.4 GeV, 130 GeV, and 200 GeV Au+Au collisions. The MC Glauber results are already listed in Table II in the main text. As seen from the tables, different implementations of the Glauber model lead to slightly different values for Npart and Ncoll, as has been noted before in Ref. [158]. The results are different for non-peripheral collisions even though the differential cross-sections match between the two Glauber calculations. This is because the impact parameter ranges corresponding to the same measured centrality bin differ slightly due to the different total cross-sections. The disagreement in the Glauber results is more significant in peripheral collisions due to reasons noted above. Thus, any results reported in terms of Glauber quantities must be carefully interpreted based upon specifics of the underlying calculations. TABLE XI: The optical Glauber model results corresponding to the centrality bins used in the 62.4 GeV, 130 GeV, and 200 GeV Au+Au data. The quoted errors are systematic uncertainties. centrality b-range (fm) b (fm) Npart Ncoll Au+Au 200 GeV (σpp = 41 mb) 90-100% 14.3-15.7 14.8 +1.1 −0.5 1.43+0.73 −0.64 1.02+0.57 −0.47 80-90% 13.4-14.3 13.8 ± 0.4 4.5 +1.3 −1.1 3.7 +1.2 −1.0 70-80% 12.5-13.4 13.0 ± 0.3 10.7 +2.2 −2.0 10.0 +2.7 −2.3 60-70% 11.6-12.5 12.1 ± 0.3 22.0 +3.3 −3.1 25.1 +5.3 −4.8 50-60% 10.6-11.6 11.1 ± 0.3 40.6 ± 4.3 56.2 +9.1 −8.6 40-50% 9.48-10.6 10.0 ± 0.3 67.8 ± 5.0 113 ± 14 30-40% 8.21-9.48 8.86 ± 0.23 105.4 ± 5.3 206 ± 19 20-30% 6.70-8.21 7.48 ± 0.19 155.9 ± 5.1 351 ± 26 10-20% 4.74-6.70 5.78 ± 0.15 223.6 ± 4.2 571 ± 36 5-10% 3.35-4.74 4.08 ± 0.11 289.6 +2.9 −3.1 807 ± 48 0-5% 0 -3.35 2.23 ± 0.06 345.8 +1.8 −2.0 1027 ± 61 Au+Au 130 GeV (σpp = 39 mb) 85-100% 13.6-15.2 14.3 +1.0 −0.5 2.7 +1.7 −1.3 2.0 +1.4 −1.0 58-85% 11.3-13.6 12.5 ± 0.4 17.0 +4.6 −3.9 18.6 +6.6 −5.2 45-58% 9.92-11.3 10.6 ± 0.4 51.8 +7.6 −7.0 76+16 −14 34-45% 8.62-9.92 9.29 ± 0.31 89.7 +8.4 −8.0 161 ± 23 26-34% 7.54-8.62 8.10 ± 0.27 131.0 +8.3 −8.1 268 ± 28 18-26% 6.28-7.54 6.93 ± 0.23 175.7 ± 7.6 398 ± 33 11-18% 4.91-6.28 5.62 ± 0.19 228.2 ± 6.3 564 ± 39 6-11% 3.62-4.91 4.30 ± 0.14 280.0 ± 4.7 740 ± 47 0-6% 0 -3.62 2.42 ± 0.08 339.3 ± 2.6 958 ± 59 Au+Au 62.4 GeV (σpp = 36 mb) 90-100% 14.2-15.6 14.7 +1.0 −0.5 1.47+0.73 −0.64 1.02+0.56 −0.46 80-90% 13.3-14.2 13.7 +0.4 −0.3 4.6 +1.2 −1.1 3.6 +1.2 −1.0 70-80% 12.5-13.3 12.9 ± 0.3 10.6 +2.2 −1.9 9.7 +2.5 −2.2 60-70% 11.5-12.5 12.0 ± 0.3 21.8 +3.3 −3.1 23.6 +4.9 −4.4 50-60% 10.5-11.5 11.0 ± 0.3 40.0 +4.3 −4.1 52.0 +8.2 −7.7 40-50% 9.42-10.5 9.98 ± 0.26 66.8 ± 4.9 103 ± 12 30-40% 8.15-9.42 8.80 ± 0.22 103.8 ± 5.2 186 ± 17 20-30% 6.66-8.15 7.43 ± 0.19 153.5 ± 5.0 314 ± 24 10-20% 4.71-6.66 5.74 ± 0.15 220.4 +4.1 −4.3 506 ± 34 5-10% 3.33-4.71 4.06 ± 0.10 285.9 +3.1 −3.3 712 ± 46 0-5% 0 -3.33 2.22 ± 0.06 342.2 ± 2.3 903 ± 59 In the following we will briefly describe the optical and MC Glauber calculations. 42 1. The Optical Glauber Model For our optical Glauber calculation, we start by assuming a spherically symmetric Woods-Saxon density profile, ρ(r) = ρ0 1 + exp( r−r0 a ) , (A1) with the parameter a = 0.535 ± 0.027 fm as experimentally measured in e-Au scattering reported in Refs. [160, 161]. From the same publication we extracted the value for r0, but increased it from 6.38 fm to 6.5 ± 0.1 fm to approximate the effect of the neutron skin. The normalization factor ρ0 = 0.161 fm−3 is fixed by R ∞ 0 ρ(r)4πr2dr = 197, the total number of nucleons in the Au nucleus. We concentrate on symmetric Au+Au collisions. Let the beam-axis be along ˆz. The nuclear thickness density function is given by TA(~s) = TA(s) = Z ∞ −∞ ρ(~s, z)dz , (A2) where ~s is a vector perpendicular to the beam-axis ˆz, and s = |~s|; ρ(~s, z) is the nuclear density in the volume element ds2dz at (~s, z), and for our spherical nucleus, ρ(~s, z) = ρ(s, z) = ρ( √ s 2 + z 2) as given by Eq. (A1). For a Au+Au collision with impact parameter ~b, the nuclear overlap integral can be calculated as the integral over two density profiles, TAA(b) = Z TA(~s)TA(~s −~b)ds2 . (A3) The number of binary nucleon-nucleon collisions is given by Ncoll(b) = σppTAA(b) . (A4) Here, we assume that the interaction probability is solely given by the proton-proton cross-section σpp, thus neglecting effects like excitation and energy loss. The number of participant nucleons (nucleons suffering at least one collision) is derived from TA by Npart(b) = 2 Z TA(~s) 1 − e −σppTA(~s−~b) ds2 . (A5) By definition, there is no fluctuation in the optical Glauber model. For a given b, quantities like TA, TAA, Ncoll, and Npart are analytically defined. In order to calculate
the cross-section, however, one has to invoke the concept of fluctuation. In this sense, Eq. (A4) gives the average number of binary collisions for Au+Au collisions at impact parameter b, and taking Poisson statistics, the probability for no interaction is e −Ncoll(b) . The differential cross-section is thus given by dσAA db = 2πb 1 − e −σppTAA(b) . (A6) The total hadronic cross-section for Au+Au collisions can hence be obtained as σAA = Z ∞ 0 dbdσAA db . (A7) The values of σpp are taken to be σpp = 36 ± 2 mb, 39 ± 2 mb and 41 ± 2 mb for 62.4 GeV, 130 GeV, and 200 GeV, respectively. With these pp cross-sections, the corresponding total cross sections for Au+Au are calculated to be approximately σAA = 7.18 barns, 7.24 barns, and 7.27 barns, respectively. To relate Npart and Ncoll to the experimental observable Nch, the mean of the total number of charged tracks in our centrality bin, we use Eqs. (A6) and (A7) to obtain the impact parameters corresponding to the fraction of the total geometric cross-section for our centrality bin. For a given impact parameter range b1 < b < b2 for each centrality bin, we then use Eqs.(A6), (A4), and (A5) to calculate the Ncoll and Npart by Ncoll = R b2 b1 Ncoll(b) dσAA db db R b2 b1 dσAA db db , (A8) Npart = R b2 b1 Npart(b) dσAA db db R b2 b1 dσAA db db . (A9) 2. The Monte-Carlo Glauber Model The MC method simulates a number of independent Au+Au collisions. For each collision, a target and a projectile nucleus are modeled according to the WoodsSaxon nucleon density profile of Eq. (A1). The nucleons are separated by a minimum distance dmin = 0.4 fm which is characteristic of the range of the repulsive nucleon-nucleon force. The target and projectile nuclei are separated by the impact parameter b, with b 2 chosen randomly from a flat distribution. The nucleons follow straight-line trajectories in collisions. A pair of nucleons along the path is determined to ‘interact’ if they are separated by a transverse distance d ≤ r σpp π , (A10) where σpp is the nucleon-nucleon interaction crosssection. The colliding nuclei are considered to have interacted (resulting in an Au+Au event) if at least one pair of nucleons has interacted. Again, the values of σpp are taken to be σpp = 36 ± 2 mb, 39 ± 2 mb and 41 ± 2 mb for 62.4 GeV, 130 GeV, and 200 GeV, respectively. With these pp cross-sections, the corresponding total cross sections for Au+Au are calculated to be approximately σAA = 6.84 barns, 6.89 barns, and 6.93 barns, respectively. The normalized differential cross-section, 1 σAA dσAA db , is obtained from the normalized event distribution. The 43 1 σAA dσAA db distribution is divided into bins corresponding to the fractions of the measured total cross-section of the used centrality bins. The number of participants Npart is defined as the total number of nucleons that undergo at least one interaction. The number of binary collisions Ncoll is defined as the total number of nucleon-nucleon interactions in the collision. The mean values of Npart and Ncoll are determined for each centrality bin in the same way as for the optical Glauber model, by Eq. (A8) and Eq. (A9). The transverse overlap area, S⊥, for pp collisions is taken to be the pp cross-section σpp. To calculate the transverse overlap area between the colliding nuclei of Au+Au collisions, the individual pp interaction crosssections are projected onto the transverse plane. The overlap area in the transverse plane, S⊥, is then calculated. The overlapping portion of the projected areas from two or more nucleon-nucleon interactions is counted only once. The mean S⊥, weighted by the differential cross-section, is determined in the same manner as in Eq. (A8) and Eq. (A9). Table II lists the obtained S⊥ along with Npart and Ncoll. 