Measurements of Phi Meson Production in Relativistic Heavy- Ion Collisions at the BNL Relativistic Heavy Ion Collider (RHIC)

Measurements of phi meson production in relativistic heavy- ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC)

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Citation STAR Collaboration et al. “Measurements of phi meson production in relativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC).” Physical Review C 79.6 (2009): 064903. © 2009 The American Physical Society

As Published http://dx.doi.org/10.1103/PhysRevC.79.064903

Publisher American Physical Society

Version Final published version

Citable link http://hdl.handle.net/1721.1/51838

Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. PHYSICAL REVIEW C 79, 064903 (2009)

Measurements of φ meson production in relativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC)

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 S.-L. Blyth,22 M. Bombara,2 B. E. Bonner,36 M. Botje,28 J. Bouchet,19 E. Braidot,28 A. V. Brandin,26 E. Bruna,51 S. Bueltmann,3 T. P. Burton,2 M. Bystersky,11 X. Z. Cai,39 H. Caines,51 M. Calderon´ de la Barca Sanchez,´ 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 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 J. G. Ma,6 Y. G. Ma, 39 D. P. Mahapatra,14 R. Majka,51 M. 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 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 T. A. Trainor,48 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,19 R. Varma Jr.,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 (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, CZ-25068 Reˇ z/Prague,ˇ Czech Republic 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, People’s Republic of China 22Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 23Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA 24Max-Planck-Institut fur¨ 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, People’s Republic of China 39Shanghai Institute of Applied Physics, Shanghai 201800, People’s Republic of China 40SUBATECH, Nantes, France 41Texas A&M University, College Station, Texas 77843, USA 42University of Texas, Austin, Texas 78712, USA 43Tsinghua University, Beijing 100084, People’s Republic of China 44United States Naval Academy, Annapolis, Maryland 21402, USA 45Valparaiso University, Valparaiso, Indiana 46383, USA 46Variable Energy Cyclotron Centre, Kolkata 700064, India 47Warsaw University of Technology, Warsaw, Poland 48University of Washington, Seattle, Washington 98195, USA 49Wayne State University, Detroit, Michigan 48201, USA 50Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, People’s Republic of China 51Yale University, New Haven, Connecticut 06520, USA 52University of Zagreb, Zagreb, HR-10002, Croatia (Received 17 September 2008; published 15 June 2009)

→ + − We present results for the√ measurement of φ meson production via its charged kaon decay channel φ √K K in Au + Au collisions at sNN = 62.4, 130, and 200 GeV, and in p + p and d + Au collisions at sNN = 200 GeV from the STAR experiment at the BNL Relativistic Heavy Ion Collider (RHIC). The midrapidity

(|y| < 0.5) φ meson transverse momentum (pT ) spectra in central Au + Au collisions are found to be well described by a single exponential distribution. On the other hand, the pT spectra from p + p, d + Au, and peripheral Au + Au collisions show power-law tails at intermediate and high pT and are described better by Levy distributions. The constant φ/K− yield ratio vs beam species, collision centrality, and colliding energy is in contradiction with expectations from models having kaon coalescence as the dominant mechanism for φ

production at RHIC. The /φ yield ratio as a function of pT is consistent with a model based on the recombination of thermal s quarks up to pT ∼ 4 GeV/c, but disagrees at higher transverse momenta. The measured nuclear modiﬁcation factor, RdAu, for the φ meson increases above unity at intermediate pT , similar to that for pions and protons, while RAA is suppressed due to the energy loss effect in central Au + Au collisions. Number of constituent quark scaling of both Rcp and v2 for the φ meson with respect to other hadrons in Au + Au collisions

064903-2 MEASUREMENTS OF φ MESON PRODUCTION IN ... PHYSICAL REVIEW C 79, 064903 (2009) √ at sNN = 200 GeV at intermediate pT is observed. These observations support quark coalescence as being the dominant mechanism of hadronization in the intermediate pT region at RHIC.

DOI: 10.1103/PhysRevC.79.064903 PACS number(s): 25.75.Dw

I. INTRODUCTION However, after including three- and four-vector meson vertices into their hidden local symmetry model, Alvarez-Ruso and The φ(1020) vector meson’s properties and its transport in Koch [24] found that the φ meson mean free path in nuclear the nuclear medium have been of interest since its discovery media is smaller than that usually estimated. Ishikawa et al. [1]. The proper lifetime of the φ meson is about 45 fm/c, and + − [25] presented new data on near-threshold φ photoproduction it decays into charged kaons K K with a branching ratio of + − on several nuclear targets. They found that the cross section 49.2%, and more rarely into the dilepton pairs e e (B.R. of +17 − + − − between a φ meson and a nucleon, σ , is equal to 35 mb, 2.97 × 10 4) and µ µ (B.R. of 2.86 × 10 4). φN −11 which appears to be much larger than previous expectations, The mechanism for φ meson production in high energy although the experimental uncertainty is very large [26]. collisions has remained an open issue. As the lightest bound Meanwhile, Sibirtsev et al. [27] presented a new analysis state of strange quarks (ss¯) with hidden strangeness, φ meson of existing φ photoproduction data and found σ ∼ 10 mb. production is suppressed in elementary collisions because of φN Thus, σ in heavy-ion collisions is still unclear. the Okubo-Zweig-Iizuka (OZI) rule [2–4]. The OZI rule states φN The measurement of collective radial flow (represented that processes with disconnected quark lines in the initial by p ) probes the equation of state of matter produced and final state are suppressed. In an environment with many T in nuclear collisions [28,29]. Strong radial flow has been strange quarks, φ mesons can be produced readily through observed for many particles such as π, K, and p(p¯)[30]. If the coalescence, bypassing the OZI rule [5]. The φ meson has φ meson has indeed small hadronic rescattering cross sections been predicted to be a probe of the quark-gluon plasma (QGP) and decouples early from the collision system, contributions formed in ultrarelativistic heavy-ion collisions [6–11]. to the radial flow of the φ meson will be mostly from the On the other hand, a naive interpretation of φ meson partonic stage instead of the hadronic stage. Thus the φ enhancement in heavy-ion collisions would be that the φ meson may have a significantly smaller radial flow than other meson is produced via KK¯ → φ in the hadronic rescattering hadrons with similar mass, such as the proton, especially in stage. Models that include hadronic rescatterings such as central heavy-ion collisions. Therefore, φ mesons may carry RQMD [12] and UrQMD [13] have predicted an increase of − information about the conditions of nuclear collisions before the φ to K production ratio at midrapidity as a function of the chemical freeze-out. Thus it is important to experimentally number of participant nucleons.√ This prediction was disproved measure and compare the freeze-out properties of the φ to in Au + Au collisions at sNN = 200 GeV, from STAR year other hadrons as a function of centrality and collision species. 2001 data [14]. With the higher statistics data newly recorded A comprehensive set of measurements will shed light on the from the Solenoidal Tracker at RHIC (STAR) experiment [15], characteristics of φ meson production and the evolution of the a precise measurement of the φ/K− ratio as a function of collision system. beam energy and collision centrality is presented to confirm The elliptic flow parameter v2 is a good tool for studying this finding in this paper. the system formed in the early stages of high energy collisions The in-medium properties of vector mesons in the hot at RHIC. It has been found that at low pT (0 invariant mass spectrum from relativistic heavy-ion collisions seems to depend on the number of constituent quarks in was proposed as a signature of a phase transition from the the hadron rather than its mass, consistent with the results QGP to hadronic matter [18]. Other calculations have predicted from coalescence/recombination models [39–44]. Since φ is that the φ meson width can be widened significantly due to a meson but has a mass close to that of the proton and , nuclear medium effects [19–21]. Recently, an interesting φ the measurement of the φ meson elliptic flow will provide a mass modification at normal nuclear density in 12 GeV p + A unique tool for testing the above statement. interactions was observed in the dilepton channel (e+ + e−) Current measurements of various hadrons by STAR 0 ∗ ± from the KEK experiment [22,23]. In STAR, we measure (, p, KS ,K(892) ,h , etc.) show that the nuclear modifi- the φ meson mass and width to compare with these predic- cation factor Rcp for baryons differs from that of mesons tions/measurements, using the decay channel φ → K+K−. [45,46], consistent with the prediction of quark coales- From phenomenological analysis, it is suggested that the φ cence/recombination models [42,43,47,48]. Because of the meson mean free path in hadronic media is large because value of the φ meson mass, a comparison of Rcp for the φ with of its small cross section of scattering with hadrons [5]. these previous measurements will conclusively determine if Many other calculations also indicate that the φ meson has the observed difference is driven by particle mass or particle small rescattering cross sections with hadronic matter [19,20]. type.