3. Uncertainties The uncertainties on Npart, Ncoll, and S⊥ from both the optical and MC Glauber model calculations are evaluated by varying the Woods-Saxon parameters, the values of σpp and dmin, and by including an uncertainty in the determination of the measured total Au+Au crosssection. • The Woods-Saxon nuclear density profile parameters a and r0 are varied within their respective uncertainties: a = 0.535 ± 0.027 fm and r = 6.50 ± 0.12 fm. • The σpp values are 36 mb (62.4 GeV), 39 mb (130 GeV), and 41 mb (200 GeV) as default and are varied within an uncertainty of ±2 mb. • The dmin value is 0.4 fm as default and is varied between 0.2 fm and 0.5 fm. This only applies to the MC Glauber calculation. • Due to inefficiencies in the online trigger and offline primary vertex reconstruction for peripheral collisions, our measured total (minimum bias) crosssection does not fully account for the total Au+Au hadronic cross-section. The measured fractions of the total cross-section are determined to be 97 ± 3% [47, 162], 95±5% [23, 25], and 97±3% [13, 163] for minimum bias Au+Au collisions at 62.4 GeV, 130 GeV, and 200 GeV, respectively. These fractions are used in the determination of our Glauber model results, and their uncertainties are included in the quoted uncertainties on the results. The uncertainties from these sources are determined separately and summed in quadrature in the quoted uncertainties on the Glauber results in Table II and Table XI. In peripheral collisions, the uncertainties are dominated by those in the minimum bias cross-section measurements. In central collisions, the uncertainty in Ncoll is dominated by the uncertainty in σpp, while all sources contribute significantly to the uncertainties in Npart and S⊥. The uncertainties on Npart, Ncoll, and S⊥ are correlated. APPENDIX B: RESONANCE EFFECT ON BLAST-WAVE FIT The blast-wave fit in Section VII B treats all particles as primordial, ignoring resonance decays. However, the measured identified inclusive particle spectra contain contributions from resonance decays. The question arises whether or not resonance decays have a signifi- cant effect on the extracted kinetic freeze-out parameters. To answer this question, the blast-wave model fit is extended to include resonance decays. The identified particle p⊥ spectra measured at mid-rapidity in minimum bias pp and in the most central 5% Au+Au collisions at 200 GeV [17] are utilized to study the effect of resonance decays on the extracted kinetic freeze-out parameters [5]. 1. Effect of Resonance Decays The study is based on the combination of the chemical equilibrium model [120, 121, 122, 123] and the blastwave model by Wiedemann and Heinz [164]. Several changes have been implemented with respect to the original code [164] to provide the same basis for the calculation as in data [17]. The Wiedemann-Heinz blast-wave model uses the same temperature to determine the relative abundances of particles and resonances and to calculate their kinetic distributions. In this study, two distinct freeze-out temperatures are implemented: the chemical freeze-out temperature and the kinetic freeze-out temperature. The relative abundances of particles and resonances are determined by chemical freeze-out parameters and are fixed in our study. We used the following chemical freeze-out parameters: Tchem= 159 MeV, µB= 18 MeV, µS= 2.3 MeV, and γ=0.62 for pp collisions at 200 GeV [17, 52], and Tchem= 160 MeV, µB= 24 MeV, µS= 1.4 MeV, and γ=0.99 for the top 5% central Au+Au collisions at 200 GeV [17, 165]. More particles are included than in Ref. [164]: ρ, ω, η, η ′ , K∗0 , K∗±, φ and Λ, ∆, Σ, Ξ, Λ1520, Σ1385, Ω. A box flow profile is chosen, similarly to Ref. [17]: β = βS (r/R) n , where n is fixed to be 0.82 for Au+Au collisions and set free for pp collisions. A flat rapidity distribution is implemented at mid-rapidity. This is needed because, although the measured spectra are in |y| < 0.1, resonances outside this region can decay into particles falling within the region. 44 TABLE XII: Extracted kinetic freeze-out parameters and the fit χ 2 /ndf from the blast-wave model including resonances for minimum bias pp and top 5% central Au+Au collisions at 200 GeV. Three cases of treating ρ decays are studied. The flow profile n parameter is f
ixed to 0.82 for the Au+Au fit and is free for the pp fit. All errors are statistical. pp minimum bias Au+Au top 5% Case Tkin (MeV ) hβi n χ2 /ndf Tkin (MeV ) hβi n χ2 /ndf 100% ρ 117.8 ± 3.2 0.29 ± 0.01 3.1 ± 0.6 1.1 77.2 +0.8 −0.9 0.604+0.004 −0.003 0.82 fixed 0.60 0% ρ 121.9 ± 0.9 0.35 ± 0.01 1.2 ± 0.1 4.4 94.6 +0.9 −1.0 0.603+0.004 −0.002 0.82 fixed 0.37 50% ρ 122.2 ± 1.2 0.35 ± 0.01 1.0 ± 0.3 2.5 87.4 +0.9 −1.1 0.605+0.002 −0.002 0.82 fixed 0.45 The resonance kinematics are calculated at a given kinetic freeze-out temperature and average flow velocity. The spectra of the decay products are combined with those of the primordial ones. Spin, isospin degeneracies and decay branching ratios are properly taken into account. The calculated particle spectra are fit to the measured identified particle spectra [17], and the kinetic freezeout temperature and the transverse flow velocity are extracted for both pp and the 5% central Au+Au collisions. The extracted parameters are summarized in Table XII (the row labeled by “100% ρ”). Figures 43 and 44 show the calculated, best-fit particle spectra of π −, K− and p for pp and central Au+Au collisions, respectively. Calculated inclusive pion spectra do not contain weak decay pions, just as in Ref. [17]. Resonance contributions are labeled by the initial resonance particle (e.g. a ¯p emerging from the Ξ¯ → Λ¯ → p¯ decays is labeled as “Ξ decay”). Only major resonance decay contributions are shown, but all contributions including minor ones are included in the calculated inclusive spectra. Those minor contributions include η, η ′ , φ, ∆, Σ, Σ1385, and Λ1520 decays to pions, Ω and Λ1520 decays to kaons, and Ω and Λ1520 decays to (anti)protons. The lower panels of Figs. 43 and 44 show the resonance contributions to the inclusive spectra relative to the primordial ones for pp and central Au+Au collisions, respectively. The inclusive kaon and antiproton spectra do not show significant changes in the spectral shapes compared to the primordial ones for both pp and central Au+Au collisions in the measured p⊥ ranges. The shape of the inclusive π spectrum in pp is also similar to the primordial one, but is more significantly modified in central Au+Au collisions due to light meson contributions (ρ, ω and η) at both small and large p⊥. The largest contribution is from the ρ meson. The shapes of the modi- fications are different for pp and central Au+Au because of the significant flattening of the spectra in Au+Au but not in pp. The η and ω mesons are less significant in pp as compared to those in central Au+Au. However, in our measured p⊥ range of 0.2-0.7 GeV/c, any modification in the shape of the pion spectrum is still not large, as seen from Fig. 44. For comparison, the default blast-wave fit with no resonances is also shown in Figs. 43 and 44. These fits are the spectra for the thermal particles with the corresponding fit parameters. As can be seen from Tables X and XII and the figure, blast-wave fits with and without the resonances give similar quality fits to the data. The extracted kinetic freeze-out temperature and average flow velocity agree within the systematic uncertainties [17]. In other words, resonance decays appear to have no significant effect on the extracted kinetic freeze-out parameters. This is primarily due to the limited p⊥ ranges of the measured data where resonance decay products have more or less the same spectral shapes as the primordial particles do. It was claimed in Refs. [166, 167, 168] that a single freeze-out temperature for chemical and kinetic freezeout can satisfactorily describe the data. To test this, the spectra are also fit with a single, fixed kinetic freeze-out temperature Tkin = Tchem = 160 MeV including resonances. The fit hβi is 0.520+0.001 −0.002 with χ 2/ndf=19.6; the quality of our fit is similar to those in Refs. [166, 167, 168]. Based on this fit quality, a single temperature scenario is ruled out by the data, and we are not able to confirm the conclusion in Refs. [166, 167, 168]. 2. Regeneration of Short-Lived Resonances The blast-wave model assumes that all particles and resonances decouple at the same Tkin and β. Shortlived resonances (e.g. ρ and ∆), due to their short lifetimes relative to the system evolution time, decay and are regenerated continuously, hence they might have different flow velocities and temperatures than long-lived resonances (and the bulk itself). Thus, it is reasonable to expect that short-lived resonances do not gain signifi- cantly larger flow velocity than the net flow of their decay daughters, as would be naively expected from their large masses. The ρ meson contributes to the pion spectrum and could alter the inclusive pion spectrum shape signifi- cantly. In the default treatment of resonances in the blast-wave parameterization, the ρ acquires p⊥ as given by the kinetic freeze-out temperature and the common transverse flow velocity (with the corresponding ρ mass), and the decay pions are calculated from decay kinematics. To test the validity of the regeneration picture, two additional cases of different ρ contributions are studied: (1) The ρ decay pions have the same p⊥ spectral shape as the primordial pions. This is equivalent to a zero ρ lifetime; the ρ does not have time to interact with the medium and gain its own flow; the flow it has is from that 45 p [GeV/c] ] -2 [(GeV/c) 2 dN/dp component / thermal 0.2 0.4 0.6 0.8 1 1.2 1.4 -5 10 -4 10 -3 10 -2 10 -1 10 1 spectra – π inclusive – π thermal – π ρ decay ω decay 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 3.5 inclusive – π thermal – π ρ decay ω decay p [GeV/c] ] -2 [(GeV/c) 2 dN/dp component / thermal 0.2 0.4 0.6 0.8 1 1.2 1.4 -5 10 -4 10 -3 10 -2 10 -1 10 1 spectra – K inclusive – K thermal – K decay 0 K* φ decay 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 3.5 inclusive – K thermal – K decay 0 K* φ decay p [GeV/c] ] -2 [(GeV/c) 2 dN/dp component / thermal 0.2 0.4 0.6 0.8 1 1.2 1.4 -4 10 -3 10 -2 10 -1 10 inclusive p spectra p p thermal ∆ decay Λ decay Ξ decay 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 3.5 p inclusive p thermal ∆ decay Λ decay Ξ decay FIG. 43: Upper panels: Calculated π −, K−, and ¯p transverse momentum spectra from the primordial thermal component and major resonance decay contributions for pp collisions at 200 GeV. The kinetic freeze-out parameters fit to data are used for the thermal calculations [17]. Lower panels: Resonance contributions relative to the thermal spectrum. K∗− decay (not shown) has the same contribution to K− (and K+) spectra as K∗0 decay. Σ and Σ1385 decays (not shown) contribute to the p (and proton) spectra with similar magnitude as Λ decays. p [GeV/c] ] -2 [(GeV/c) 2 dN/dp component / thermal 0.2 0.4 0.6 0.8 1 1.2 1.4 -2 10 -1 10 1 10 2 10 3 10 spectra – π inclusive – π thermal – π ρ decay ω decay 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 3.5 inclusive – π thermal – π ρ decay ω decay p [GeV/c] ] -2 [(GeV/c) 2 dN/dp component / thermal 0.2 0.4 0.6 0.8 1 1.2 1.4 -2 10 -1 10 1 10 2 10 spectra – K inclusive – K thermal – K decay 0 K* φ decay 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 3.5 inclusive – K thermal – K decay 0 K* φ decay p [GeV/c] ] -2 [(GeV/c) 2 dN/dp component / thermal 0.2 0.4 0.6 0.8 1 1.2 1.4 -1 10 1 10 p spectra p inclusive p thermal ∆ decay Λ decay Ξ decay 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 3.5 p inclusive p thermal ∆ decay Λ decay Ξ decay FIG. 44: Same as Fig. 43 but for the top 5% central Au+Au collisions at 200 GeV [17]. of the resonant pion pair that flow with the medium. In this case the existence of ρ’s does not make differences in the final fit results. This case is referred to as “0% ρ” below. (2) Half of the ρ contribution is taken like in (1) and the other half as in the default treatment. This case is referred to as “50% ρ” below. Since ρ is very efficient at gaining flow compared to the much lighter pions, the default treatment of blast-wave parameterization gives the largest
flow to ρ, and case (1) gives the smallest flow. Table XII shows the fit results for the two cases, together with the default case of resonance treatment (i.e. the “100% ρ” case), for both pp and central Au+Au collisions. Figures 45 and 46 show the fits of the calculated inclusive pion spectra to the measured ones for pp and central Au+Au, respectively. Fits are performed to the six measured spectra simultaneously, but only negatively charged particles are shown. The fit results from the 0% and 50% ρ cases are only shown for the pions. As can be seen from the table and the figures, the models with all three cases of ρ contribution describe the 46 p [GeV/c] 0.2 0.4 0.6 0.8 1 1.2 1.4 ] -2 [(GeV/c) 2 dN/dp -2 10 -1 10 1 No resonance ρ 100% ρ 50% ρ 0% Data – π Data – K p Data p [GeV/c] 0 0.2 0.4 0.6 0.8 1 Data / Calculation 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 – π No resonance ρ 100% ρ 50% ρ 0% p [GeV/c] 0 0.2 0.4 0.6 0.8 1 Data / Calculation 0.7 0.8 0.9 1 1.1 1.2 1.3 – K No resonance ρ 100% p [GeV/c] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Data / Calculation 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 p No resonance ρ 100% FIG. 45: Left panel: Fit of the calculated spectra (curves) to the measured ones (data points) in pp collisions at 200 GeV [17]. Four calculated spectra are shown for π − (upper curves): including resonances with three different ρ contributions and excluding resonances. Only two calculated curves are shown for K− (middle curves) and ¯p (lower curves): including resonances with 100% ρ and excluding resonances. Other panels: Ratios of data spectrum to calculations. Two calculations are shown for K− and p, while four calculations are shown for π −. Error bars are the quadratic sum of the statistical and point-to-point systematic errors on the data, and are shown for two sets of the data points for π − and only one set for K− and p. p [GeV/c] 0.2 0.4 0.6 0.8 1 1.2 1.4 ] -2 [(GeV/c) 2 dN/dp 1 10 2 10 3 10 No resonance ρ 100% ρ 50% ρ 0% Data – π Data – K p Data p [GeV/c] 0 0.2 0.4 0.6 0.8 1 Data / Calculation 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 – π No resonance ρ 100% ρ 50% ρ 0% p [GeV/c] 0 0.2 0.4 0.6 0.8 1 Data / Calculation 0.7 0.8 0.9 1 1.1 1.2 1.3 – K No resonance ρ 100% p [GeV/c] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Data / Calculation 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 p No resonance ρ 100% FIG. 46: Same as Fig. 45 but for the top 5% central Au+Au collisions at 200 GeV [17]. spectra data well. The fit Tkin and hβi values from all three cases agree; they also agree with those obtained without including resonances within systematic uncertainties (shown in Table X). It is interesting to note, however, that for the three ρ cases, the lowest χ 2/ndf is found for the 100% ρ case in pp collisions and for the 0% ρ case in central Au+Au collisions. If taken literally, this could imply that pp collisions favor no regeneration, and central Au+Au collisions favor complete regeneration, hence a long time span between chemical freeze-out and kinetic freeze-out, lending support to the similar observation made by the K∗ measurement [48, 51]. APPENDIX C: INVARIANT p⊥ SPECTRA DATA TABLES The transverse momentum spectra of the invariant yield per event are tabulated in Tables XIII – XXXVII. ACKNOWLEDGMENTS We thank the RHIC Operations Group and RCF at BNL, and the NERSC Center at LBNL and the resources provided by the Open Science Grid consortium for their support. 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Molnar, Ph.D. thesis, Purdue University, 2006. arXiv:0805.3086. 47 TABLE XIII: Identified π ±, K±, antiproton and proton invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in minimum bias pp collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. For proton, systematic uncertainties due to proton background subtraction are also included in quadrature. See Section V A for other systematic uncertainties. Data were published in Ref. [17]. p⊥ π − π + K− K+ p p 0.225 2.02±0.06 2.07±0.06 (1.43±0.11)×10−1 (1.52±0.11)×10−1 0.275 1.52±0.03 1.54±0.03 (1.26±0.05)×10−1 (1.30±0.05)×10−1 0.325 1.13±0.02 1.14±0.02 (1.08±0.02)×10−1 (1.08±0.02)×10−1 0.375 (8.44±0.09)×10−1 (8.57±0.09)×10−1 (8.77±0.24)×10−2 (9.16±0.25)×10−2 (5.54±0.13)×10−2 0.425 (6.35±0.07)×10−1 (6.38±0.07)×10−1 (7.34±0.26)×10−2 (7.47±0.27)×10−2 (4.81±0.11)×10−2 0.475 (4.69±0.05)×10−1 (4.76±0.05)×10−1 (6.17±0.63)×10−2 (6.26±0.64)×10−2 (4.25±0.10)×10−2 (5.07±0.25)×10−2 0.525 (3.54±0.04)×10−1 (3.59±0.04)×10−1 (4.87±0.50)×10−2 (5.26±0.54)×10−2 (3.77±0.09)×10−2 (4.69±0.19)×10−2 0.575 (2.67±0.03)×10−1 (2.73±0.03)×10−1 (4.11±0.42)×10−2 (4.41±0.45)×10−2 (3.38±0.08)×10−2 (4.08±0.14)×10−2 0.625 (2.02±0.04)×10−1 (2.07±0.04)×10−1 (3.70±0.28)×10−2 (3.81±0.28)×10−2 (2.78±0.07)×10−2 (3.42±0.10)×10−2 0.675 (1.53±0.03)×10−1 (1.55±0.03)×10−1 (2.86±0.22)×10−2 (3.06±0.24)×10−2 (2.49±0.06)×10−2 (2.87±0.07)×10−2 0.725 (1.16±0.03)×10−1 (1.16±0.03)×10−1 (2.42±0.27)×10−2 (2.49±0.28)×10−2 (2.03±0.06)×10−2 (2.41±0.07)×10−2 0.775 (8.65±0.30)×10−2 (8.95±0.31)×10−2 (1.75±0.06)×10−2 (2.13±0.06)×10−2 0.825 (1.52±0.05)×10−2 (1.82±0.05)×10−2 0.875 (1.27±0.04)×10−2 (1.54±0.05)×10−2 0.925 (1.05±0.04)×10−2 (1.31±0.04)×10−2 0.975 (8.95±0.34)×10−3 (1.11±0.04)×10−2 1.025 (7.36±0.34)×10−3 (9.78±0.40)×10−3 1.075 (6.59±0.32)×10−3 (8.56±0.37)×10−3 1.125 (5.21±0.29)×10−3 (7.38±0.38)×10−3 [6] J. 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Arnold et al. , Nucl. Instrum. Meth A499, 652 (2003). [42] M. Gyulassy and X.-N. Wang, Comput. Phys. Commun. 