064903-3 B. I. ABELEV et al. PHYSICAL REVIEW C 79, 064903 (2009)

In previous studies, the production of√ the φ meson has trigger for selecting d + Au and Au + Au collisions for their + = + been measured in Au Au collisions at sNN 130√ GeV respective runs. For p p data taking, the BBCs were used as [49] and in Au + Au and p + p collisions at sNN = trigger detectors. The central trigger corresponds to approx- 200 GeV [14] at RHIC. The Au + Au 200 GeV data presented imately the top 15% and 12% of the measured cross section in this paper were taken from the year 2004 run, where for Au + Au collisions at 130 GeV and 200 GeV, respectively. the number of events is approximately ten times larger than Data from both the MB and central triggers were used for the previously reported number for the Au + Au run in year this analysis. For the Au + Au 62.4 GeV data set, only MB 2001 [14]. The data from the year 2004 run contain the data triggered events were used. For p + p collisions at 200 GeV, reported in Refs. [50,51]. It has been found that the results from the MB trigger was used in the analysis. It was based on a the two runs are consistent with each other. In this paper, we coincidence between the two BBCs. The BBCs are sensitive present systematic measurements of φ meson production over only to the non-single diffractive (NSD) part (30 mb) of the a broad range of collision√ energies and system sizes, including p + p total inelastic cross section (42 mb) [14]. + = Au Au collisions at sNN 62.4, 130 [√49], and 200 GeV, and p + p [14] and d + Au collisions at sNN = 200 GeV from the STAR experiment. In Sec. II, we briefly introduce the 2. Vertex cuts and centrality selection STAR detector and discuss our analysis method (event-mixing The longitudinal z position of the interaction point is technique) in detail. In Sec. III, we present the measurement of determined on-line by the measured time difference of the φ meson invariant mass distributions (III A), transverse mass two ZDCs’s signals. A cut on the z position of the interaction + mT spectra (III B), particle ratios (III C), nuclear modification point is applied on-line for all data sets (except p p) in order factors (III D), and the elliptic flow parameter v2 (III E); we to maximize the amount of useful data for physics analysis, also discuss the physics implication of each of these results. A since events with primary vertices far away from the center of summary and conclusions are presented in Sec. IV. the TPC have a significant non-uniform acceptance. In the off-line data analysis further cuts are applied on the z position II. DATA ANALYSIS of the reconstructed primary vertex (VZ), to ensure nearly uniform detector acceptance. These cuts are listed in Table I. A. Experimental setup To define the collision centrality for the Au + Au data, the The STAR detector [15] consists of several subsystems raw charged hadron multiplicity distribution in the TPC within | | | | in a large solenoidal analyzing magnet. We discuss here a pseudorapidity window η 0.5(η 0.75 was used for + the subdetectors used in the analyses relevant to this paper. the Au Au 130 GeV data) was divided into several bins. Each bin corresponds to a certain fraction of the total inelastic With its axis aligned along the beam direction, the time + projection chamber (TPC) [52] is the main tracking device for cross section [56]. For the d Au data, the raw charged − . < charged particles, covering a pseudorapidity range |η| 1.8 hadron multiplicity in the east (Au-direction) FTPC ( 3 8 η<− . and providing complete azimuthal coverage. The entire TPC 2 8) was used for the centrality definition to avoid auto-correlation between centrality and the measurements is located inside a solenoidal magnet, and data are taken at the of charged particles at midrapidity in the TPC [56]. We maximum magnetic field |B |=0.5 Tesla, where the z axis is z defined four centrality bins for the Au + Au 62.4 GeV data parallel to the beam direction. Radial-drift TPCs (FTPCs) [53] (0–20%, 20–40%, 40–60%, 60–80%), three centrality bins are also installed to extend particle tracking into the forward for the Au + Au 130 GeV data (0–11%, 11–26%, 26–85%), and backward regions (2.5 < |η| < 4.0). Surrounding the TPC nine centrality bins for the Au + Au 200 GeV data (0– is the central trigger barrel (CTB) [54], which is a scintillator 5%, 0–10%, 10–20%, 20–30%, 30–40%, 40–50%, 50–60%, counter array whose analog signal is sensitive to the total 60–70%, 70–80%) and three centrality bins for the d + Au charged particle multiplicity with coverage |η| 1.0. A pair 200 GeV data (0–20%, 20–40%, 40–100%). The 80–100% of beam-beam counters (BBCs) at 3.3 <η<5.0 and a pair most peripheral Au + Au collision data were not used because of zero degree calorimeters (ZDCs) [55]atθ<2mradare of the rapidly decreasing trigger and vertex finding efficiencies located on either side of the collision region along the beam line, and are used to provide event triggers for data taking. A more detailed description of the STAR detector can be found TABLE I. Data sets used in the analysis. Cuts on VZ, the selected in Ref. [15] and references therein. centrality ranges, and the final number of events included in the analysis after all cuts/selections are also shown. B. Event selection √ System sNN Trigger |VZ| Centrality Events Year 1. Trigger selection (GeV) (cm) The Au + Au data used in this analysis were taken with two Au + Au 62.4MB30 0–80% 6.2 × 106 2004 different trigger conditions. One was a minimum-bias (MB) Au + Au 130 MB 80 0–85% 7.6 × 105 2000 trigger requiring only a coincidence between both ZDCs. The Au + Au 130 Central 80 0–11% 8.8 × 105 2000 other was a central trigger additionally requiring both a large Au + Au 200 MB 30 0–80% 1.4 × 107 2004 analog signal in the CTB indicating a high charged particle Au + Au 200 Central 30 0–5% 4.8 × 106 2004 multiplicity at midrapidity and a small ZDC signal. The ZDCs p + p 200 MB 50 MB (NSD) 6.5 × 106 2002 measure beam-velocity neutrons from the fragmentation of d + Au 200 MB 50 MB 1.4 × 107 2003 colliding nuclei and were used as the experimental level-0

064903-4 MEASUREMENTS OF φ MESON PRODUCTION IN ... PHYSICAL REVIEW C 79, 064903 (2009) for low multiplicity events. Table I lists the data sets used along ×10-6 with centrality selections and final numbers of events after 10 these cuts. Note that the elliptic flow v measurement only - 2 9 p K K+ p from 200 GeV MB Au + Au data is presented in this paper, 8 as the statistics for the v2 analysis is not sufficient for the 62.4 + - + and 130 GeV Au Au data. 7 π π