83, 307 (1994). [43] D. Ashery and J.P. Schiffer, 48 TABLE XIV: Identified π − invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in d+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. p⊥ min. bias 40-100% 20-40% 0-20% 0.225 6.59 ± 0.07 4.16 ± 0.04 8.84 ± 0.09 (1.16 ± 0.01) × 101 0.275 4.84 ± 0.05 3.07 ± 0.03 6.29 ± 0.06 8.70 ± 0.09 0.325 3.60 ± 0.04 2.28 ± 0.02 4.69 ± 0.05 6.51 ± 0.07 0.375 2.69 ± 0.03 1.69 ± 0.02 3.51 ± 0.04 4.89 ± 0.05 0.425 2.05 ± 0.08 1.28 ± 0.05 2.66 ± 0.11 3.74 ± 0.15 0.475 1.56 ± 0.06 (9.66 ± 0.39) × 10−1 2.04 ± 0.08 2.87 ± 0.12 0.525 1.20 ± 0.05 (7.31 ± 0.29) × 10−1 1.57 ± 0.06 2.22 ± 0.09 0.575 (9.27 ± 0.37) × 10−1 (5.64 ± 0.23) × 10−1 1.21 ± 0.05 1.73 ± 0.07 0.625 (7.22 ± 0.43) × 10−1 (4.38 ± 0.26) × 10−1 (9.45 ± 0.57) × 10−1 1.35 ± 0.08 0.675 (5.67 ± 0.17) × 10−1 (3.40 ± 0.10) × 10−1 (7.43 ± 0.23) × 10−1 1.07 ± 0.03 TABLE XV: Identified π + invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in d+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. p⊥ min. bias 40-100% 20-40% 0-20% 0.225 6.54 ± 0.07 4.10 ± 0.04 8.53 ± 0.09 (1.19 ± 0.01) × 101 0.275 4.78 ± 0.05 3.00 ± 0.03 6.23 ± 0.06 8.69 ± 0.09 0.325 3.59 ± 0.04 2.27 ± 0.02 4.65 ± 0.05 6.49 ± 0.07 0.375 2.68 ± 0.03 1.65 ± 0.02 3.48 ± 0.04 4.94 ± 0.05 0.425 2.07 ± 0.08 1.31 ± 0.05 2.66 ± 0.11 3.77 ± 0.15 0.475 1.54 ± 0.06 (9.23 ± 0.37) × 10−1 2.04 ± 0.08 2.90 ± 0.12 0.525 1.22 ± 0.05 (7.55 ± 0.30) × 10−1 1.58 ± 0.06 2.23 ± 0.09 0.575 (9.32 ± 0.37) × 10−1 (5.67 ± 0.23) × 10−1 1.22 ± 0.05 1.74 ± 0.07 0.625 (7.40 ± 0.44) × 10−1 (4.60 ± 0.28) × 10−1 (9.54 ± 0.57) × 10−1 1.37 ± 0.08 0.675 (5.67 ± 0.17) × 10−1 (3.32 ± 0.10) × 10−1 (7.49 ± 0.23) × 10−1 1.09 ± 0.03 TABLE XVI: Identified K− invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in d+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. p⊥ min. bias 40-100% 20-40% 0-20% 0.225 (5.15 ± 0.16) × 10−1 (3.21 ± 0.11) × 10−1 (6.65 ± 0.23) × 10−1 (9.47 ± 0.32) × 10−1 0.275 (4.34 ± 0.05) × 10−1 (2.73 ± 0.04) × 10−1 (5.63 ± 0.09) × 10−1 (7.85 ± 0.12) × 10−1 0.325 (3.64 ± 0.08) × 10−1 (2.25 ± 0.05) × 10−1 (4.75 ± 0.11) × 10−1 (6.70 ± 0.15) × 10−1 0.375 (3.13 ± 0.28) × 10−1 (1.96 ± 0.18) × 10−1 (4.06 ± 0.37) × 10−1 (5.75 ± 0.52) × 10−1 0.425 (2.62 ± 0.37) × 10−1 (1.61 ± 0.23) × 10−1 (3.43 ± 0.48) × 10−1 (4.81 ± 0.68) × 10−1 0.475 (2.11 ± 0.23) × 10−1 (1.24 ± 0.14) × 10−1 (2.76 ± 0.31) × 10−1 (4.07 ± 0.45) × 10−1 0.525 (1.85 ± 0.13) × 10−1 (1.09 ± 0.08) × 10−1 (2.44 ± 0.17) × 10−1 (3.52 ± 0.25) × 10−1 0.575 (1.63 ± 0.15) × 10−1 (9.63 ± 0.87) × 10−2 (2.15 ± 0.20) × 10−1 (3.09 ± 0.28) × 10−1 0.625 (1.32 ± 0.07) × 10−1 (7.67 ± 0.40) × 10−2 (1.72 ± 0.09) × 10−1 (2.57 ± 0.13) × 10−1 0.675 (1.16 ± 0.09) × 10−1 (6.76 ± 0.55) × 10−2 (1.57 ± 0.13) × 10−1 (2.21 ± 0.18) × 10−1 0.725 (1.01 ± 0.05) × 10−1 (6.16 ± 0.36) × 10−2 (1.31 ± 0.08) × 10−1 (1.91 ± 0.11) × 10−1 TABLE XVII: Identified K+ invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in d+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. p⊥ min. bias 40-100% 20-40% 0-20% 0.225 (4.84 ± 0.15) × 10−1 (2.99 ± 0.10) × 10−1 (6.32 ± 0.22) × 10−1 (8.93 ± 0.30) × 10−1 0.275 (4.28 ± 0.05) × 10−1 (2.71 ± 0.04) × 10−1 (5.50 ± 0.09) × 10−1 (7.78 ± 0.11) × 10−1 0.325 (3.68 ± 0.08) × 10−1 (2.31 ± 0.05) × 10−1 (4.83 ± 0.11) × 10−1 (6.68 ± 0.15) × 10−1 0.375 (3.24 ± 0.29) × 10−1 (1.99 ± 0.18) × 10−1 (4.28 ± 0.39) × 10−1 (5.94 ± 0.54) × 10−1 0.425 (2.73 ± 0.38) × 10−1 (1.68 ± 0.24) × 10−1 (3.58 ± 0.50) × 10−1 (5.04 ± 0.71) × 10−1 0.475 (2.25 ± 0.25) × 10−1 (1.34 ± 0.15) × 10−1 (2.95 ± 0.33) × 10−1 (4.30 ± 0.47) × 10−1 0.525 (2.00 ± 0.14) × 10−1 (1.22 ± 0.09) × 10−1 (2.64 ± 0.19) × 10−1 (3.72 ± 0.26) × 10−1 0.575 (1.74 ± 0.16) × 10−1 (1.05 ± 0.09) × 10−1 (2.30 ± 0.21) × 10−1 (3.26 ± 0.30) × 10−1 0.625 (1.41 ± 0.07) × 10−1 (8.23 ± 0.42) × 10−2 (1.88 ± 0.10) × 10−1 (2.70 ± 0.14) × 10−1 0.675 (1.27 ± 0.10) × 10−1 (7.36 ± 0.60) × 10−2 (1.68 ± 0.14) × 10−1 (2.45 ± 0.20) × 10−1 49 TABLE XVIII: Identified p invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in d+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. p⊥ min. bias 40-100% 20-40% 0-20% 0.425 (1.37 ± 0.02) × 10−1 (8.46 ± 0.12) × 10−2 (1.76 ± 0.03) × 10−1 (2.55 ± 0.04) × 10−1 0.475 (1.22 ± 0.01) × 10−1 (7.39 ± 0.11) × 10−2 (1.55 ± 0.02) × 10−1 (2.35 ± 0.03) × 10−1 0.525 (1.11 ± 0.01) × 10−1 (6.58 ± 0.09) × 10−2 (1.43 ± 0.02) × 10−1 (2.12 ± 0.03) × 10−1 0.575 (1.01 ± 0.01) × 10−1 (5.97 ± 0.09) × 10−2 (1.33 ± 0.02) × 10−1 (1.93 ± 0.03) × 10−1 0.625 (9.00 ± 0.19) × 10−2 (5.27 ± 0.12) × 10−2 (1.18 ± 0.03) × 10−1 (1.74 ± 0.04) × 10−1 0.675 (8.05 ± 0.17) × 10−2 (4.65 ± 0.11) × 10−2 (1.06 ± 0.02) × 10−1 (1.57 ± 0.04) × 10−1 0.725 (7.22 ± 0.09) × 10−2 (4.12 ± 0.06) × 10−2 (9.47 ± 0.15) × 10−2 (1.43 ± 0.02) × 10−1 0.775 (6.37 ± 0.20) × 10−2 (3.60 ± 0.12) × 10−2 (8.48 ± 0.27) × 10−2 (1.26 ± 0.04) × 10−1 0.825 (5.77 ± 0.29) × 10−2 (3.20 ± 0.16) × 10−2 (7.88 ± 0.41) × 10−2 (1.14 ± 0.06) × 10−1 0.875 (5.21 ± 0.26) × 10−2 (2.93 ± 0.15) × 10−2 (7.18 ± 0.37) × 10−2 (1.01 ± 0.05) × 10−1 0.925 (4.57 ± 0.10) × 10−2 (2.55 ± 0.06) × 10−2 (6.37 ± 0.15) × 10−2 (8.80 ± 0.20) × 10−2 0.975 (3.95 ± 0.08) × 10−2 (2.12 ± 0.05) × 10−2 (5.47 ± 0.13) × 10−2 (7.92 ± 0.19) × 10−2 1.025 (3.43 ± 0.24) × 10−2 (1.85 ± 0.13) × 10−2 (4.69 ± 0.34) × 10−2 (6.90 ± 0.49) × 10−2 1.075 (3.03 ± 0.10) × 10−2 (1.64 ± 0.06) × 10−2 (4.03 ± 0.14) × 10−2 (6.21 ± 0.21) × 10−2 TABLE XIX: Identified proton invariant transverse momentum spectra at mid-rapidity (|y| < 0.1)
in d+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and pointto-point systematic errors. See Section V A for other systematic uncertainties including those due to proton background subtraction. p⊥ min. bias 40-100% 20-40% 0-20% 0.425 (1.69 ± 0.02) × 10−1 (1.03 ± 0.01) × 10−1 (2.35 ± 0.03) × 10−1 (3.03 ± 0.04) × 10−1 0.475 (1.47 ± 0.02) × 10−1 (8.40 ± 0.11) × 10−2 (2.04 ± 0.03) × 10−1 (2.79 ± 0.03) × 10−1 0.525 (1.34 ± 0.01) × 10−1 (7.86 ± 0.10) × 10−2 (1.84 ± 0.02) × 10−1 (2.48 ± 0.03) × 10−1 0.575 (1.19 ± 0.01) × 10−1 (6.87 ± 0.09) × 10−2 (1.64 ± 0.02) × 10−1 (2.26 ± 0.03) × 10−1 0.625 (1.10 ± 0.02) × 10−1 (6.30 ± 0.14) × 10−2 (1.51 ± 0.03) × 10−1 (2.08 ± 0.04) × 10−1 0.675 (9.87 ± 0.20) × 10−2 (5.73 ± 0.13) × 10−2 (1.33 ± 0.03) × 10−1 (1.89 ± 0.04) × 10−1 0.725 (8.74 ± 0.10) × 10−2 (4.91 ± 0.07) × 10−2 (1.19 ± 0.02) × 10−1 (1.70 ± 0.02) × 10−1 0.775 (7.95 ± 0.24) × 10−2 (4.49 ± 0.15) × 10−2 (1.08 ± 0.03) × 10−1 (1.55 ± 0.05) × 10−1 0.825 (6.98 ± 0.35) × 10−2 (3.88 ± 0.20) × 10−2 (9.45 ± 0.48) × 10−2 (1.38 ± 0.07) × 10−1 0.875 (6.49 ± 0.33) × 10−2 (3.54 ± 0.18) × 10−2 (8.93 ± 0.46) × 10−2 (1.29 ± 0.07) × 10−1 0.925 (5.55 ± 0.12) × 10−2 (2.98 ± 0.07) × 10−2 (7.57 ± 0.17) × 10−2 (1.12 ± 0.02) × 10−1 0.975 (4.93 ± 0.10) × 10−2 (2.60 ± 0.06) × 10−2 (7.08 ± 0.16) × 10−2 (9.78 ± 0.22) × 10−2 1.025 (4.15 ± 0.29) × 10−2 (2.21 ± 0.16) × 10−2 (5.84 ± 0.42) × 10−2 (8.27 ± 0.59) × 10−2 1.075 (3.61 ± 0.12) × 10−2 (1.91 ± 0.06) × 10−2 (4.90 ± 0.22) × 10−2 (7.39 ± 0.24) × 10−2 50 TABLE XX: Identified π − invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 62.4 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. p⊥ 70-80% 60-70% 50-60% 40-50% 0.225 (1.07 ± 0.02) × 101 (2.02 ± 0.04) × 101 (3.63 ± 0.07) × 101 (5.91 ± 0.12) × 101 0.275 7.93 ± 0.16 (1.53 ± 0.03) × 101 (2.74 ± 0.05) × 101 (4.45 ± 0.09) × 101 0.325 5.89 ± 0.12 (1.15 ± 0.02) × 101 (2.08 ± 0.04) × 101 (3.36 ± 0.07) × 101 0.375 4.39 ± 0.05 8.69 ± 0.09 (1.58 ± 0.02) × 101 (2.57 ± 0.03) × 101 0.425 3.28 ± 0.04 6.59 ± 0.07 (1.20 ± 0.01) × 101 (1.97 ± 0.02) × 101 0.475 2.49 ± 0.03 5.02 ± 0.05 9.27 ± 0.10 (1.51 ± 0.02) × 101 0.525 1.89 ± 0.02 3.85 ± 0.04 7.12 ± 0.07 (1.17 ± 0.01) × 101 0.575 1.44 ± 0.03 2.96 ± 0.06 5.51 ± 0.11 9.08 ± 0.18 0.625 1.10 ± 0.02 2.28 ± 0.05 4.28 ± 0.09 7.07 ± 0.14 0.675 (8.37 ± 0.26) × 10−1 1.77 ± 0.05 3.35 ± 0.10 5.55 ± 0.17 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.225 (8.87 ± 0.18) × 101 (1.31 ± 0.03) × 102 (1.88 ± 0.04) × 102 (2.44 ± 0.05) × 102 (3.00 ± 0.06) × 102 0.275 (6.71 ± 0.13) × 101 (1.00 ± 0.02) × 102 (1.44 ± 0.03) × 102 (1.89 ± 0.04) × 102 (2.33 ± 0.05) × 102 0.325 (5.14 ± 0.10) × 101 (7.68 ± 0.15) × 101 (1.10 ± 0.02) × 102 (1.45 ± 0.03) × 102 (1.80 ± 0.04) × 102 0.375 (3.95 ± 0.04) × 101 (5.91 ± 0.06) × 101 (8.48 ± 0.09) × 101 (1.12 ± 0.01) × 102 (1.39 ± 0.01) × 102 0.425 (3.04 ± 0.03) × 101 (4.58 ± 0.05) × 101 (6.57 ± 0.07) × 101 (8.69 ± 0.09) × 101 (1.07 ± 0.01) × 102 0.475 (2.36 ± 0.02) × 101 (3.54 ± 0.04) × 101 (5.10 ± 0.05) × 101 (6.75 ± 0.07) × 101 (8.32 ± 0.08) × 101 0.525 (1.82 ± 0.02) × 101 (2.76 ± 0.03) × 101 (3.98 ± 0.04) × 101 (5.26 ± 0.05) × 101 (6.47 ± 0.07) × 101 0.575 (1.42 ± 0.03) × 101 (2.15 ± 0.04) × 101 (3.11 ± 0.06) × 101 (4.10 ± 0.08) × 101 (5.05 ± 0.10) × 101 0.625 (1.11 ± 0.02) × 101 (1.68 ± 0.03) × 101 (2.44 ± 0.05) × 101 (3.22 ± 0.06) × 101 (3.96 ± 0.08) × 101 0.675 8.78 ± 0.26 (1.33 ± 0.04) × 101 (1.93 ± 0.06) × 101 (2.54 ± 0.08) × 101 (3.14 ± 0.09) × 101 TABLE XXI: Identified π + invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 62.4 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. p⊥ 70-80% 60-70% 50-60% 40-50% 0.225 (1.07 ± 0.02) × 101 (2.11 ± 0.04) × 101 (3.66 ± 0.07) × 101 (5.89 ± 0.12) × 101 0.275 7.79 ± 0.16 (1.56 ± 0.03) × 101 (2.71 ± 0.05) × 101 (4.37 ± 0.09) × 101 0.325 5.81 ± 0.12 (1.16 ± 0.02) × 101 (2.04 ± 0.04) × 101 (3.31 ± 0.07) × 101 0.375 4.32 ± 0.05 8.77 ± 0.09 (1.56 ± 0.02) × 101 (2.53 ± 0.03) × 101 0.425 3.27 ± 0.04 6.60 ± 0.07 (1.19 ± 0.01) × 101 (1.95 ± 0.02) × 101 0.475 2.44 ± 0.03 5.04 ± 0.05 9.13 ± 0.09 (1.50 ± 0.02) × 101 0.525 1.86 ± 0.02 3.81 ± 0.04 7.03 ± 0.07 (1.15 ± 0.01) × 101 0.575 1.43 ± 0.03 2.93 ± 0.06 5.45 ± 0.11 8.94 ± 0.18 0.625 1.08 ± 0.02 2.26 ± 0.05 4.21 ± 0.09 6.99 ± 0.14 0.675 (8.34 ± 0.26) × 10−1 1.75 ± 0.05 3.26 ± 0.10 5.45 ± 0.16 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.225 (8.82 ± 0.18) × 101 (1.28 ± 0.03) × 102 (1.87 ± 0.04) × 102 (2.39 ± 0.05) × 102 (2.95 ± 0.06) × 102 0.275 (6.61 ± 0.13) × 101 (9.70 ± 0.19) × 101 (1.41 ± 0.03) × 102 (1.85 ± 0.04) × 102 (2.27 ± 0.05) × 102 0.325 (5.06 ± 0.10) × 101 (7.44 ± 0.15) × 101 (1.08 ± 0.02) × 102 (1.44 ± 0.03) × 102 (1.75 ± 0.04) × 102 0.375 (3.89 ± 0.04) × 101 (5.77 ± 0.06) × 101 (8.36 ± 0.08) × 101 (1.12 ± 0.01) × 102 (1.36 ± 0.01) × 102 0.425 (3.00 ± 0.03) × 101 (4.47 ± 0.05) × 101 (6.49 ± 0.07) × 101 (8.69 ± 0.09) × 101 (1.05 ± 0.01) × 102 0.475 (2.32 ± 0.02) × 101 (3.47 ± 0.03) × 101 (5.04 ± 0.05) × 101 (6.74 ± 0.07) × 101 (8.21 ± 0.08) × 101 0.525 (1.80 ± 0.02) × 101 (2.71 ± 0.03) × 101 (3.92 ± 0.04) × 101 (5.24 ± 0.05) × 101 (6.38 ± 0.06) × 101 0.575 (1.40 ± 0.03) × 101 (2.11 ± 0.04) × 101 (3.07 ± 0.06) × 101 (4.09 ± 0.08) × 101 (4.99 ± 0.10) × 101 0.625 (1.09 ± 0.02) × 101 (1.66 ± 0.03) × 101 (2.41 ± 0.05) × 101 (3.21 ± 0.06) × 101 (3.90 ± 0.08) × 101 0.675 8.66 ± 0.26 (1.31 ± 0.04) × 101 (1.90 ± 0.06) × 101 (2.53 ± 0.08) × 101 (3.09 ± 0.09) × 101 Ann. Rev. Nucl. Part. Sci. 36, 207 (1986). [44] C. Adler, et al. (STAR Collaboration), Phys. Rev. Lett. 89, 092301 (2002). [45] C. Adler, et al. (STAR Collaboration), Phys. Rev. Lett. 86, 4778 (2001). Erratum: ibid 90, 119903 (2003). [46] C. Adler, et al. (STAR Collaboration), Phys. Lett. B 616, 8 (2005). [47] B.I. Abelev et al. (STAR Collaboration), Phys. Lett. B 655, 104 (2007). [48] C. Adler et al. (STAR Collaboration), Phys. Rev. C 66, 061901 (2002). 