C. Track selection and particle identiﬁcation 5

1. Track selection dE/dx (GeV/cm) 4 - e e+ Several quality cuts were applied to ensure selection of 3 good tracks. During the TPC track reconstruction, a charged 2 track was extrapolated back to the beam line by using the -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 reconstructed helix parameters. If the distance of closest momentum × charge (GeV/c) approach (DCA) of the track to the event vertex was less than 3 cm and the track had at least ten hit points in the FIG. 1. (Color online) Measured dE/dx vs momentum × TPC, the reconstructed track was labeled as a primary track. charge of reconstructed tracks in the TPC. The figure is generated The helix parameters for primary tracks were then refitted from Au + Au 62.4 GeV data. by requiring that the helix pass through the primary vertex location. This procedure improved the momentum resolution of tracks. Since the φ meson has a very short lifetime, it decays and depends on the event multiplicity and the number of at the primary vertex position. Thus only primary tracks were dE/dx samples from the track used to calculate the mean used for the φ meson analysis. As a systematic check, the value. Tracks within 2σ of the kaon Bethe-Bloch curve were DCA selection for primary tracks was changed from 3 cm selected as kaon candidates. Figure 1 presents the measured to 1 cm. The differences in the results were small and were dE/dx versus momentum × charge in Au + Au collisions included in the estimate of systematic uncertainties. Tracks at 62.4 GeV. Table II lists all the track cuts applied in the with transverse momentum less than 0.1 GeV/c were not used, analysis. as their combined acceptance and efficiency becomes very Note that from the dE/dx measurement, kaons cannot small. Each track included in the φ analysis was required to be clearly separated from pions above p ∼ 0.6 GeV/c and have at least 15 hit points out of 45 used in the fitting of the from protons/antiprotons above p ∼ 1.1GeV/c. Also note tracks helix parameters. The ratio of the number of space points that the electron and positron dE/dx bands cross the bands for used in the track reconstruction to the maximum possible pions, kaons, and protons/antiprotons. Therefore selected kaon number of hit points was required to be greater than 55% candidates are contaminated by electrons/positrons, pions, and to avoid split tracks where a real track is reconstructed in two protons/antiprotons varying with p. Contamination by these or more segments. A pseudorapidity cut |η| < 1.0(|η| < 1.1 charged particles in the kaon sample brings in additional for Au + Au 130 GeV data) was applied to select tracks that real correlations (such as particle decays) which cannot be are well within the TPC acceptance. subtracted by the event-mixing method. We have varied the nσ cut for kaon to investigate the efficiency and combinatorial background dependence of the φ signal extraction on this cut. 2. Kaon selection The resulting systematic uncertainties have been included in the estimate of the total systematic errors. Particle identification (PID) was achieved by correlating the ionization energy loss (dE/dx) of charged particles in the TPC gas with their measured momentum. The measurement of TABLE II. Track cuts used in the analysis, where NFit and NMax mean dE/dx was achieved by averaging the measured dE/dx represent the number of fitted hits and the maximum number of hits samples along the track after truncating the top 30%. The for TPC tracks, respectively. measured dE/dx versus momentum curve is reasonably well described by the Bethe-Bloch function [57] smeared with the Cut parameter Value detector’s resolution (note that the Bichsel function was used to fit the dE/dx plot in Au + Au 200 GeV from the year Track DCA (cm) <3 Track N 15 2004 run [58]). The nσ values for kaons are calculated via Fit Track NFit/NMax >0.55 1 dE/dxmeasured Track momentum (GeV/c)0.1 0.04 sured by TPC and calculated analytically, respectively, and R φ candidate’s rapidity |y| < 0.5 (for spectra) denotes the dE/dx resolution of the track which is found to |y| < 1.0 (for v2) range between 6% and 10%. R is determined experimentally

064903-5 B. I. ABELEV et al. PHYSICAL REVIEW C 79, 064903 (2009)

D. Event mixing and raw yield extraction 1400 The φ meson signal was generated by pairing all K+K− d+Au 200 GeV (0-100%) 1200 0.4

[59,60] was applied to calculate the shape of the combinatorial Entries/MeV 400 background, where the invariant mass was calculated by pairing two kaons from two different events with same primary 200 vertex and multiplicity bins (mixed event). Ideally, since it 0 combines two different events, the mixed-event distribution contains everything except the real same-event correlations. 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 The STAR TPC has symmetric coverage about the center Invariant Mass (GeV/c2) of the collision region. However, variations in the acceptance occur, since the collision vertex position may change FIG. 2. (Color online) Background-subtracted invariant mass + considerably event-by-event. This variation in the collision distributions at 0.4 photon conversions (γ → background, two events were only mixed if they had similar e+ + e−). The δ-dip-angle between the photon converted event multiplicities. These requirements ensure that the two electron and positron is usually quite small. The δ-dip-angle events used in mixing have similar event structures, so the is calculated from mixed-event invariant mass distribution can better represent the combinatorial background in the same-event invariant − pT 1pT 2 + pz1pz2 δ-dip-angle = cos 1 , (2) mass distribution. Consistent results were obtained when we p1p2 constructed the background distribution using like-sign pairs from the same event. where p1,p2,pT 1,pT 2,pz1,pz2 are momentum and trans- To reduce statistical uncertainty in the mixed event, each verse and longitudinal momentum components of the two event was mixed with ﬁve to ten other events (depending on the tracks; this represents the opening angle of a pair in the pz-pT collision system). To extract the φ meson signal, the mixed- plane. We required the δ-dip-angle to be greater than 0.04 event and same-event K+K− invariant mass distributions were radians. This cut was found to be very effective in removing accumulated, and the mixed-event distribution normalized the photon conversion background while only reducing the to the same-event distribution in the region above the φ φ reconstruction efﬁciency by ∼12%. Figure 2 shows two 2 mass, 1.04

064903-6 MEASUREMENTS OF φ MESON PRODUCTION IN ... PHYSICAL REVIEW C 79, 064903 (2009)

×103 (a) (c) 10000 (e) 2500 6000 8000 2000 4000 6000 1500 4000 1000 0.8 < p < 1.2 GeV/c 0.8 < p < 1.2 GeV/c 0.6 < p < 1.4 GeV/c 2000 T T T 500 p+p 200 GeV Au+Au 62.4 GeV (60-80%) 2000 Au+Au 200 GeV (0-10%)

(b) 1500 (d) (f) Entries/2MeV Entries/2MeV Entries/2MeV 1500 40000 + - φ → K++ K- 1000 φ → K + K φ → K++ K- 1000 20000 500 500 0 0 0

0.98 1 1.02 1.04 1.06 0.98 1 1.02 1.04 1.06 0.98 1 1.02 1.04 1.06 Invariant Mass (GeV/c2) Invariant Mass (GeV/c2) Invariant Mass (GeV/c2)

FIG. 3. (Color online) Upper panels: same-event (full points) and mixed-event (solid line) K+K− invariant mass distributions at 0.6 < pT < 1.4 GeV/c in p + p 200 GeV collisions (a), 0.8

were determined by fitting the background-subtracted minv low pT is mainly due to poor acceptance of the daughter tracks. distribution with a Breit-Wigner function superimposed on a The efficiency is lower in more central collisions because of linear (or polynomial) background function the increasing occupancy in the TPC [56]. dN A = + B(m ), (3) 2 2 inv dminv (minv − m0) + /4 where A is the area under the peak corresponding to the number F. Vertex finding and trigger efficiency correction of φ mesons, is the full width at half maximum (FWHM) For p + p and d + Au data, the trigger efficiency is less of the peak, and m0 is the resonance mass position. B(minv) than 100% [63]. The MB trigger for p + p data was found = + denotes a linear [B(minv) p0 p1minv, shown by a dashed to trigger ∼87% of p + p NSD events. For d + Au data, = line in Figs. 3(b), 3(d) and 3(f)] or polynomial [B(minv) the trigger efficiency was found to be ∼95%. These trigger + + 2 p0 p1minv p2minv, shown by a dot-dashed line in Fig. 3(f)] efficiencies were used to normalize the measured yield, and the residual background function. The parameters p0,p1, and p2 corresponding uncertainties are added to the total systematic of B(minv) and A, m0, and are free parameters.

E. Efficiency correction 0.5 The φ acceptance and reconstruction efficiency were calculated using an embedding technique, in which simulated tracks 0.4 were embedded into real events. The number of embedded simulated tracks is approximately 5% of the measured multi- 0.3 plicity of the real event. The φ meson decay (φ → K+K−) and Acceptance the detector responses were simulated by the GEANT program × p+p 200 GeV package [62] and the simulated output signals were embedded 0.2 d+Au 200 GeV (40-100%) into real events before being processed by the standard STAR Au+Au 200 GeV (70-80%) Au+Au 200 GeV (30-40%) event reconstruction code. Embedded data were then analyzed Efficiency 0.1 to calculate tracking efficiencies and detector acceptance by Au+Au 200 GeV (10-20%) dividing the number of reconstructed φ by the number of input Au+Au 200 GeV (0-5%) 0 φ in the desired kinematic regions. Figure 4 shows examples 0123456 of correction factors (tracking efficiency × acceptance) for our p (GeV/c) T analysis as a function of φ meson pT for selected centrality bins for Au + Au, d + Au, and p + p 200 GeV collisions. It FIG. 4. (Color online) Reconstruction efficiency including ac- can be seen that the overall correction factors increase from a ceptance of φ meson as a function of pT in several centrality bins of few percent at low pT to over 30% at high pT . Low efficiency at Au + Au, d + Au, and p + p 200 GeV collisions.

064903-7 B. I. ABELEV et al. PHYSICAL REVIEW C 79, 064903 (2009) errors for p + p and d + Au data. The MB trigger efficiency 0.9 for Au + Au data is essentially 100% [56]. It was found that the event vertex finding efficiency, which 0.8 is the fraction of events having reconstructed vertices, drops rapidly for low multiplicity events [56]. For d + Au collisions, the vertex efficiency was 88% for the most peripheral bin 0.7 (40–100%), 93% for the MB events, and 100% for the central and middle central bins (0–20% and 20–40%). For Au + Au 0.6 Au+Au 200 GeV collisions, the vertex finding efficiency was 99.9% and p resolution T 2 independent [64] due to the increased track multiplicity in Ψ 0.5 those collisions. However, the overall vertex finding efficiency p + p was found to be 98.8% for the MB data by applying 0.4 an additional BBC time difference selection (i.e., the NSD Central Peripheral requirement), and the effect of correction was negligible in 0.3 this analysis. 0 1020304050607080 Most Central (%)

FIG. 5. Event plane resolution as a function of centrality in G. v measurement 2 2 Au + Au 200 GeV collisions, where the vertical axis starts from 0.3 1. Reaction plane method for clarity. We employed the STAR standard reaction plane method as a where 2 is the calculated reaction plane angle of the described in Refs. [65,66], which uses a Fourier expansion to subevent, and C is a constant calculated from the known describe particle emission with respect to the reaction plane multiplicity dependence of the resolution [66]. This resolution angle, that is, was determined by dividing each event into two random ∞ subevents, a and b, with equal multiplicities. The reaction d3N 1 d2N plane resolution therefore corresponds to how accurately the E = 1 + 2v cos[n(ϕ − )] , (4) d3p 2π p dp dy n r event plane angle represents the real reaction plane; due to t t n=1 its the definition in Eq. (6), a value of unity indicates ideal where r is the real reaction plane angle and ϕ is the particle’s resolution. Figure 5 presents the reaction plane resolutions in + azimuthal angle. The coefficient v2 in the second-order term different centrality bins for Au Au 200 GeV collisions. of the expansion is the dominant part and is called the second The combinatorial background in the φ invariant mass harmonic anisotropic flow parameter, or elliptic flow. distribution was also calculated by an event-mixing technique The real reaction plane angle r is not known but can be as described above. To guarantee the mixed-event sample estimated experimentally [67]. In our analysis, the estimated would represent the combinatorial background, an additional reaction plane angle from the second-order harmonic ( 2)was cut, the reaction plane angle difference between two mixed used. This has a finite resolution due to a limited number of events, was required to be less than 0.1π rad in the event- particles available in each event and a different event-by-event mixing procedure. After background subtraction, the φ meson − v2, which is used for the estimation. The estimated reaction yield was extracted in each (pT ,ϕ 2) bin. The yield plane resolution was used to correct the observed vobs to obtain distribution as a function of ϕ − was fitted by the function 2 2 the final estimation of v2. + obs − A 1 2v2 cos[2(ϕ 2)] , (7) The event plane angle 2 was calculated by the equation obs to extract the v2 value, where A is a constant. A typical result 1 − wi sin(2ϕi ) + = tan 1 i , (5) for the Au Au data at 200 GeV is presented in Fig. 6. 2 2 w cos(2ϕ ) obs i i i The measured v2 was then divided by the reaction plane resolution to obtain the final v , i.e., where the sums are over all charged particles used for 2 obs reaction plane determination, and wi and ϕi are the weight v2 v2 = . (8) and azimuthal angle for the ith particle in a given event, cos[2( 2 − r )] respectively. The weights include both a p weight and ϕ T Simulation studies have found that the measured v is about weight. The p weight was taken to be the particle p up to 2 T T 7% (relative to the real v ) lower than the real v due to binning 2.0 GeV/c and constant (2.0) above that [66]. The ϕ weight was 2 2 effects (five bins in ϕ − ); a correction has been made to taken to be the reciprocal of the ϕ distribution (normalized by 2 the measured v to account for this effect. the average entries) for all selected tracks. The autocorrelations 2 were eliminated by excluding all kaon tracks used in the φ invariant mass calculation from the reaction plane angle 2. Invariant mass method estimation [64]. The reaction plane resolution was then calculated by A new method, namely, the invariant mass method,was also used to extract the elliptic flow v2 of the φ meson. The − = a − cos[2( 2 r )] C cos 2 2 r , (6) method was proposed in Ref. [68], which decomposes the

064903-8 MEASUREMENTS OF φ MESON PRODUCTION IN ... PHYSICAL REVIEW C 79, 064903 (2009)

×103 0.04 0.02 380 χ2 / ndf 1.898 / 3 A 2.943×105 ± 4442 360 0.035 0.015 obs ± v2 0.07392 0.01018 〉 ) 〉 ) 340 2 2

Ψ 0.03 0.01 - Ψ π - - -

Au+Au 200 GeV (0-80%) K + 320 Au+Au 200 GeV (0-80%) K + K K φ

1.5 < p < 2.0 GeV/c 0.5 < p < 1.0 GeV/c φ 300 T 0.025 T 0.005 cos2( sin2( 〈 〈 Entries/0.2 280 0.02 0 260 0.015 -0.005 240 1 1.02 1.04 1.06 1.08 1.1 0 0.5 1 1.5 2 2.5 3 Invariant Mass (GeV/c2) ϕ - Ψ (rad) 2 FIG. 7. (Color online) cos[2(ϕK+K− − 2)] (full red points) − FIG. 6. ϕ 2 distribution for φ meson at 1.5

064903-9 B. I. ABELEV et al. PHYSICAL REVIEW C 79, 064903 (2009)

Systematic uncertainties for the v2 measurement from the φ meson mass is lower and the width is larger than from two different v2 extraction methods show pT and centrality simulation. The drop of the φ meson mass in both real data dependences, which mainly result from the determination of and simulation at low pT is due to the multiple scattering S/(S + B) ratios for the invariant mass method and from the energy loss of low pT tracks in the detector, which is not fully removal of residual background in the reaction plane method, corrected during track reconstruction. respectively. In our analysis, the point-to-point systematic Figure 9 shows shape comparisons between experimental errors included contributions from the following: and MC invariant mass distributions for the φ meson at 0.6 < p < 1.0GeV/c in p + p 200 GeV (NSD) and Au + Au (i) Difference in finding the φ-meson signal via bin-by-bin T 200 GeV (0–5%) collisions. The real data φ invariant mass counting or Breit-Wigner function fitting methods; peak (solid circles) is wider than that from standard MC data (ii) Difference due to the residual background fitting func- set (1) (open circles). If the momentum resolution for low pT tion: first- or third-order polynomial functions; kaons used in the simulations is increased by 50%, e.g., kaon (iii) Difference in combinatorial background determination: momentum resolution at 350 MeV/c increases from ∼2% [MC rotation of the background (the mixed event is from data set (1)] to ∼3% [MC data set (2)], the φ meson width the azimuthal angle rotation of all tracks from the same from simulation reproduces the measured width from real event) or event-mixing (the current method); data as shown by open diamonds. This decreased momentum v v (iv) Difference in 2 calculation: centrality-by-centrality 2 resolution in MC could be possible considering uncertainties in v calculation and then weighting to get the final MB 2 or simulations for the amount of material between the TPC active v direct calculation of the 2 through MB raw yield fitting. volume and the primary collision vertex and residual geometry alignment issues. These remaining issues for the differences in mass and width of φ mesons between real data and simulations III. RESULTS have limited our sensitivity to possible small modifications of φ meson properties in the medium produced at RHIC collisions. A. Mass and width It should also be noted that to really trace down the possible Figure 8 shows the φ invariant mass peak position and modification of the φ meson mass and width in heavy-ion width (FWHM) as a function of pT for Au + Au 200 GeV collisions, measurements through the dilepton decay channel (0–5%), Au + Au 62.4 GeV (0–20%), d + Au 200 GeV are needed. An interesting excess on the low-mass side of the (0–20%), and p + p 200 GeV (NSD) collisions. In the larger φ meson invariant mass peak was observed by an e+ + e− pT region (>1GeV/c), the measured mass and width for channel in the low βγ region (βγ < 1.25) for 12 GeV p + Cu the φ meson are consistent with those from Monte Carlo interactions from the recent KEK experiment [22,23]. This (MC) embedding simulations in various collision systems and may indicate a vector meson mass modification at normal at different energies. At low pT (<1GeV/c), the measured nuclear density. φ measurements using the dilepton channel