51 TABLE XXII: Identified K− invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 62.4 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. p⊥ 70-80% 60-70% 50-60% 40-50% 0.275 (7.03 ± 0.19) × 10−1 1.41 ± 0.03 2.51 ± 0.06 4.07 ± 0.09 0.325 (5.95 ± 0.20) × 10−1 1.18 ± 0.04 2.18 ± 0.07 3.48 ± 0.11 0.375 (4.89 ± 0.26) × 10−1 1.04 ± 0.05 1.91 ± 0.10 3.08 ± 0.16 0.425 (4.05 ± 0.49) × 10−1 (8.79 ± 1.06) × 10−1 1.63 ± 0.20 2.71 ± 0.33 0.475 (3.14 ± 0.38) × 10−1 (7.23 ± 0.87) × 10−1 1.31 ± 0.16 2.24 ± 0.27 0.525 (2.70 ± 0.33) × 10−1 (5.86 ± 0.71) × 10−1 1.13 ± 0.14 1.92 ± 0.23 0.575 (2.27 ± 0.19) × 10−1 (5.04 ± 0.41) × 10−1 (9.71 ± 0.78) × 10−1 1.70 ± 0.14 0.625 (1.83 ± 0.19) × 10−1 (4.37 ± 0.44) × 10−1 (8.27 ± 0.83) × 10−1 1.48 ± 0.15 0.675 (1.61 ± 0.20) × 10−1 (3.71 ± 0.45) × 10−1 (7.48 ± 0.90) × 10−1 1.30 ± 0.16 0.725 (1.50 ± 0.10) × 10−1 (3.30 ± 0.20) × 10−1 (6.51 ± 0.36) × 10−1 1.16 ± 0.06 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.275 5.88 ± 0.12 9.01 ± 0.19 (1.21 ± 0.02) × 101 (1.67 ± 0.03) × 101 (1.89 ± 0.02) × 101 0.325 5.19 ± 0.16 7.
92 ± 0.24 (1.10 ± 0.03) × 101 (1.46 ± 0.04) × 101 (1.70 ± 0.03) × 101 0.375 4.72 ± 0.24 7.19 ± 0.36 (1.01 ± 0.05) × 101 (1.35 ± 0.07) × 101 (1.61 ± 0.14) × 101 0.425 4.20 ± 0.50 6.37 ± 0.76 9.06 ± 1.09 (1.20 ± 0.14) × 101 (1.44 ± 0.20) × 101 0.475 3.49 ± 0.42 5.27 ± 0.63 7.50 ± 0.90 (1.06 ± 0.13) × 101 (1.27 ± 0.14) × 101 0.525 3.04 ± 0.37 4.59 ± 0.55 6.58 ± 0.79 8.86 ± 1.06 (1.13 ± 0.08) × 101 0.575 2.68 ± 0.22 4.06 ± 0.33 5.84 ± 0.47 8.03 ± 0.64 (1.04 ± 0.09) × 101 0.625 2.37 ± 0.24 3.63 ± 0.36 5.32 ± 0.53 7.21 ± 0.72 9.36 ± 0.47 0.675 2.09 ± 0.25 3.24 ± 0.39 4.68 ± 0.56 6.36 ± 0.77 7.73 ± 0.62 0.725 1.80 ± 0.09 2.84 ± 0.15 4.17 ± 0.22 5.43 ± 0.29 5.94 ± 0.31 TABLE XXIII: Identified K+ invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 62.4 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. p⊥ 70-80% 60-70% 50-60% 40-50% 0.275 (7.29 ± 0.19) × 10−1 1.54 ± 0.04 2.63 ± 0.06 4.90 ± 0.10 0.325 (5.82 ± 0.19) × 10−1 1.31 ± 0.04 2.32 ± 0.07 4.14 ± 0.13 0.375 (5.07 ± 0.26) × 10−1 1.14 ± 0.06 2.09 ± 0.11 3.63 ± 0.18 0.425 (4.40 ± 0.53) × 10−1 (9.92 ± 1.20) × 10−1 1.81 ± 0.22 3.13 ± 0.38 0.475 (3.58 ± 0.43) × 10−1 (8.04 ± 0.97) × 10−1 1.53 ± 0.18 2.61 ± 0.31 0.525 (3.20 ± 0.39) × 10−1 (6.89 ± 0.83) × 10−1 1.31 ± 0.16 2.23 ± 0.27 0.575 (2.52 ± 0.21) × 10−1 (5.78 ± 0.47) × 10−1 1.14 ± 0.09 1.93 ± 0.16 0.625 (2.13 ± 0.22) × 10−1 (4.97 ± 0.50) × 10−1 (9.80 ± 0.98) × 10−1 1.67 ± 0.17 0.675 (1.86 ± 0.23) × 10−1 (4.13 ± 0.50) × 10−1 (8.52 ± 1.03) × 10−1 1.42 ± 0.17 0.725 (1.64 ± 0.10) × 10−1 (3.78 ± 0.22) × 10−1 (7.26 ± 0.39) × 10−1 1.28 ± 0.07 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.275 7.11 ± 0.15 (1.03 ± 0.02) × 101 (1.43 ± 0.03) × 101 (1.91 ± 0.04) × 101 (2.25 ± 0.05) × 101 0.325 6.20 ± 0.19 8.86 ± 0.27 (1.25 ± 0.04) × 101 (1.67 ± 0.05) × 101 (2.03 ± 0.06) × 101 0.375 5.52 ± 0.28 8.02 ± 0.40 (1.15 ± 0.06) × 101 (1.55 ± 0.08) × 101 (1.88 ± 0.09) × 101 0.425 4.85 ± 0.58 7.19 ± 0.86 (1.04 ± 0.13) × 101 (1.40 ± 0.17) × 101 (1.68 ± 0.20) × 101 0.475 4.07 ± 0.49 6.09 ± 0.73 8.97 ± 1.08 (1.21 ± 0.14) × 101 (1.44 ± 0.17) × 101 0.525 3.54 ± 0.42 5.32 ± 0.64 7.86 ± 0.94 (1.05 ± 0.13) × 101 (1.28 ± 0.15) × 101 0.575 3.06 ± 0.25 4.69 ± 0.38 6.95 ± 0.56 9.32 ± 0.75 (1.14 ± 0.09) × 101 0.625 2.65 ± 0.27 4.13 ± 0.41 6.09 ± 0.61 8.25 ± 0.83 (1.01 ± 0.10) × 101 0.675 2.34 ± 0.28 3.61 ± 0.43 5.33 ± 0.64 7.20 ± 0.87 8.71 ± 1.05 0.725 2.02 ± 0.10 3.12 ± 0.16 4.55 ± 0.23 6.27 ± 0.33 7.41 ± 0.38 [49] J. Adams et al. (STAR Collaboration), Phys. Lett. B 567, 167 (2003). [50] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. 92, 182301 (2004). [51] J. Adams et al. (STAR Collaboration), Phys. Rev. C 71, 064902 (2005). [52] B.I. Abelev et al. (STAR Collaboration), Phys. Rev. C 75, 064901 (2007). [53] B.I. Abelev et al. (STAR Collaboration), Phys. Rev. Lett. 97, 132301 (2006). [54] J. Adams et al. (STAR Collaboration), Phys. Rev. D 74, 032006 (2006). 52 TABLE XXIV: Identified p invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 62.4 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. p⊥ 70-80% 60-70% 50-60% 40-50% 0.375 (2.05 ± 0.04) × 10−1 (3.87 ± 0.06) × 10−1 (6.19 ± 0.09) × 10−1 (9.12 ± 0.12) × 10−1 0.425 (1.85 ± 0.04) × 10−1 (3.53 ± 0.06) × 10−1 (5.93 ± 0.08) × 10−1 (8.75 ± 0.11) × 10−1 0.475 (1.76 ± 0.03) × 10−1 (3.37 ± 0.05) × 10−1 (5.59 ± 0.08) × 10−1 (8.31 ± 0.11) × 10−1 0.525 (1.53 ± 0.03) × 10−1 (3.11 ± 0.05) × 10−1 (5.18 ± 0.07) × 10−1 (7.89 ± 0.10) × 10−1 0.575 (1.34 ± 0.03) × 10−1 (2.82 ± 0.04) × 10−1 (4.87 ± 0.07) × 10−1 (7.29 ± 0.09) × 10−1 0.625 (1.20 ± 0.03) × 10−1 (2.51 ± 0.06) × 10−1 (4.37 ± 0.10) × 10−1 (6.85 ± 0.15) × 10−1 0.675 (1.05 ± 0.03) × 10−1 (2.24 ± 0.05) × 10−1 (3.96 ± 0.09) × 10−1 (6.24 ± 0.13) × 10−1 0.725 (8.84 ± 0.24) × 10−2 (2.04 ± 0.05) × 10−1 (3.54 ± 0.08) × 10−1 (5.65 ± 0.12) × 10−1 0.775 (7.49 ± 0.21) × 10−2 (1.70 ± 0.04) × 10−1 (3.16 ± 0.07) × 10−1 (5.11 ± 0.11) × 10−1 0.825 (6.87 ± 0.19) × 10−2 (1.53 ± 0.04) × 10−1 (2.92 ± 0.07) × 10−1 (4.83 ± 0.10) × 10−1 0.875 (5.99 ± 0.22) × 10−2 (1.41 ± 0.05) × 10−1 (2.42 ± 0.08) × 10−1 (4.06 ± 0.13) × 10−1 0.925 (4.93 ± 0.18) × 10−2 (1.18 ± 0.04) × 10−1 (2.15 ± 0.07) × 10−1 (3.63 ± 0.11) × 10−1 0.975 (4.21 ± 0.16) × 10−2 (1.01 ± 0.03) × 10−1 (1.88 ± 0.06) × 10−1 (3.25 ± 0.10) × 10−1 1.025 (3.57 ± 0.14) × 10−2 (8.90 ± 0.31) × 10−2 (1.62 ± 0.05) × 10−1 (2.89 ± 0.09) × 10−1 1.075 (3.15 ± 0.15) × 10−2 (7.47 ± 0.33) × 10−2 (1.41 ± 0.06) × 10−1 (2.48 ± 0.10) × 10−1 1.125 (2.68 ± 0.14) × 10−2 (6.31 ± 0.31) × 10−2 (1.20 ± 0.05) × 10−1 (2.21 ± 0.10) × 10−1 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.375 1.26 ± 0.02 1.70 ± 0.02 2.17 ± 0.02 2.72 ± 0.03 3.11 ± 0.04 0.425 1.19 ± 0.01 1.64 ± 0.02 2.12 ± 0.02 2.62 ± 0.03 3.04 ± 0.04 0.475 1.16 ± 0.01 1.57 ± 0.02 2.07 ± 0.02 2.60 ± 0.03 2.98 ± 0.03 0.525 1.11 ± 0.01 1.53 ± 0.02 2.05 ± 0.02 2.49 ± 0.03 2.92 ± 0.03 0.575 1.05 ± 0.01 1.45 ± 0.02 1.96 ± 0.02 2.43 ± 0.03 2.87 ± 0.03 0.625 (9.79 ± 0.21) × 10−1 1.37 ± 0.03 1.86 ± 0.04 2.35 ± 0.05 2.75 ± 0.06 0.675 (9.20 ± 0.19) × 10−1 1.29 ± 0.03 1.77 ± 0.04 2.23 ± 0.05 2.63 ± 0.05 0.725 (8.36 ± 0.18) × 10−1 1.20 ± 0.02 1.65 ± 0.03 2.09 ± 0.04 2.50 ± 0.05 0.775 (7.77 ± 0.16) × 10−1 1.10 ± 0.02 1.53 ± 0.03 1.96 ± 0.04 2.33 ± 0.05 0.825 (7.12 ± 0.15) × 10−1 1.05 ± 0.02 1.45 ± 0.03 1.89 ± 0.04 2.31 ± 0.05 0.875 (6.76 ± 0.21) × 10−1 (9.89 ± 0.30) × 10−1 1.39 ± 0.04 1.80 ± 0.06 2.07 ± 0.06 0.925 (5.98 ± 0.18) × 10−1 (8.74 ± 0.27) × 10−1 1.24 ± 0.04 1.65 ± 0.05 1.89 ± 0.06 0.975 (5.25 ± 0.16) × 10−1 (7.85 ± 0.24) × 10−1 1.14 ± 0.03 1.47 ± 0.05 1.78 ± 0.05 1.025 (4.68 ± 0.15) × 10−1 (6.97 ± 0.22) × 10−1 (9.97 ± 0.31) × 10−1 1.32 ± 0.04 1.62 ± 0.05 1.075 (4.11 ± 0.17) × 10−1 (6.32 ± 0.26) × 10−1 (9.37 ± 0.38) × 10−1 1.23 ± 0.05 1.51 ± 0.06 1.125 (3.70 ± 0.15) × 10−1 (5.77 ± 0.24) × 10−1 (8.62 ± 0.35) × 10−1 1.15 ± 0.05 1.36 ± 0.05 [55] Z. 