1.022 (a) 1.022 (c) 1.02 1.02 ) 2

) 1.018 1.018 2 1.016 1.016 full: experimental data open: MC data (GeV/c full: experimental data open: MC data ss (GeV/c 1.014 1.014 ss

p+p 200 GeV Ma Au+Au 200 GeV 1.012 1.012 Ma d+Au 200 GeV Au+Au 62.4 GeV 1.01 PDG value 1.01 PDG value

14 (b) 14 (d) 12 12 )

2 10 10

8 ) 8 2 6 6 4 4 2 2 full: experimental data open: MC data full: experimental data open: MC data Width (MeV/c 0 0 p+p 200 GeV Au+Au 200 GeV

-2 d+Au 200 GeV Width (MeV/c -2 Au+Au 62.4 GeV -4 PDG value -4 PDG value -6 -6 0 0.5 1 1.5 2 2.5 33.5 4 4.5 5 0 0.5 1 1.5 2 2.5 33.5 4 4.5 5 p (GeV/c) p (GeV/c) T T

FIG. 8. (Color online) Masses and widths (FWHMs) of φ as a function of pT in p + p 200 GeV (NSD), d + Au 200 GeV (0–20%), Au + Au 62.4 GeV (0–20%), and Au + Au 200 GeV (0–5%) collisions, with the corresponding PDG values.

064903-10 MEASUREMENTS OF φ MESON PRODUCTION IN ... PHYSICAL REVIEW C 79, 064903 (2009)

data, the distributions were ﬁtted by a Levy function [69,70], p+p 200 GeV 0.6 < p < 1.0 GeV/c T i.e., 400 Exp. data mass = 1.019 GeV 2 − − width = 8.28 MeV 1 d N = dN/dy(n 1)(n 2) MC data (1) 2πmT dmT dy 2πnTLevy(nTLevy + m0(n − 2)) mass = 1.019 GeV 200 width = 6.15 MeV − m − m n × 1 + T 0 , (13) nTLevy

where n, the slope parameter T , and yield dN/dy are free 0 Levy parameters. For the four most peripheral centrality bins (40– 50%, 50–60%, 60–70%, and 70–80%) in Au + Au collisions

Entries/MeV Au+Au 200 GeV 0.6 < p < 1.0 GeV/c T at 200 GeV, the distributions were better fit by a Levy than Exp. data by an exponential function. In fact, the exponential function 100000 mass = 1.019 GeV width = 8.46 MeV [Eq. (12)] is the limit of the Levy function [Eq. (13)] as n = →∞ MC data (1) approaches infinity; i.e., Texp TLevy (n ). Table III lists mass = 1.019 GeV the extracted slope parameter T , mean transverse momentum width = 6.36 MeV 50000 pT , and yield dN/dy from the best fits to the spectra. Overall MC data (2) mass = 1.019 GeV estimated systematic uncertainties on these quantities are also width = 8.45 MeV listed. The φ meson transverse mass spectra in central Au + Au 0 collisions can be well described by a single mT -exponential function, while the spectra in d + Au, p + p, and peripheral 1 1.02 1.04 1.06 Au + Au are better described by a Levy function, due to Invariant Mass (GeV/c2) the power-law tail at intermediate and high pT . Figure 11 compares the transverse momentum spectra shapes in different FIG. 9. (Color online) Invariant mass distributions of φ meson + + .

064903-11 B. I. ABELEV et al. PHYSICAL REVIEW C 79, 064903 (2009)

] (a) Au+Au 62.4 GeV (b) Au+Au 130 GeV -2 1 ) ] 2 -2

1 ) 2

10-1 10-1 0-11% dy) [(GeV/c T

-2 dy) [(GeV/c T

dm 10

T 0-80%×10 dm m T π 11-26%×0.25 FIG. 10. (Color online) φ meson -3 0-20% m (2 10 π -2 ⁄ 10 transverse mass distributions for dif-

20-40% (2 N ⁄ 2 ferent collision systems and different d -4 40-60% N 10 2 26-85%×0.15

d energies. For clarity, distributions 60-80% for some centrality bins have been 10-5 -3 0 0.5 1 1.5 2 2.5 33.5 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 scaled by factors indicated in the ﬁg- 2 ure. Curves represent the exponential m -m (GeV/c ) m -m (GeV/c2) T 0 T 0 (solid) and Levy (dashed) function 10 ﬁts to the distributions. Error bars 10 ] (c) Au+Au 200 GeV (d) d+Au 200 GeV are statistical only. Note that a scale ] -2 ) -2 2 )

2 factor of 1.09 is applied to the φ me- 10-2 son spectra for Au + Au collisions -1 0-5% 10 at 200 GeV in Ref. [50] to correct -5 10 0-10%/10 for the kaon identiﬁcation efﬁciency

dy) [(GeV/c 2 dy) [(GeV/c T 10-20%/10 T 3 -3 effect missed previously.

dm 20-30%/10

dm 10

T -8

10 4 T m 30-40%/10 0-100%×500 m π

5 π (2 40-50%/10 0-20%×50 (2 ⁄ -11 6 ⁄ -5 N 10 50-60%/10 N 2 10

2 × d 7 20-40% 10 60-70%/10 d 8 p+p 200 GeV (NSD) 40-100%×4 10-14 70-80%/10 -7 0123 456 10 0123 45678 2 2 mT-m0 (GeV/c ) mT-m0 (GeV/c )

systems) are produced by or evolve with different mechanisms, extracted from the best fit to the mT spectra as described and such as hydrodynamics [35–38], coalescence/recombination shown in Table III. The measured pT of the φ meson shows [39–44], fragmentation [75–77] and jet quenching [72–74] no significant centrality dependence within systematic errors. mechanisms. The observed change of the φpT spectra At the same Npart value, the φ meson pT increases slightly shape in our measurements is likely due to the change of with collision energy from 62.4 to 200 GeV. these production mechanisms in different kinematic regions The mean values of transverse momentum pT as a and collision systems. Further evidence of this will be function of hadron mass from 62.4 and 200 GeV central discussed later, based on the measurements of different Au + Au collisions are presented in the lower panel of Fig. 13. observables. These data are taken from Refs. [30,79]. The pT of ordinary Figure 12 presents the φ meson midrapidity yield per hadrons π −,K−, and p¯ follows a trend that is increasing participant pair (dN/dy)/(0.5Npart) as a function of Npart (ap- with the mass of the hadron, as expected from the dynamics proximately proportional to the size of the collision system). of these particles coming from a common radial velocity The measured midrapidity yield per participant pair increases field shown as the hatched band [Hydro. model (1)] in the nonlinearly with Npart, except for the largest centrality bins plot [80,81]. However, heavy hyperons such as and show and the Au + Au 130 GeV results where there are only three a deviation from the trend. Their values of pT are lower than centrality bins with big error bars due to the limited statistics. the expected ones. The observed pT values for φ meson For 200 GeV collisions, the yield increases rapidly from and are similar to those of and . Meanwhile, another p + p and d + Au to peripheral Au + Au collisions and then hydrodynamic model (2) shown by the curve [82,83], which saturates for midcentral Au + Au collisions. For the same considers possible different chemical freeze-out temperatures Npart, (dN/dy)/0.5Npart increases with the collision energy for ordinary and strange hadrons, gives a better description of the Au + Au collisions. This is expected because of the for strange particle pT . This behavior can be explained increase of energy available to produce the φ mesons. The if strange hadrons have a smaller scattering cross section centrality and energy dependences of the enhancement of φ than ordinary hadrons in the later hadronic stage of the meson production can reflect the mechanism of strangeness collisions. These strange particles would then decouple earlier enhancement in a dense medium formed in high energy from the system. The collective motion of the φ meson and heavy-ion collisions [78]. multistrange hadrons and should have been developed The upper panel of Fig. 13 shows the Npart dependence of at the early partonic stage in Au + Au collisions at RHIC. If φ meson pT in different collision systems, where pT is radial flow is built up through the evolution of the system, the

064903-12 MEASUREMENTS OF φ MESON PRODUCTION IN ... PHYSICAL REVIEW C 79, 064903 (2009)

TABLE III. Results from fits to the transverse mass distributions of the φ meson. The fit functions used to extract the results are also listed. All values are for midrapidity |y| <0.5. The first error is statistical; the second is systematic.

2 Centrality Fit χ /ndf Texp/Levy n pT dN/dy function (MeV) (MeV/c)

Au + Au 0–20% Exp. 8.4/9 328 ± 6 ± 22 – 922 ± 13 ± 61 3.52 ± 0.08 ± 0.45 (62.4 GeV) 20–40% Exp. 8.4/9 324 ± 6 ± 23 – 913 ± 12 ± 65 1.59 ± 0.03 ± 0.15 40–60% Exp. 14.5/9 308 ± 8 ± 25 – 881 ± 16 ± 71 0.58 ± 0.01 ± 0.07 60–80% Exp. 13.3/9 279 ± 9 ± 28 – 822 ± 19 ± 82 0.15 ± 0.004 ± 0.02 Au + Au 0–11% Exp. 5.3/7 379 ± 50 ± 45 – 1095 ± 147 ± 131 5.73 ± 0.37 ± 0.57 (130 GeV [49]) 11–26% Exp. 3.2/5 369 ± 73 ± 44 – 1001 ± 144 ± 120 3.33 ± 0.38 ± 0.33 26–85% Exp. 9.0/6 417 ± 75 ± 50 – 1021 ± 99 ± 123 0.98 ± 0.12 ± 0.10 Au + Au 0–5% Exp. 11.0/12 357 ± 3 ± 23 – 977 ± 7 ± 64 7.95 ± 0.11 ± 0.73 (200 GeV) 0–10% Exp. 10.2/12 359 ± 5 ± 24 – 979 ± 20 ± 66 7.42 ± 0.14 ± 0.68 10–20% Exp. 9.7/12 373 ± 4 ± 26 – 1010 ± 8 ± 69 5.37 ± 0.09 ± 0.50 20–30% Exp. 26.7/12 387 ± 4 ± 26 – 1022 ± 14 ± 68 3.47 ± 0.06 ± 0.44 30–40% Exp. 21.1/12 371 ± 4 ± 24 – 1005 ± 8 ± 64 2.29 ± 0.04 ± 0.23 40–50% Levy 17.4/11 315 ± 11 ± 38 22.7 ± 4.3 949 ± 13 ± 67 1.44 ± 0.03 ± 0.14 50–60% Levy 6.9/11 290 ± 13 ± 34 13.8 ± 1.9 955 ± 14 ± 87 0.82 ± 0.02 ± 0.09 60–70% Levy 7.4/11 291 ± 13 ± 29 18.6 ± 3.6 926 ± 15 ± 75 0.45 ± 0.01 ± 0.05 70–80% Levy 5.5/11 243 ± 15 ± 25 13.0 ± 2.3 851 ± 19 ± 85 0.20 ± 0.01 ± 0.02 p + p (200 GeV, NSD [14]) 0–100% Levy 10.1/10 202 ± 14 ± 11 8.3 ± 1.2 812 ± 30 ± 41 0.018 ± 0.001 ± 0.003 d + Au 0–20% Levy 4.7/11 323 ± 20 ± 32 15.5 ± 3.9 1030 ± 57 ± 103 0.146 ± 0.005 ± 0.014 (200 GeV) 20–40% Levy 13.6/11 316 ± 19 ± 32 16.9 ± 4.7 1007 ± 35 ± 101 0.103 ± 0.003 ± 0.010 40–100% Levy 12.4/11 263 ± 15 ± 26 12.2 ± 2.1 920 ± 35 ± 92 0.040 ± 0.001 ± 0.004 0–100% (MB) Levy 17.5/11 297 ± 11 ± 30 13.9 ± 1.8 973 ± 26 ± 97 0.071 ± 0.001 ± 0.005

particles with a smaller hadronic cross section would have C. Ratios smaller radial velocity and relatively smaller p . − T The yield ratio φ/π as√ a function of the center-of-mass energy per nucleon pair ( sNN) is presented in the upper − ] -1 panel of Fig. 14.Theφ/π ratio increases with energy in both -2 10 Au+Au 200 GeV (0-5%) /N binary + + exponential fit A A [14,30,49,84–86] and p p collisions [87–90], indi- -2 d+Au 200 GeV (0-20%) /N 10 binary cating that the yield of the φ increases faster than that√ of the Levy fit − + + ) [(GeV/c) -3 p+p 200 GeV π in A A and p p collisions with increasing sNN. T 10 − Levy fit The φ/π ratio in A + A collisions is enhanced compared

dydp -4

T 10 to that for p + p collisions, which indicates that A + A p π 10-5 collisions may provide a more advantageous environment for N/(2

2 the production of φ mesons. In fact, an enhanced production of -6 )d 10

binary 10-7

(1/N 0.06

] -1 Au+Au 200 GeV (0-5%) /(N /2)

-2 10 part exponential fit -2 d+Au 200 GeV (0-20%) /(N /2) 0.05 10 part Levy fit -3 p+p 200 GeV ) [(GeV/c) 10 0.04 T Levy fit -4 dydp 10 part

T 0.03 p

π -5 dN/dy

10 0.5N

N/(2 0.02 2 10-6 Au+Au 200 GeV

/2)]d Au+Au 130 GeV -7 0.01 p+p 200 GeV part 10 d+Au 200 GeV Au+Au 62.4 GeV

[1/(N 0123456 0 0 50 100 150 200 250 300 350 400 p (GeV/c) T Npart

FIG. 11. (Color online) Comparison of transverse momentum FIG. 12. (Color online) Npart dependence of (dN/dy)/0.5Npart in spectra shape among different 200 GeV collision systems: Au + Au ﬁve different collision systems: Au + Au 62.4, 130, 200 GeV; p + p (0–5%), d + Au (0–20%), and p + p (inelastic). The spectra are 200 GeV (inelastic); and d + Au 200 GeV. Statistical and systematic normalized by Nbin (top panel) and Npart/2 (bottom panel). errors are included.

064903-13 B. I. ABELEV et al. PHYSICAL REVIEW C 79, 064903 (2009)

1400 0.03 A + A 0.025 1200 p + p 0.02 1000 - π

/ 0.015 (MeV/c) φ φ 〉

T 800 p

〈 0.01 Au+Au 200 GeV 600 p+p 200 GeV Au+Au 130 GeV 0.005 d+Au 200 GeV Au+Au 62.4 GeV 0 400 2 1 10 102 103 10 10 s (GeV) N part NN 0.04 1600 p+p 200 GeV Au+Au 200 GeV Au+Au 200 GeV d+Au 200 GeV Au+Au 130 GeV 1400 0.035 Au+Au 62.4 GeV Au+Au 62.4 GeV 1200 0.03 Ω

1000 -

Λ Ξ π 0.025 (MeV/c) p φ / φ 〉

T 800 p

〈 0.02 Au+Au 200 GeV 600 K Hydro. model (1) 0.015 400 π Hydro. model (2) 200 0.01 0 50 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Npart Hadron mass (GeV/c2) FIG. 14. (Color online) Top panel: Energy dependence of the − FIG. 13. (Color online) Top panel: Npart dependence of pT φ in ratio φ/π in A + A (full points) and p + p (open points) collisions. different collision systems. Bottom panel: Hadron mass dependence Stars are data from the STARexperiment at RHIC. Bottom panel: Npart + − of pT in central Au Au collisions at 62.4 and 200 GeV. The band dependence of ratio φ/π in different collision systems. Systematic and curve show two hydrodynamic model calculations for central errors are included for the STAR data points. Au + Au collisions at 200 GeV. Note: Hadron masses for the Au + Au 62.4 GeV data are shifted slightly in the x-axis direction for sumption that kaon coalescence is the dominant mechanism for clarity, and systematic errors are included for φ. φ production. The KK¯ and K-hyperon modes are included in these rescattering models [12,13]. They predict an increasing φ meson in a heavy-ion environment has been predicted to be φ/K− ratio vs centrality (shown by the dashed line in the a signal of QGP formation [5]. However, no clear conclusion lower panel of Fig. 15), which is again in contradiction with can be drawn from the experimental measurements, since the the approximately ﬂat trend of our measurements. Note also − relative enhancement from√ p + p to A + A collisions does that the φ/K ratio from the UrQMD model is scaled by not seem to change for sNN > 10 GeV. The bottom panel of a factor of 3.4 to match the magnitude of our measurement − Fig. 14 shows the Npart dependence of the φ/π ratio in for peripheral Au + Au collisions. The comparisons of the − different collisions. The φ/π ratio ﬁrst increases with Npart, data to predictions from these rescattering models including − and then seems to be saturated in the high Npart region. pT and φ/K effectively rule out kaon coalescence as To further study whether φ meson production, or just that of the dominant production mechanism for the φ meson. These strange particles, is enhanced in high energy A + A collisions measurements of the φ/K− ratio may point to a common with respect to elementary collisions, we have plotted the yield underlying production mechanism for φ and strange mesons − √ ratio of φ/K as a function of sNN in A + A, e + e, and in all collision systems. p + p collisions in the top panel of Fig. 15. For these In addition, statistical models [91–95] based on the as- collisions, at energies above the threshold for φ production, sumption that the accessible phase space is fully saturated the φ/K− ratio is essentially independent of collision species and thermalized can reproduce the STAR measurements of and energy from a few GeV up to 200 GeV [14,30,49,84–90]. integrated hadron yield ratios (including φ/π− and φ/K−) The lower panel of Fig. 15 shows that the yield ratio φ/K− at midrapidity in p + p and Au + Au collisions at 200 GeV from our analysis is also almost constant as a function of [34]. In these statistical models, the strangeness phase-space centrality. This is remarkable considering that the environment occupancy factor γs approaches unity with increasing Npart, created by p + p collisions is so drastically different from that which indicates that strangeness approaches/reaches chemical of Au + Au collisions that have both partonic and hadronic equilibration for midcentral and central Au + Au collisions at interactions. RHIC energies. The centrality dependence of the φ/K− ratio provides Because the mechanisms of (multi)strange particle produc- another serious test for rescattering models based on the as- tion are predicted to be very sensitive to the early phase of