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See Section V A for other systematic uncertainties including those due to proton background subtraction. p⊥ 70-80% 60-70% 50-60% 40-50% 0.425 (2.66 ± 0.04) × 10−1 (5.28 ± 0.06) × 10−1 (9.21 ± 0.10) × 10−1 1.43 ± 0.02 0.475 (2.45 ± 0.03) × 10−1 (5.25 ± 0.06) × 10−1 (9.27 ± 0.11) × 10−1 1.43 ± 0.02 0.525 (2.21 ± 0.03) × 10−1 (4.95 ± 0.06) × 10−1 (8.87 ± 0.10) × 10−1 1.38 ± 0.02 0.575 (2.12 ± 0.03) × 10−1 (4.69 ± 0.06) × 10−1 (8.26 ± 0.10) × 10−1 1.32 ± 0.01 0.625 (1.92 ± 0.04) × 10−1 (4.17 ± 0.09) × 10−1 (7.89 ± 0.16) × 10−1 1.26 ± 0.03 0.675 (1.70 ± 0.04) × 10−1 (3.90 ± 0.08) × 10−1 (7.13 ± 0.15) × 10−1 1.17 ± 0.02 0.725 (1.56 ± 0.04) × 10−1 (3.39 ± 0.07) × 10−1 (6.45 ± 0.14) × 10−1 1.07 ± 0.02 0.775 (1.30 ± 0.03) × 10−1 (3.03 ± 0.07) × 10−1 (5.85 ± 0.12) × 10−1 (9.65 ± 0.20) × 10−1 0.825 (1.15 ± 0.03) × 10−1 (2.72 ± 0.06) × 10−1 (5.14 ± 0.11) × 10−1 (8.71 ± 0.18) × 10−1 0.875 (9.48 ± 0.32) × 10−2 (2.21 ± 0.07) × 10−1 (4.33 ± 0.13) × 10−1 (7.55 ± 0.23) × 10−1 0.925 (8.13 ± 0.28) × 10−2 (1.95 ± 0.06) × 10−1 (3.84 ± 0.12) × 10−1 (6.71 ± 0.21) × 10−1 0.975 (6.67 ± 0.23) × 10−2 (1.69 ± 0.05) × 10−1 (3.39 ± 0.11) × 10−1 (5.94 ± 0.18) × 10−1 1.025 (6.17 ± 0.22) × 10−2 (1.47 ± 0.05) × 10−1 (2.96 ± 0.09) × 10−1 (5.23 ± 0.16) × 10−1 1.075 (5.11 ± 0.23) × 10−2 (1.24 ± 0.05) × 10−1 (2.57 ± 0.11) × 10−1 (4.62 ± 0.19) × 10−1 1.125 (4.24 ± 0.20) × 10−2 (1.05 ± 0.05) × 10−1 (2.25 ± 0.09) × 10−1 (4.05 ± 0.17) × 10−1 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.425 2.14 ± 0.02 2.98 ± 0.03 4.22 ± 0.04 5.35 ± 0.06 6.47 ± 0.07 0.475 2.10 ± 0.02 3.00 ± 0.03 4.20 ± 0.04 5.37 ± 0.06 6.50 ± 0.07 0.525 2.07 ± 0.02 2.99 ± 0.03 4.16 ± 0.04 5.38 ± 0.06 6.44 ± 0.07 0.575 2.03 ± 0.02 2.89 ± 0.03 4.08 ± 0.04 5.27 ± 0.06 6.38 ± 0.07 0.625 1.90 ± 0.04 2.78 ± 0.06 3.93 ± 0.08 5.05 ± 0.10 6.09 ± 0.12 0.675 1.78 ± 0.04 2.62 ± 0.05 3.75 ± 0.08 4.80 ± 0.10 5.84 ± 0.12 0.725 1.66 ± 0.03 2.44 ± 0.05 3.49 ± 0.07 4.52 ± 0.09 5.49 ± 0.11 0.775 1.51 ± 0.03 2.25 ± 0.05 3.24 ± 0.07 4.21 ± 0.09 5.11 ± 0.10 0.825 1.37 ± 0.03 1.92 ± 0.04 3.01 ± 0.06 3.90 ± 0.08 4.80 ± 0.10 0.875 1.21 ± 0.04 1.74 ± 0.05 2.69 ± 0.08 3.45 ± 0.10 4.29 ± 0.13 0.925 1.09 ± 0.03 1.59 ± 0.05 2.43 ± 0.07 3.18 ± 0.10 3.90 ± 0.12 0.975 (9.63 ± 0.29) × 10−1 1.44 ± 0.04 2.20 ± 0.07 2.93 ± 0.09 3.60 ± 0.11 1.025 (8.63 ± 0.26) × 10−1 1.32 ± 0.04 1.98 ± 0.06 2.66 ± 0.08 3.27 ± 0.10 1.075 (7.73 ± 0.31) × 10−1 1.17 ± 0.05 1.81 ± 0.07 2.41 ± 0.10 3.00 ± 0.12 1.125 (6.85 ± 0.27) × 10−1 1.07 ± 0.04 1.63 ± 0.07 2.18 ± 0.09 2.69 ± 0.11 Nucl. 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Lett. 94, 54 TABLE XXVI: Identified π − invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 130 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. p⊥ 58-85% 45-58% 34-45% 26-34% 0.225 (2.34 ± 0.08) × 101 (5.88 ± 0.16) × 101 (9.56 ± 0.27) × 101 (1.45 ± 0.04) × 102 0.275 (1.73 ± 0.05) × 101 (4.52 ± 0.12) × 101 (7.46 ± 0.18) × 101 (1.05 ± 0.03) × 102 0.325 (1.28 ± 0.03) × 101 (3.37 ± 0.07) × 101 (5.56 ± 0.10) × 101 (7.98 ± 0.14) × 101 0.375 9.11 ± 0.21 (2.53 ± 0.05) × 101 (4.13 ± 0.08) × 101 (6.01 ± 0.11) × 101 0.425 6.92 ± 0.17 (1.85 ± 0.04) × 101 (3.22 ± 0.06) × 101 (4.73 ± 0.09) × 101 0.475 5.49 ± 0.14 (1.39 ± 0.03) × 101 (2.37 ± 0.05) × 101 (3.45 ± 0.07) × 101 0.525 3.88 ± 0.11 (1.10 ± 0.03) × 101 (1.90 ± 0.04) × 101 (2.77 ± 0.07) × 101 0.575 3.09 ± 0.11 8.54 ± 0.29 (1.43 ± 0.05) × 101 (2.09 ± 0.07) × 101 0.625 2.32 ± 0.09 6.76 ± 0.24 (1.13 ± 0.04) × 101 (1.73 ± 0.06) × 101 0.675 1.86 ± 0.07 4.92 ± 0.18 8.56 ± 0.24 (1.29 ± 0.04) × 101 p⊥ 18-26% 11-18% 6-11% 0-6% 0.225 (1.90 ± 0.05) × 102 (2.55 ± 0.06) × 102 (3.11 ± 0.08) × 102 (3.71 ± 0.08) × 102 0.275 (1.42 ± 0.03) × 102 (1.89 ± 0.04) × 102 (2.25 ± 0.07) × 102 (2.77 ± 0.06) × 102 0.325 (1.09 ± 0.02) × 102 (1.43 ± 0.02) × 102 (1.75 ± 0.03) × 102 (2.13 ± 0.02) × 102 0.375 (8.16 ± 0.14) × 101 (1.09 ± 0.02) × 102 (1.35 ± 0.03) × 102 (1.62 ± 0.02) × 102 0.425 (6.38 ± 0.11) × 101 (8.15 ± 0.14) × 101 (1.00 ± 0.02) × 102 (1.24 ± 0.01) × 102 0.475 (4.80 ± 0.09) × 101 (6.56 ± 0.11) × 101 (7.96 ± 0.16) × 101 (9.76 ± 0.11) × 101 0.525 (3.69 ± 0.08) × 101 (5.04 ± 0.11) × 101 (6.22 ± 0.16) × 101 (7.57 ± 0.15) × 101 0.575 (2.97 ± 0.09) × 101 (3.74 ± 0.12) × 101 (4.80 ± 0.17) × 101 (5.95 ± 0.18) × 101 0.625 (2.28 ± 0.07) × 101 (3.10 ± 0.10) × 101 (3.84 ± 0.14) × 101 (4.66 ± 0.14) × 101 0.675 (1.77 ± 0.04) × 101 (2.47 ± 0.06) × 101 (2.85 ± 0.09) × 101 (3.76 ± 0.04) × 101 TABLE XXVII: Identified π + invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 130 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. p⊥ 58-85% 45-58% 34-45% 26-34% 0.225 (2.31 ± 0.07) × 101 (5.96 ± 0.18) × 101 (9.82 ± 0.27) × 101 (1.44 ± 0.04) × 102 0.275 (1.75 ± 0.05) × 101 (4.43 ± 0.12) × 101 (7.60 ± 0.18) × 101 (1.05 ± 0.03) × 102 0.325 (1.29 ± 0.03) × 101 (3.35 ± 0.06) × 101 (5.66 ± 0.10) × 101 (7.82 ± 0.14) × 101 0.375 9.76 ± 0.22 (2.60 ± 0.05) × 101 (4.21 ± 0.08)
× 101 (6.06 ± 0.11) × 101 0.425 6.97 ± 0.17 (1.85 ± 0.04) × 101 (3.14 ± 0.06) × 101 (4.57 ± 0.09) × 101 0.475 5.01 ± 0.14 (1.39 ± 0.03) × 101 (2.40 ± 0.05) × 101 (3.68 ± 0.07) × 101 0.525 4.04 ± 0.12 (1.07 ± 0.03) × 101 (1.92 ± 0.05) × 101 (2.68 ± 0.06) × 101 0.575 2.86 ± 0.11 8.37 ± 0.28 (1.47 ± 0.05) × 101 (2.15 ± 0.07) × 101 0.625 2.39 ± 0.09 6.38 ± 0.23 (1.12 ± 0.04) × 101 (1.65 ± 0.06) × 101 0.675 1.88 ± 0.07 4.87 ± 0.18 8.82 ± 0.23 (1.29 ± 0.04) × 101 p⊥ 18-26% 11-18% 6-11% 0-6% 0.225 (1.85 ± 0.05) × 102 (2.49 ± 0.06) × 102 (3.01 ± 0.09) × 102 (3.63 ± 0.08) × 102 0.275 (1.43 ± 0.03) × 102 (1.86 ± 0.04) × 102 (2.27 ± 0.06) × 102 (2.75 ± 0.06) × 102 0.325 (1.08 ± 0.02) × 102 (1.41 ± 0.02) × 102 (1.80 ± 0.03) × 102 (2.10 ± 0.02) × 102 0.375 (8.25 ± 0.14) × 101 (1.11 ± 0.02) × 102 (1.31 ± 0.03) × 102 (1.60 ± 0.02) × 102 0.425 (6.26 ± 0.11) × 101 (8.31 ± 0.15) × 101 (9.76 ± 0.23) × 101 (1.25 ± 0.01) × 102 0.475 (4.89 ± 0.09) × 101 (6.39 ± 0.11) × 101 (7.94 ± 0.16) × 101 (9.70 ± 0.11) × 101 0.525 (3.71 ± 0.09) × 101 (5.03 ± 0.11) × 101 (6.29 ± 0.17) × 101 (7.67 ± 0.15) × 101 0.575 (2.90 ± 0.09) × 101 (3.90 ± 0.12) × 101 (4.71 ± 0.17) × 101 (5.94 ± 0.18) × 101 0.625 (2.29 ± 0.08) × 101 (3.14 ± 0.10) × 101 (3.83 ± 0.14) × 101 (4.71 ± 0.14) × 101 0.675 (1.77 ± 0.05) × 101 (2.44 ± 0.06) × 101 (2.98 ± 0.11) × 101 (3.69 ± 0.04) × 101 052301 (2005). [106] A.M. Rossi, G. Vannini, A. Bussiere, E. Albini, D. D’Alessandro and G. Giacomelli, Nucl. Phys. B84, 269 (1975). [107] J.L. Bailly et al. (EHS-RCBC Collaboration), Phys. Lett. B 195, 609 (1987). [108] T. Alexopoulos et al. (E735 Collaboration), Phys. Rev. D 48, 984 (1993). [109] Bocquet et al. (UA1 Collaboration), Phys. Lett. B 366, 441 (1996). [110] K. Adcox et al. (PHENIX Collaboration), Phys. Rev. Lett. 88, 242301 (2002). 55 TABLE XXVIII: Identified K− invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 130 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. Data were published in Ref. [18]. p⊥ 58-85% 45-58% 34-45% 26-34% 0.175 1.93 ± 0.25 3.78 ± 0.50 7.13 ± 0.79 (1.12 ± 0.13) × 101 0.225 2.03 ± 0.18 4.24 ± 0.56 7.42 ± 0.61 (1.08 ± 0.09) × 101 0.275 1.45 ± 0.13 4.09 ± 0.33 6.52 ± 0.50 9.93 ± 0.71 0.325 1.48 ± 0.12 3.91 ± 0.30 6.09 ± 0.42 7.85 ± 0.54 0.375 1.30 ± 0.10 3.26 ± 0.23 5.46 ± 0.36 7.61 ± 0.51 0.425 1.09 ± 0.09 2.89 ± 0.21 4.58 ± 0.32 6.34 ± 0.43 0.475 (8.70 ± 0.69) × 10−1 2.42 ± 0.18 4.49 ± 0.32 6.40 ± 0.42 0.525 (7.72 ± 0.91) × 10−1 1.98 ± 0.26 3.64 ± 0.54 5.32 ± 0.58 0.575 (6.83 ± 0.81) × 10−1 2.24 ± 0.29 3.38 ± 0.38 4.58 ± 0.51 0.625 (6.56 ± 0.80) × 10−1 1.77 ± 0.24 2.72 ± 0.32 4.08 ± 0.47 0.675 (5.28 ± 0.73) × 10−1 1.17 ± 0.18 2.74 ± 0.35 3.08 ± 0.43 0.725 (4.64 ± 1.08) × 10−1 1.34 ± 0.20 1.93 ± 0.37 2.78 ± 0.43 0.775 (2.95 ± 1.45) × 10−1 (6.56 ± 2.20) × 10−1 (9.90 ± 3.54) × 10−1 2.32 ± 0.52 p⊥ 18-26% 11-18% 6-11% 0-6% 0.175 (1.17 ± 0.13) × 101 (1.61 ± 0.17) × 101 (2.27 ± 0.14) × 101 (2.68 ± 0.16) × 101 0.225 (1.23 ± 0.10) × 101 (1.70 ± 0.13) × 101 (2.25 ± 0.13) × 101 (2.75 ± 0.15) × 101 0.275 (1.26 ± 0.09) × 101 (1.55 ± 0.11) × 101 (1.91 ± 0.11) × 101 (2.37 ± 0.13) × 101 0.325 (1.07 ± 0.07) × 101 (1.42 ± 0.09) × 101 (1.71 ± 0.09) × 101 (2.20 ± 0.12) × 101 0.375 (1.03 ± 0.07) × 101 (1.31 ± 0.09) × 101 (1.60 ± 0.09) × 101 (2.01 ± 0.10) × 101 0.425 9.22 ± 0.62 (1.12 ± 0.07) × 101 (1.50 ± 0.08) × 101 (1.85 ± 0.10) × 101 0.475 8.28 ± 0.56 (1.04 ± 0.07) × 101 (1.39 ± 0.07) × 101 (1.69 ± 0.09) × 101 0.525 6.93 ± 0.63 8.65 ± 0.94 (1.19 ± 0.14) × 101 (1.48 ± 0.15) × 101 0.575 6.78 ± 1.06 8.52 ± 1.33 9.81 ± 1.51 (1.30 ± 0.13) × 101 0.625 6.00 ± 0.95 8.13 ± 1.29 8.89 ± 0.92 (1.10 ± 0.11) × 101 0.675 5.29 ± 0.89 5.77 ± 0.98 8.00 ± 0.86 8.86 ± 0.93 0.725 3.74 ± 0.57 5.69 ± 0.98 6.83 ± 0.79 8.30 ± 0.93 0.775 3.51 ± 0.68 4.43 ± 0.77 4.36 ± 1.03 6.78 ± 0.90 TABLE XXIX: Identified K+ invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 130 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. Data were published in Ref. [18]. p⊥ 58-85% 45-58% 34-45% 26-34% 0.175 1.58 ± 0.22 6.26 ± 0.70 7.02 ± 0.79 (1.19 ± 0.12) × 101 0.225 2.14 ± 0.20 5.56 ± 0.46 8.18 ± 0.63 9.21 ± 0.74 0.275 1.90 ± 0.15 4.91 ± 0.37 7.00 ± 0.49 9.27 ± 0.69 0.325 1.38 ± 0.11 3.82 ± 0.28 6.37 ± 0.42 9.31 ± 0.62 0.375 1.32 ± 0.10 3.69 ± 0.26 5.70 ± 0.38 8.65 ± 0.55 0.425 1.06 ± 0.09 3.23 ± 0.22 5.47 ± 0.37 6.99 ± 0.46 0.475 (9.09 ± 0.72) × 10−1 2.88 ± 0.22 4.55 ± 0.33 6.13 ± 0.40 0.525 (9.23 ± 1.06) × 10−1 2.49 ± 0.28 3.77 ± 0.41 5.61 ± 0.61 0.575 (7.45 ± 0.88) × 10−1 2.29 ± 0.26 3.91 ± 0.43 5.51 ± 0.60 0.625 (5.90 ± 0.79) × 10−1 1.98 ± 0.24 3.23 ± 0.36 4.73 ± 0.54 0.675 (6.55 ± 0.90) × 10−1 1.80 ± 0.28 3.09 ± 0.38 4.97 ± 0.81 0.725 (4.52 ± 0.87) × 10−1 1.23 ± 0.31 2.03 ± 0.31 3.45 ± 0.57 0.775 (2.83 ± 0.92) × 10−1 (8.81 ± 2.61) × 10−1 2.15 ± 0.40 2.55 ± 0.54 p⊥ 18-26% 11-18% 6-11% 0-6% 0.175 (1.47 ± 0.14) × 101 (1.82 ± 0.18) × 101 (2.26 ± 0.14) × 101 (2.99 ± 0.17) × 101 0.225 (1.60 ± 0.12) × 101 (1.89 ± 0.14) × 101 (2.36 ± 0.13) × 101 (3.02 ± 0.16) × 101 0.275 (1.27 ± 0.09) × 101 (1.74 ± 0.12) × 101 (2.16 ± 0.12) × 101 (2.58 ± 0.14) × 101 0.325 (1.27 ± 0.08) × 101 (1.51 ± 0.10) × 101 (1.92 ± 0.10) × 101 (2.45 ± 0.13) × 101 0.375 (1.03 ± 0.07) × 101 (1.37 ± 0.09) × 101 (1.76 ± 0.09) × 101 (2.19 ± 0.11) × 101 0.425 (1.01 ± 0.06) × 101 (1.34 ± 0.09) × 101 (1.56 ± 0.08) × 101 (1.99 ± 0.10) × 101 0.475 8.13 ± 0.53 (1.14 ± 0.07) × 101 (1.38 ± 0.07) × 101 (1.78 ± 0.09) × 101 0.525 7.36 ± 0.79 (1.04 ± 0.11) × 101 (1.22 ± 0.12) × 101 (1.57 ± 0.16) × 101 0.575 7.34 ± 0.80 8.15 ± 0.89 (1.06 ± 0.16) × 101 (1.43 ± 0.14) × 101 0.625 6.17 ± 0.71 8.13 ± 0.91 9.93 ± 1.02 (1.23 ± 0.13) × 101 0.675 6.05 ± 0.76 7.18 ± 0.94 8.74 ± 0.94 9.78 ± 1.02 0.725 5.06 ± 0.84 5.43 ± 0.82 7.61 ± 0.87 9.10 ± 1.01 56 TABLE XXX: Identified p invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 130 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-to-point systematic errors. See Section V A for other systematic uncertainties. Data were published in Ref. [20]. p⊥ 58-85% 45-58% 34-45% 26-34% 0.375 (5.05 ± 0.29) × 10−1 1.14 ± 0.06 1.62 ± 0.09 2.01 ± 0.11 0.425 (4.84 ± 0.20) × 10−1 1.02 ± 0.04 1.56 ± 0.06 1.99 ± 0.07 0.475 (4.37 ± 0.13) × 10−1 1.00 ± 0.03 1.53 ± 0.04 1.98 ± 0.05 0.525 (4.02 ± 0.12) × 10−1 (9.70 ± 0.26) × 10−1 1.42 ± 0.04 1.93 ± 0.05 0.575 (3.61 ± 0.11) × 10−1 (8.84 ± 0.23) × 10−1 1.32 ± 0.03 1.77 ± 0.04 0.625 (3.37 ± 0.10) × 10−1 (8.13 ± 0.22) × 10−1 1.24 ± 0.03 1.72 ± 0.04 0.675 (3.24 ± 0.09) × 10−1 (7.62 ± 0.20) × 10−1 1.18 ± 0.03 1.64 ± 0.04 0.725 (2.71 ± 0.08) × 10−1 (6.52 ± 0.17) × 10−1 1.10 ± 0.03 1.49 ± 0.03 0.775 (2.36 ± 0.07) × 10−1 (6.37 ± 0.17) × 10−1 1.02 ± 0.02 1.36 ± 0.03 0.825 (2.12 ± 0.07) × 10−1 (5.93 ± 0.16) × 10−1 (9.12 ± 0.22) × 10−1 1.29 ± 0.03 0.875 (1.95 ± 0.06) × 10−1 (5.08 ± 0.14) × 10−1 (8.02 ± 0.20) × 10−1 1.21 ± 0.03 0.925 (1.61 ± 0.05) × 10−1 (4.36 ± 0.12) × 10−1 (7.40 ± 0.19) × 10−1 1.13 ± 0.03 0.975 (1.45 ± 0.05) × 10−1 (3.92 ± 0.11) × 10−1 (6.69 ± 0.17) × 10−1 (9.31 ± 0.23) × 10−1 p⊥ 18-26% 11-18% 6-11% 0-6% 0.375 2.56 ± 0.13 3.05 ± 0.15 3.54 ± 0.12 4.24 ± 0.13 0.425 2.62 ± 0.09 3.06 ± 0.11 3.49 ± 0.07 4.25 ± 0.08 0.475 2.41 ± 0.06 2.94 ±
0.07 3.45 ± 0.04 4.14 ± 0.04 0.525 2.49 ± 0.06 2.88 ± 0.06 3.37 ± 0.03 4.08 ± 0.03 0.575 2.39 ± 0.05 2.78 ± 0.06 3.29 ± 0.03 3.92 ± 0.03 0.625 2.12 ± 0.05 2.74 ± 0.06 3.16 ± 0.03 3.84 ± 0.03 0.675 2.05 ± 0.05 2.56 ± 0.05 3.04 ± 0.03 3.67 ± 0.03 0.725 1.92 ± 0.04 2.42 ± 0.05 2.88 ± 0.03 3.49 ± 0.03 0.775 1.78 ± 0.04 2.17 ± 0.05 2.76 ± 0.03 3.31 ± 0.03 0.825 1.63 ± 0.04 2.07 ± 0.04 2.54 ± 0.03 3.09 ± 0.03 0.875 1.50 ± 0.03 1.85 ± 0.04 2.31 ± 0.02 2.89 ± 0.02 0.925 1.38 ± 0.03 1.77 ± 0.04 2.15 ± 0.02 2.72 ± 0.02 0.975 1.33 ± 0.03 1.60 ± 0.04 2.00 ± 0.02 2.50 ± 0.02 TABLE XXXI: Identified proton invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 130 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors, point-to-point systematic errors, and systematic uncertainties due to proton background subtraction. See Section V A for other systematic uncertainties. Data were published in Ref. [20]. p⊥ 58-85% 45-58% 34-45% 26-34% 0.375 (6.40 ± 0.66) × 10−1 1.46 ± 0.15 2.19 ± 0.22 2.78 ± 0.28 0.425 (5.99 ± 0.47) × 10−1 1.45 ± 0.11 2.07 ± 0.16 2.74 ± 0.21 0.475 (5.54 ± 0.32) × 10−1 1.34 ± 0.07 1.81 ± 0.10 2.59 ± 0.14 0.525 (5.12 ± 0.24) × 10−1 1.25 ± 0.05 1.87 ± 0.08 2.54 ± 0.10 0.575 (4.50 ± 0.21) × 10−1 1.19 ± 0.05 1.82 ± 0.07 2.44 ± 0.10 0.625 (4.61 ± 0.16) × 10−1 1.05 ± 0.03 1.65 ± 0.05 2.27 ± 0.07 0.675 (3.72 ± 0.13) × 10−1 (9.52 ± 0.31) × 10−1 1.57 ± 0.05 2.24 ± 0.06 0.725 (3.51 ± 0.12) × 10−1 (9.17 ± 0.30) × 10−1 1.47 ± 0.04 2.03 ± 0.06 0.775 (3.09 ± 0.08) × 10−1 (8.34 ± 0.19) × 10−1 1.38 ± 0.03 1.90 ± 0.04 0.825 (2.79 ± 0.08) × 10−1 (7.48 ± 0.17) × 10−1 1.23 ± 0.03 1.73 ± 0.03 0.875 (2.43 ± 0.07) × 10−1 (6.65 ± 0.16) × 10−1 1.10 ± 0.02 1.64 ± 0.03 0.925 (2.02 ± 0.06) × 10−1 (5.84 ± 0.14) × 10−1 (9.43 ± 0.21) × 10−1 1.51 ± 0.03 0.975 (1.77 ± 0.05) × 10−1 (5.13 ± 0.13) × 10−1 (9.62 ± 0.21) × 10−1 1.36 ± 0.03 p⊥ 18-26% 11-18% 6-11% 0-6% 0.375 3.54 ± 0.34 4.29 ± 0.42 4.95 ± 0.41 6.01 ± 0.49 0.425 3.50 ± 0.26 4.25 ± 0.31 4.75 ± 0.28 5.73 ± 0.33 0.475 3.25 ± 0.17 4.16 ± 0.21 4.80 ± 0.19 5.69 ± 0.21 0.525 3.22 ± 0.13 3.96 ± 0.16 4.66 ± 0.13 5.67 ± 0.15 0.575 3.09 ± 0.12 3.89 ± 0.15 4.62 ± 0.13 5.62 ± 0.15 0.625 3.04 ± 0.09 3.70 ± 0.10 4.44 ± 0.08 5.39 ± 0.09 0.675 2.96 ± 0.08 3.53 ± 0.10 4.29 ± 0.08 5.18 ± 0.09 0.725 2.64 ± 0.08 3.28 ± 0.09 4.03 ± 0.07 4.96 ± 0.08 0.775 2.49 ± 0.05 3.11 ± 0.05 3.74 ± 0.03 4.73 ± 0.03 0.825 2.26 ± 0.04 2.96 ± 0.05 3.52 ± 0.03 4.36 ± 0.03 0.875 2.12 ± 0.04 2.62 ± 0.05 3.27 ± 0.03 4.08 ± 0.03 0.925 1.91 ± 0.04 2.41 ± 0.04 3.11 ± 0.03 3.87 ± 0.03 57 TABLE XXXII: Identified π − invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. Data were published in Ref. [17]. p⊥ 70-80% 60-70% 50-60% 40-50% 0.225 (1.61 ± 0.05) × 101 (3.06 ± 0.09) × 101 (5.09 ± 0.15) × 101 (7.86 ± 0.24) × 101 0.275 (1.16 ± 0.02) × 101 (2.21 ± 0.04) × 101 (3.69 ± 0.07) × 101 (5.90 ± 0.12) × 101 0.325 8.56 ± 0.18 (1.63 ± 0.03) × 101 (2.79 ± 0.06) × 101 (4.48 ± 0.09) × 101 0.375 6.46 ± 0.08 (1.25 ± 0.01) × 101 (2.12 ± 0.02) × 101 (3.45 ± 0.04) × 101 0.425 4.82 ± 0.06 9.41 ± 0.10 (1.62 ± 0.02) × 101 (2.63 ± 0.03) × 101 0.475 3.69 ± 0.05 7.17 ± 0.08 (1.25 ± 0.01) × 101 (2.05 ± 0.02) × 101 0.525 2.73 ± 0.04 5.56 ± 0.06 9.75 ± 0.11 (1.59 ± 0.02) × 101 0.575 2.13 ± 0.03 4.31 ± 0.06 7.63 ± 0.11 (1.24 ± 0.02) × 101 0.625 1.65 ± 0.04 3.38 ± 0.08 5.96 ± 0.14 9.69 ± 0.24 0.675 1.27 ± 0.03 2.63 ± 0.06 4.64 ± 0.11 7.61 ± 0.19 0.725 (9.77 ± 0.33) × 10−1 2.04 ± 0.07 3.65 ± 0.12 6.02 ± 0.21 0.775 (7.85 ± 0.29) × 10−1 1.57 ± 0.06 2.86 ± 0.10 4.81 ± 0.17 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.225 (1.24 ± 0.04) × 102 (1.74 ± 0.05) × 102 (2.46 ± 0.07) × 102 (3.27 ± 0.10) × 102 (4.10 ± 0.12) × 102 0.275 (8.93 ± 0.18) × 101 (1.32 ± 0.03) × 102 (1.86 ± 0.04) × 102 (2.46 ± 0.05) × 102 (3.05 ± 0.06) × 102 0.325 (6.77 ± 0.14) × 101 (1.02 ± 0.02) × 102 (1.45 ± 0.03) × 102 (1.92 ± 0.04) × 102 (2.39 ± 0.05) × 102 0.375 (5.18 ± 0.05) × 101 (7.91 ± 0.08) × 101 (1.13 ± 0.01) × 102 (1.50 ± 0.01) × 102 (1.88 ± 0.02) × 102 0.425 (4.01 ± 0.04) × 101 (6.13 ± 0.06) × 101 (8.84 ± 0.09) × 101 (1.18 ± 0.01) × 102 (1.47 ± 0.01) × 102 0.475 (3.13 ± 0.03) × 101 (4.76 ± 0.05) × 101 (6.90 ± 0.07) × 101 (9.18 ± 0.09) × 101 (1.15 ± 0.01) × 102 0.525 (2.45 ± 0.03) × 101 (3.72 ± 0.04) × 101 (5.41 ± 0.06) × 101 (7.22 ± 0.07) × 101 (9.07 ± 0.09) × 101 0.575 (1.91 ± 0.03) × 101 (2.94 ± 0.05) × 101 (4.27 ± 0.07) × 101 (5.68 ± 0.10) × 101 (7.20 ± 0.14) × 101 0.625 (1.50 ± 0.04) × 101 (2.32 ± 0.06) × 101 (3.37 ± 0.09) × 101 (4.50 ± 0.13) × 101 (5.67 ± 0.17) × 101 0.675 (1.19 ± 0.03) × 101 (1.82 ± 0.05) × 101 (2.67 ± 0.07) × 101 (3.55 ± 0.10) × 101 (4.48 ± 0.13) × 101 0.725 9.55 ± 0.34 (1.45 ± 0.05) × 101 (2.13 ± 0.08) × 101 (2.83 ± 0.11) × 101 (3.57 ± 0.14) × 101 0.775 7.58 ± 0.27 (1.16 ± 0.04) × 101 TABLE XXXIII: Identified π + invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. Data were published in Ref. [17]. p⊥ 70-80% 60-70% 50-60% 40-50% 0.225 (1.62 ± 0.05) × 101 (3.05 ± 0.09) × 101 (5.05 ± 0.15) × 101 (7.85 ± 0.24) × 101 0.275 (1.15 ± 0.02) × 101 (2.20 ± 0.04) × 101 (3.69 ± 0.07) × 101 (5.85 ± 0.12) × 101 0.325 8.57 ± 0.18 (1.64 ± 0.03) × 101 (2.78 ± 0.06) × 101 (4.45 ± 0.09) × 101 0.375 6.38 ± 0.08 (1.23 ± 0.01) × 101 (2.12 ± 0.02) × 101 (3.44 ± 0.04) × 101 0.425 4.80 ± 0.06 9.45 ± 0.10 (1.63 ± 0.02) × 101 (2.63 ± 0.03) × 101 0.475 3.66 ± 0.05 7.22 ± 0.08 (1.25 ± 0.01) × 101 (2.03 ± 0.02) × 101 0.525 2.81 ± 0.04 5.52 ± 0.06 9.66 ± 0.10 (1.59 ± 0.02) × 101 0.575 2.15 ± 0.03 4.30 ± 0.06 7.57 ± 0.10 (1.24 ± 0.02) × 101 0.625 1.66 ± 0.04 3.29 ± 0.08 5.95 ± 0.14 9.73 ± 0.24 0.675 1.29 ± 0.03 2.58 ± 0.06 4.66 ± 0.11 7.65 ± 0.19 0.725 (9.97 ± 0.34) × 10−1 2.09 ± 0.07 3.62 ± 0.12 6.03 ± 0.21 0.775 (7.84 ± 0.29) × 10−1 1.61 ± 0.06 2.91 ± 0.10 4.76 ± 0.17 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.225 (1.24 ± 0.04) × 102 (1.74 ± 0.05) × 102 (2.42 ± 0.07) × 102 (3.24 ± 0.10) × 102 (4.03 ± 0.12) × 102 0.275 (8.84 ± 0.18) × 101 (1.30 ± 0.03) × 102 (1.82 ± 0.04) × 102 (2.41 ± 0.05) × 102 (2.98 ± 0.06) × 102 0.325 (6.67 ± 0.13) × 101 (1.00 ± 0.02) × 102 (1.42 ± 0.03) × 102 (1.88 ± 0.04) × 102 (2.33 ± 0.05) × 102 0.375 (5.15 ± 0.05) × 101 (7.80 ± 0.08) × 101 (1.11 ± 0.01) × 102 (1.47 ± 0.01) × 102 (1.84 ± 0.02) × 102 0.425 (4.00 ± 0.04) × 101 (6.08 ± 0.06) × 101 (8.71 ± 0.09) × 101 (1.16 ± 0.01) × 102 (1.45 ± 0.01) × 102 0.475 (3.12 ± 0.03) × 101 (4.73 ± 0.05) × 101 (6.84 ± 0.07) × 101 (9.05 ± 0.09) × 101 (1.14 ± 0.01) × 102 0.525 (2.44 ± 0.03) × 101 (3.71 ± 0.04) × 101 (5.38 ± 0.06) × 101 (7.16 ± 0.07) × 101 (9.00 ± 0.09) × 101 0.575 (1.92 ± 0.03) × 101 (2.92 ± 0.05) × 101 (4.25 ± 0.07) × 101 (5.63 ± 0.10) × 101 (7.11 ± 0.14) × 101 0.625 (1.51 ± 0.04) × 101 (2.30 ± 0.06) × 101 (3.34 ± 0.09) × 101 (4.46 ± 0.13) × 101 (5.61 ± 0.16) × 101 0.675 (1.19 ± 0.03) × 101 (1.81 ± 0.05) × 101 (2.65 ± 0.07) × 101 (3.50 ± 0.10) × 101 (4.43 ± 0.13) × 101 0.725 9.44 ± 0.33 (1.44 ± 0.05) × 101 (2.13 ± 0.08) × 101 (2.81 ± 0.11) × 101 (3.58 ± 0.14) × 101 0.775 7.62 ± 0.27 (1.16 ± 0.04) × 101 58 TABLE XXXIV: Identified K− invariant transverse momentum spectra at mid-rapidity