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+ 0.25 centrality bins. The (− + ) data points are from A + A p + p Ref. [34] (for 0–12%) and from Ref. [100] for the other 0.2 e + e centralities. Also shown in the ﬁgure are three curves from two recombination model expectations for central collisions.

- A model by Ko et al., based on the dynamical recombination of /K φ 0.15 quarks [97], is compared with the data and found to overpredict the ratio by a factor of about 3 over the whole pT region. (Note: the bumpy shape for this model is due to the limited statistics 0.1 of their Monte Carlo simulation of the model.) Based on φ and production from coalescence of thermal s quarks in 0.05 the medium [96], Hwa and Yang can describe the trend of the 10 102 datauptopT ∼ 4GeV/c but fail at higher pT (solid line). In sNN (GeV) the alternative SCF scenario [98,99], a large string tension of κ = 3 GeV/fm can reproduce the data up to pT ∼ 4.5GeV/c Au+Au 62.4 GeV p+p 200 GeV 0.3 in the framework of the HIJING/BB v2.0 model, but the Au+Au 130 GeV d+Au 200 GeV effect of strong color electric ﬁelds remains an open issue and Au+Au 200 GeV 0.25 needs to be further investigated. With decreasing centrality, the Au+Au 200 GeV (UrQMD×3.4) observed /φ ratios seem to turn over at successively lower

- values of p , possibly indicating a smaller contribution from 0.2 T /K

φ thermal quark coalescence in more peripheral collisions [96]. This is also reﬂected in the smooth evolution of the pT spectra 0.15 shapes from the thermal-like exponentials to Levy-like curves.

0.1 0 50 100 150 200 250 300 350 400 D. Nuclear modiﬁcation factor

Npart The measurement of the nuclear modification factors Rcp and RAB provides a sensitive tool to probe the production FIG. 15. (Color online) Top panel: Energy dependence of ratio dynamics and hadronization process in relativistic heavy-ion φ/K− in A + A and elementary (e + e and p + p) collisions. Stars collisions [39–44]. Rcp, which is the ratio of yields in central are data from STAR experiments at RHIC. Bottom panel: Npart − to peripheral heavy-ion collisions normalized by Nbin,is dependence of ratio φ/K in different collision systems. The dashed defined as line shows results from UrQMD model calculations. Systematic errors are included for the STAR data points. [dN/(N dp )]central R (p ) = bin T , (14) cp T peripheral [dN/(NbindpT )] nuclear collisions, the ratio of /φ is expected to reflect and RAB , which is the yield ratio of nucleus (A) + nucleus (B) the partonic nature of the thermal source that characterizes collisions to inelastic p + p collisions normalized by Nbin,is QGP [96] and the effects of the strong color field (SCF) [98]. In defined as Fig. 16, the ratios of /φ vs pT are presented for different [dN/(N dp )]A+B R (p ) = bin T , (15) AB T p+p [dN/dpT ] 0.4 Hwa & Yang (total) where Nbin is the number of binary inelastic nucleon-nucleon 0.35 Hwa & Yang (thermal) Ko reco. (x1/3) collisions determined from Glauber model calculations 0.3 SCF (κ=3 GeV/fm) [71,101]. It is obvious that these two ratios will be unity Ω/φ (0-12%) 0.25 if nucleus-nucleus collisions are just simple superpositions Ω/φ (20-40%) of nucleon-nucleon collisions. Deviation of these ratios from

φ Ω/φ (40-60%) / 0.2 unity would imply contributions from nuclear or QGP effects. Ω 0.15 It should be mentioned that when using p + p collisions in 0.1 the RAB ratio, inelastic collisions should be used instead of the measured NSD collisions, therefore a correction factor 30/42, 0.05 which was discussed in the above subsection B, was applied to 0 0123456 correct the NSD yield to the inelastic yield in p + p collisions. p (GeV/c) There is a pT -dependent correction to the NSD distribution T from singly diffractive (SD) events, which is small in our measured p range, being 1.05 at p = 0.4GeV/c and unity above FIG.√ 16. (Color online) The /φ ratio vs pT for three centrality T T bins in sNN = 200 GeV Au + Au collisions, where the data points 1.2 GeV/c as determined from PYTHIA simulations [71]. for 40–60% are shifted slightly for clarity. As shown in the legend, Figure 17 presents the pT dependence of Rcp for the φ the lines represent results from Hwa and Yang [96], Ko et al. [97], with respect to midperipheral (top panel) and most-peripheral and, for SCF, Refs. [98,99]. (bottom panel) bins in Au + Au collisions at 200 GeV. Results

064903-15 B. I. ABELEV et al. PHYSICAL REVIEW C 79, 064903 (2009)

0 Λ Λ φ KS + 1 1 cp cp R R Au+Au 200 GeV Scaling Scaling binary participant 0-5% binary Au+Au 200 GeV Au+Au 62.4 GeV d+Au 200 GeV 40-60% participant 0-5% 0-20% 0-20% -1 60-80% 60-80% 40-100% 10 10-1 Au+Au 200 GeV 012345 p (GeV/c) 1 T

FIG. 18. (Color online) pT dependence of the nuclear modiﬁca- tion factor Rcp in Au + Au 62.4 and 200 GeV and d + Au 200 GeV cp

R collisions, where rectangular bands represent the uncertainties of binary and participant scalings (see legend). Statistical and systematic errors are included. 0-5% : 0 Λ Λ φ 60-80% KS + 0-12% + - -1 : π +π p+p 10 60-80% Our measured Rcp for the φ meson further supports the 012345 proposed partonic coalescence/recombination scenario at in- p (GeV/c) termediate pT [42,43,47,48], where the centrality dependence T of particle yield depends on the number of constituent quarks