(|y| < 0.1) in Au+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. Data were published in Ref. [17]. p⊥ 70-80% 60-70% 50-60% 40-50% 0.225 1.35 ± 0.11 2.34 ± 0.17 3.77 ± 0.27 6.47 ± 0.47 0.275 1.14 ± 0.05 2.18 ± 0.08 3.49 ± 0.12 5.66 ± 0.18 0.325 (9.22 ± 0.25) × 10−1 1.89 ± 0.04 3.05 ± 0.06 4.79 ± 0.09 0.375 (7.44 ± 0.24) × 10−1 1.61 ± 0.04 2.83 ± 0.07 4.31 ± 0.11 0.425 (6.63 ± 0.27) × 10−1 1.37 ± 0.05 2.38 ± 0.09 3.66 ± 0.15 0.475 (5.57 ± 0.59) × 10−1 1.14 ± 0.12 2.11 ± 0.23 3.26 ± 0.35 0.525 (4.78 ± 0.50) × 10−1 (9.60 ± 1.00) × 10−1 1.81 ± 0.19 2.80 ± 0.30 0.575 (4.35 ± 0.46) × 10−1 (8.78 ± 0.93) × 10−1 1.55 ± 0.17 2.54 ± 0.28 0.625 (3.61 ± 0.28) × 10−1 (7.16 ± 0.54) × 10−1 1.34 ± 0.10 2.17 ± 0.16 0.675 (2.81 ± 0.23) × 10−1 (5.63 ± 0.46) × 10−1 1.13 ± 0.09 1.86 ± 0.16 0.725 (2.41 ± 0.28) × 10−1 (4.73 ± 0.53) × 10−1 (9.60 ± 1.10) × 10−1 1.58 ± 0.18 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.225 9.54 ± 0.68 (1.16 ± 0.08) × 101 (1.68 ± 0.12) × 101 (2.20 ± 0.16) × 101 (2.63 ± 0.19) × 101 0.275 8.01 ± 0.25 (1.09 ± 0.03) × 101 (1.56 ± 0.05) × 101 (2.06 ± 0.06) × 101 (2.47 ± 0.08) × 101 0.325 7.03 ± 0.12 (1.02 ± 0.02) × 101 (1.44 ± 0.03) × 101 (1.92 ± 0.04) × 101 (2.27 ± 0.05) × 101 0.375 6.38 ± 0.17 9.31 ± 0.25 (1.32 ± 0.04) × 101 (1.77 ± 0.05) × 101 (2.11 ± 0.06) × 101 0.425 5.80 ± 0.24 8.42 ± 0.36 (1.22 ± 0.05) × 101 (1.59 ± 0.07) × 101 (1.98 ± 0.10) × 101 0.475 5.23 ± 0.58 7.53 ± 0.85 (1.09 ± 0.12) × 101 (1.44 ± 0.17) × 101 (1.77 ± 0.21) × 101 0.525 4.55 ± 0.50 6.73 ± 0.76 9.80 ± 1.10 (1.31 ± 0.15) × 101 (1.58 ± 0.19) × 101 0.575 4.14 ± 0.46 6.03 ± 0.68 8.80 ± 1.00 (1.18 ± 0.14) × 101 (1.47 ± 0.17) × 101 0.625 3.42 ± 0.27 5.35 ± 0.41 7.91 ± 0.61 (1.06 ± 0.08) × 101 (1.27 ± 0.10) × 101 0.675 2.93 ± 0.25 4.68 ± 0.42 6.45 ± 0.59 8.58 ± 0.82 (1.08 ± 0.11) × 101 0.725 2.50 ± 0.28 3.65 ± 0.42 5.21 ± 0.61 TABLE XXXV: Identified K+ invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. Data were published in Ref. [17]. p⊥ 70-80% 60-70% 50-60% 40-50% 0.225 1.31 ± 0.10 2.43 ± 0.18 3.95 ± 0.29 6.69 ± 0.48 0.275 1.08 ± 0.04 2.22 ± 0.08 3.65 ± 0.12 5.79 ± 0.19 0.325 (9.40 ± 0.25) × 10−1 1.90 ± 0.04 3.17 ± 0.06 5.02 ± 0.09 0.375 (7.82 ± 0.24) × 10−1 1.66 ± 0.05 2.94 ± 0.08 4.39 ± 0.11 0.425 (6.79 ± 0.27) × 10−1 1.43 ± 0.05 2.56 ± 0.10 3.85 ± 0.15 0.475 (5.78 ± 0.61) × 10−1 1.19 ± 0.13 2.20 ± 0.24 3.46 ± 0.38 0.525 (4.80 ± 0.51) × 10−1 1.04 ± 0.11 1.91 ± 0.20 2.98 ± 0.32 0.575 (4.27 ± 0.45) × 10−1 (8.66 ± 0.91) × 10−1 1.64 ± 0.18 2.65 ± 0.29 0.625 (3.80 ± 0.29) × 10−1 (7.26 ± 0.54) × 10−1 1.41 ± 0.10 2.25 ± 0.17 0.675 (3.24 ± 0.26) × 10−1 (6.11 ± 0.49) × 10−1 1.11 ± 0.09 1.93 ± 0.16 0.725 (2.49 ± 0.29) × 10−1 (4.88 ± 0.55) × 10−1 (9.50 ± 1.10) × 10−1 1.56 ± 0.17 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.225 9.84 ± 0.70 (1.21 ± 0.09) × 101 (1.72 ± 0.12) × 101 (2.31 ± 0.16) × 101 (2.73 ± 0.19) × 101 0.275 8.11 ± 0.26 (1.15 ± 0.04) × 101 (1.65 ± 0.05) × 101 (2.09 ± 0.06) × 101 (2.54 ± 0.08) × 101 0.325 7.27 ± 0.13 (1.06 ± 0.02) × 101 (1.50 ± 0.03) × 101 (1.97 ± 0.04) × 101 (2.39 ± 0.05) × 101 0.375 6.71 ± 0.18 9.70 ± 0.26 (1.38 ± 0.04) × 101 (1.80 ± 0.05) × 101 (2.22 ± 0.07) × 101 0.425 5.91 ± 0.24 8.73 ± 0.37 (1.27 ± 0.06) × 101 (1.68 ± 0.08) × 101 (2.05 ± 0.10) × 101 0.475 5.46 ± 0.60 7.97 ± 0.89 (1.14 ± 0.13) × 101 (1.49 ± 0.17) × 101 (1.81 ± 0.21) × 101 0.525 4.75 ± 0.52 7.05 ± 0.79 (1.01 ± 0.11) × 101 (1.34 ± 0.16) × 101 (1.65 ± 0.20) × 101 0.575 4.20 ± 0.46 6.29 ± 0.71 9.20 ± 1.00 (1.22 ± 0.14) × 101 (1.48 ± 0.18) × 101 0.625 3.42 ± 0.27 5.55 ± 0.42 8.14 ± 0.63 (1.05 ± 0.08) × 101 (1.31 ± 0.10) × 101 0.675 3.10 ± 0.27 4.71 ± 0.42 6.77 ± 0.62 8.91 ± 0.85 (1.08 ± 0.11) × 101 0.725 2.61 ± 0.29 3.79 ± 0.43 5.39 ± 0.63 59 TABLE XXXVI: Identified p invariant transverse momentum spectra at mid-rapidity (|y| < 0.1) in Au+Au collisions at 200 GeV: d 2N/(2πp⊥dp⊥dy) [(GeV/c) −2 ] versus p⊥ [GeV/c]. Errors are the quadratic sum of statistical errors and point-topoint systematic errors. See Section V A for other systematic uncertainties. Data were published in Ref. [17]. p⊥ 70-80% 60-70% 50-60% 40-50% 0.375 (3.63 ± 0.12) × 10−1 (6.68 ± 0.19) × 10−1 (9.92 ± 0.26) × 10−1 1.48 ± 0.04 0.425 (3.42 ± 0.10) × 10−1 (6.23 ± 0.14) × 10−1 (9.31 ± 0.18) × 10−1 1.37 ± 0.02 0.476 (3.27 ± 0.09) × 10−1 (5.72 ± 0.12) × 10−1 (8.74 ± 0.16) × 10−1 1.31 ± 0.02 0.525 (2.86 ± 0.08) × 10−1 (5.19 ± 0.11) × 10−1 (8.32 ± 0.15) × 10−1 1.21 ± 0.02 0.574 (2.61 ± 0.07) × 10−1 (4.80 ± 0.10) × 10−1 (7.95 ± 0.14) × 10−1 1.16 ± 0.02 0.624 (2.27 ± 0.07) × 10−1 (4.27 ± 0.09) × 10−1 (7.22 ± 0.13) × 10−1 1.06 ± 0.02 0.675 (2.09 ± 0.06) × 10−1 (3.73 ± 0.09) × 10−1 (6.43 ± 0.13) × 10−1 (9.95 ± 0.19) × 10−1 0.725 (1.79 ± 0.06) × 10−1 (3.48 ± 0.10) × 10−1 (5.97 ± 0.15) × 10−1 (9.36 ± 0.22) × 10−1 0.775 (1.52 ± 0.05) × 10−1 (3.03 ± 0.09) × 10−1 (5.37 ± 0.14) × 10−1 (8.47 ± 0.20) × 10−1 0.824 (1.39 ± 0.05) × 10−1 (2.64 ± 0.08) × 10−1 (4.83 ± 0.12) × 10−1 (7.72 ± 0.18) × 10−1 0.875 (1.12 ± 0.04) × 10−1 (2.44 ± 0.07) × 10−1 (4.35 ± 0.11) × 10−1 (6.91 ± 0.17) × 10−1 0.924 (1.08 ± 0.04) × 10−1 (2.16 ± 0.07) × 10−1 (3.92 ± 0.11) × 10−1 (6.14 ± 0.17) × 10−1 0.975 (9.16 ± 0.37) × 10−2 (1.84 ± 0.06) × 10−1 (3.42 ± 0.10) × 10−1 (5.67 ± 0.16) × 10−1 1.025 (7.49 ± 0.34) × 10−2 (1.64 ± 0.06) × 10−1 (3.15 ± 0.11) × 10−1 (5.12 ± 0.17) × 10−1 1.075 (6.92 ± 0.34) × 10−2 (1.39 ± 0.06) × 10−1 (2.69 ± 0.10) × 10−1 (4.62 ± 0.16) × 10−1 1.125 (5.74 ± 0.32) × 10−2 (1.24 ± 0.06) × 10−1 (2.39 ± 0.10) × 10−1 (4.00 ± 0.16) × 10−1 1.175 (5.10 ± 0.39) × 10−2 (1.11 ± 0.06) × 10−1 (2.17 ± 0.11) × 10−1 (3.53 ± 0.17) × 10−1 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.375 1.95 ± 0.05 2.69 ± 0.06 3.44 ± 0.08 4.41 ± 0.10 5.08 ± 0.12 0.425 1.83 ± 0.03 2.54 ± 0.04 3.31 ± 0.04 4.17 ± 0.06 4.88 ± 0.07 0.476 1.81 ± 0.03 2.45 ± 0.03 3.23 ± 0.04 4.04 ± 0.06 4.84 ± 0.07 0.525 1.76 ± 0.03 2.34 ± 0.03 3.15 ± 0.04 3.95 ± 0.05 4.68 ± 0.06 0.574 1.63 ± 0.02 2.27 ± 0.03 3.06 ± 0.04 3.79 ± 0.05 4.61 ± 0.06 0.624 1.54 ± 0.02 2.15 ± 0.03 2.93 ± 0.04 3.77 ± 0.05 4.37 ± 0.06 0.675 1.47 ± 0.03 2.06 ± 0.04 2.80 ± 0.05 3.60 ± 0.07 4.29 ± 0.09 0.725 1.36 ± 0.03 1.91 ± 0.04 2.65 ± 0.06 3.35 ± 0.07 4.01 ± 0.09 0.775 1.22 ± 0.03 1.79 ± 0.04 2.50 ± 0.05 3.16 ± 0.07 3.82 ± 0.08 0.824 1.15 ± 0.03 1.67 ± 0.04 2.30 ± 0.05 3.06 ± 0.07 3.66 ± 0.08 0.875 1.04 ± 0.02 1.56 ± 0.03 2.18 ± 0.05 2.88 ± 0.06 3.50 ± 0.08 0.924 (9.70 ± 0.27) × 10−1 1.41 ± 0.04 2.00 ± 0.06 2.60 ± 0.08 3.17 ± 0.10 0.975 (8.81 ± 0.24) × 10−1 1.32 ± 0.04 1.85 ± 0.05 2.42 ± 0.07 2.99 ± 0.09 1.025 (7.86 ± 0.25) × 10−1 1.21 ± 0.04 1.72 ± 0.05 2.28 ± 0.07 2.81 ± 0.09 1.075 (7.07 ± 0.23) × 10−1 1.10 ± 0.04 1.58 ± 0.05 2.09 ± 0.07 2.60 ± 0.09 1.125 (6.50 ± 0.25) × 10−1 1.01 ± 0.04 1.48 ± 0.06 1.91 ± 0.08 2.43 ± 0.11 1.175 (6.06 ± 0.28) × 10−1 (9.05 ± 0.41) × 10−1 1.39 ± 0.06 1.78 ± 0.09 2.22 ± 0.12 [111] F. 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[17]. p⊥ 70-80% 60-70% 50-60% 40-50% 0.425 (3.87 ± 0.20) × 10−1 (7.12 ± 0.36) × 10−1 1.17 ± 0.06 1.65 ± 0.08 0.476 (3.62 ± 0.16) × 10−1 (6.65 ± 0.27) × 10−1 1.11 ± 0.04 1.61 ± 0.06 0.525 (3.43 ± 0.13) × 10−1 (6.31 ± 0.22) × 10−1 1.01 ± 0.03 1.54 ± 0.05 0.574 (3.08 ± 0.10) × 10−1 (5.56 ± 0.16) × 10−1 (9.46 ± 0.26) × 10−1 1.46 ± 0.04 0.624 (2.64 ± 0.08) × 10−1 (5.10 ± 0.13) × 10−1 (8.50 ± 0.20) × 10−1 1.34 ± 0.03 0.675 (2.37 ± 0.07) × 10−1 (4.46 ± 0.11) × 10−1 (7.85 ± 0.18) × 10−1 1.25 ± 0.03 0.725 (2.15 ± 0.07) × 10−1 (4.03 ± 0.11) × 10−1 (7.11 ± 0.18) × 10−1 1.13 ± 0.03 0.775 (1.87 ± 0.06) × 10−1 (3.71 ± 0.10) × 10−1 (6.34 ± 0.16) × 10−1 1.03 ± 0.02 0.824 (1.63 ± 0.05) × 10−1 (3.17 ± 0.09) × 10−1 (5.79 ± 0.14) × 10−1 (9.62 ± 0.22) × 10−1 0.875 (1.46 ± 0.05) × 10−1 (2.84 ± 0.08) × 10−1 (5.28 ± 0.13) × 10−1 (8.71 ± 0.20) × 10−1 0.924 (1.26 ± 0.04) × 10−1 (2.56 ± 0.08) × 10−1 (4.93 ± 0.13) × 10−1 (7.86 ± 0.21) × 10−1 0.975 (1.07 ± 0.04) × 10−1 (2.29 ± 0.07) × 10−1 (4.28 ± 0.12) × 10−1 (7.12 ± 0.19) × 10−1 1.025 (9.88 ± 0.43) × 10−2 (2.14 ± 0.08) × 10−1 (3.89 ± 0.13) × 10−1 (6.53 ± 0.21) × 10−1 1.075 (8.37 ± 0.38) × 10−2 (1.76 ± 0.07) × 10−1 (3.38 ± 0.12) × 10−1 (5.81 ± 0.19) × 10−1 1.125 (7.00 ± 0.36) × 10−2 (1.60 ± 0.07) × 10−1 (3.14 ± 0.12) × 10−1 (5.24 ± 0.20) × 10−1 1.175 (6.18 ± 0.40) × 10−2 (1.38 ± 0.07) × 10−1 (2.82 ± 0.14) × 10−1 (4.76 ± 0.21) × 10−1 p⊥ 30-40% 20-30% 10-20% 5-10% 0-5% 0.425 2.33 ± 0.11 3.34 ± 0.16 4.21 ± 0.20 5.70 ± 0.28 6.42 ± 0.31 0.476 2.31 ± 0.09 3.26 ± 0.13 4.28 ± 0.17 5.62 ± 0.22 6.45 ± 0.25 0.525 2.17 ± 0.07 3.13 ± 0.10 4.12 ± 0.13 5.38 ± 0.17 6.18 ± 0.20 0.574 2.07 ± 0.05 2.99 ± 0.08 3.97 ± 0.10 5.09 ± 0.13 5.96 ± 0.16 0.624 1.91 ± 0.04 2.79 ± 0.06 3.77 ± 0.08 4.89 ± 0.11 5.75 ± 0.13 0.675 1.78 ± 0.04 2.63 ± 0.06 3.58 ± 0.08 4.56 ± 0.11 5.44 ± 0.13 0.725 1.67 ± 0.04 2.42 ± 0.06 3.32 ± 0.08 4.30 ± 0.10 5.07 ± 0.12 0.775 1.54 ± 0.04 2.23 ± 0.05 3.13 ± 0.07 4.09 ± 0.09 4.89 ± 0.11 0.824 1.40 ± 0.03 2.11 ± 0.05 2.93 ± 0.06 3.83 ± 0.08 4.67 ± 0.10 0.875 1.30 ± 0.03 1.94 ± 0.04 2.78 ± 0.06 3.66 ± 0.08 4.44 ± 0.09 0.924 1.18 ± 0.03 1.82 ± 0.05 2.59 ± 0.07 3.42 ± 0.10 4.16 ± 0.13 0.975 1.09 ± 0.03 1.66 ± 0.05 2.37 ± 0.07 3.17 ± 0.09 3.95 ± 0.12 1.025 (9.97 ± 0.32) × 10−1 1.53 ± 0.05 2.21 ± 0.07 2.95 ± 0.09 3.68 ± 0.12 1.075 (8.82 ± 0.28) × 10−1 1.38 ± 0.04 2.06 ± 0.06 2.71 ± 0.09 3.36 ± 0.11 1.125 (8.21 ± 0.31) × 10−1 1.27 ± 0.05 1.85 ± 0.07 2.57 ± 0.10 3.24 ± 0.14 1.175 (7.36 ± 0.32) × 10−1 1.16 ± 0.05 1.70 ± 0.07 2.34 ± 0.11 2.89 ± 0.14 [136] J. 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