FIG. 17. (Color online) pT dependence of the nuclear modi- (NCQ) rather than on the mass of the particle. Das and Hwa fication factor Rcp in Au + Au 200 GeV collisions. The top and [47] proposed a recombination scenario to explain the leading + bottom panels present Rcp from midperipheral and most-peripheral particle effect in p p collisions, where the fragmenting collisions, respectively. See legend for symbol and line designations. partons would recombine with sea quarks to form hadrons. The The rectangular bands show the uncertainties of binary and participant resulting pT distribution for the leading particle is therefore scalings. Statistical and systematic errors are included. determined by the fragmenting quarks. In heavy-ion collisions, it is possible that qq¯ (qqq) come together and form a meson (baryon) due to the high density of quarks (antiquarks) in + ¯ 0 + + − + for the ,theKS [45], the π π , and the p p¯ [102] the collision system. The abundant nearby partons give the particles are also shown in the figure for comparison. Both recombination/coalescence mechanism a comparative advan- statistical and systematic errors are included. Most of the tage over the fragmentation mechanism for particle production systematic errors cancel in the ratios; however, the uncertainty in the intermediate pT region, and this successfully explains due to particle identification from dE/dx remainsasthe the relative enhancement of baryons in the intermediate pT 0 dominant source and varies from point to point over the range region, such as the ratios p/π and /KS [102–104]. Recently, ∼7%–12%. In the measured pT region, the Rcp of φ meson Hwa and Yang used their recombination model to successfully is consistent with Npart scaling at lowest pT (dot-dashed line), describe the φ meson pT spectra, but it fails to reproduce and is significantly suppressed relative to the binary collision the pT dependence of /φ at higher pT as shown in the scale (dashed horizontal line at unity) at all pT in Au + Au previous subsection. They assumed that for the production of collisions at 200 GeV. When compared to the STAR measured φ this thermal component dominates over others involving jet + ¯ 0 0 and KS data [45], the Rcp for φ follows that of KS shower contributions because of the suppression of shower rather than that of the similarly massive (¯ ), especially s quarks in central Au + Au collisions [96]. However, the for the case of 0–5%/40–60%. For 0–5%/60–80%, the Rcp partonic medium, with an intrinsic temperature, may modify 0 of φ sits between that for the KS and the . This may be the recombination probability and momentum distribution for attributed to the shape change of the φ spectra from exponential the φ [42,43,48]. at 40–60% centrality to Levy at 60–80% centrality as discussed Figure 19 presents the pT dependence of the nuclear above, which may be due to the change of the φ production modification factor RAB in Au + Au and d + Au collisions + − mechanism at intermediate pT in different environments with at 200 GeV. For comparison, data points for RdAu of π + π different degrees of strangeness equilibration. and p + p¯ are also shown in the figure. The RdAu of φ mesons + − Figure 18 presents the pT dependence of Rcp for the φ reveals a similar enhancement trend as those of π + π meson for Au + Au 62.4 and 200 GeV and d + Au 200 GeV and p + p¯ at the intermediate pT , which was attributed to collisions. For the three collision systems, the Rcp factor fol- be the Cronin effect [105–107]. The Cronin enhancement lows Npart scaling at low pT . However, the Rcp at intermediate may result either from momentum broadening due to multiple pT is strongly suppressed in Au + Au collisions at 200 GeV, soft [108] (or semihard [109–112]) scattering in the initial state is weakly suppressed in Au + Au collisions at 62.4 GeV, and or from final state interactions suggested in the recombination shows no suppression in d + Au collisions at 200 GeV. model [113]. These mechanisms lead to different particle type

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0.25 Au+Au 200 GeV Λ φ 0 0.2 Ks 1 AMPT (10mb) 0.15 φ 2 v

AB 0.1 R 0.05 φ NQ = 3 Au+Au 200 GeV (0-5%): 0 NQ = 2 d+Au 200 GeV (0-20%): φ π+ π- p+p 10-1 + 012345 012345 p (GeV/c) p (GeV/c) T T

FIG. 19. (Color online) pT dependence of the nuclear mod- FIG. 20. (Color online) pT dependence of the elliptic flow v2 0 + ification factor RAB for φ in Au + Au 200 GeV and d + Au of φ,, and KS in Au Au collisions (0–80%) at 200 GeV. Data 200 GeV collisions. For comparison, data points for π + + π − in points for φ are from the reaction plane method (full up-triangles) d + Au 200 GeV and p + p¯ in d + Au 200 GeV are also shown (see and invariant mass method (full circles), where data points from legend). Rectangular bands show the uncertainties of binary (solid the reaction plane method are shifted slightly along the x axis for line) and participant (dot-dash line) scalings. Systematic errors are clarity. Vertical error bars represent statistical errors, while the square included for φ,π+ + π −,andp + p¯. bands represent systematic uncertainties. The magenta curved band represents the v2 of the φ meson from the AMPT model with a string melting mechanism [116]. The dash and dot curves represent and/or mass dependence in the nuclear modification factors parametrizations inspired by number-of-quark scaling ideas from as a function of pT . Our measurement of RdAu of φ mesons Ref. [117]forNQ= 2andNQ= 3, respectively. does not have the precision to differentiate particle dependence scenarios [114,115]. On the other hand, the R in Au + Au AA ∼ 200 GeV is lower than that in d + Au 200 GeV and consistent In the intermediate pT region ( 2–5 GeV/c), the v2 of the φ meson is consistent with that for the K0 rather than with the binary collision scaling at intermediate pT . These S features are consistent with the scenario that features the for the . When we fit the v2(pT )ofφ mesons with the quark onset of parton-medium final state interactions in Au + Au number scaling function [117], the resulting fit parameter NCQ (number of constitute quarks) = 2.3 ± 0.4. The fact that the collisions. The two RAB observations in central d + Au and Au + Au collisions are consistent with the shape comparisons v2(pT )ofφ is the same as that of other mesons indicates that the in Fig. 11 (top panel). heavier s quarks flow as strongly as the lighter u and d quarks. The AMPT model with string melting and parton coalescence mechanisms can reproduce the experimental results well up E. Elliptic flow to 3 GeV/c, which favors the hadronization scenario of Figure 20 shows the elliptic flow v2 of the φ meson as coalescence/recombination of quarks [116,118]. + v φ √afunctionofpT in MB (0–80%) Au Au collisions at The 2 of the meson from other centralities are shown = 0 in Fig. 21. The data are analyzed from the invariant mass sNN 200 GeV. The v2 of the KS and measured by STAR [45]inAu+ Au 200 GeV collisions are also shown for comparison. Measurements of v2 for the φ meson from both Au+Au 200 GeV reaction plane and invariant mass methods are presented, and 0.3 they are consistent with each other. 40-80% 10-40% The first interesting observation is that the φ meson has 0.2 0-5% significantly nonzero v2 in the measured pT region. If the φ meson has a small interaction cross section with the evolving

2 0.1 hot-dense matter in A + A collisions, it would not participate v in the late-stage hadronic interactions in contrast to hadrons 0 such as π, K, and p(p¯) which freeze-out later. This indicates that the nonzero v of the φ meson must have been developed 2 -0.1 in the earlier partonic stage. In the low pT region (<2GeV/c), 0 the v2 value of φ is between that for the KS and the in 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Au + Au 200 GeV collisions, consistent with the expectation p (GeV/c) T of a mass ordering for v2 in hydrodynamic models. These observations support the hypothesis of the development of FIG. 21. (Color online) Elliptic ﬂow v2 as a function of partonic collectivity and possible thermalization in the early pT ,v2(pT ), for the φ meson from different centralities. The vertical stages of heavy-ion collisions at RHIC [34,100], although the error bars represent the statistical errors, while the square bands underlying mechanism for the equilibration process remains represent the systematic uncertainties. For clarity, data points of an open issue. 10–40% are shifted in the pT direction slightly.

064903-17 B. I. ABELEV et al. PHYSICAL REVIEW C 79, 064903 (2009)

− TABLE IV. Integrated elliptic flow v2 for the φ The φ/K yield ratios from p + p and A + B collisions meson for four centrality bins in Au + Au collisions over a broad range of collision energies above the φ threshold at 200 GeV. are remarkably close to each other, indicating similar underlying hadronization processes for soft strange quark pairs in Centrality (%) v2 (%) these collisions. The lack of a significant centrality dependence − 40–80 8.5 ± 1.1(stat) ± 0.2(sys) of the φ/K yield ratio and pT φ effectively rules out kaon 10–40 6.6 ± 0.8(stat) ± 0.2(sys) coalescence as a dominant production channel at RHIC. The 0–5 2.1 ± 1.2(stat) ± 0.5(sys) trend of the /φ ratio is consistent with recombination models ∼ 0–80 5.8 ± 0.6(stat) ± 0.2(sys) and a strong color field scenario up to pT 4GeV/c in central Au + Au collisions. The measurement of the φ meson nuclear modification method only. As expected, v2(pT ) increases with increasing factor RAB is consistent with the Cronin effect in d + Au eccentricity (decreasing centrality) of the initial overlap region. 200 GeV collisions, and with the energy loss mechanism in This trend is also illustrated in Table IV, which presents the Au + Au 200 GeV collisions. The φ meson was found to have pT -integrated values of φ-meson elliptic flow, v2 , calculated nonzero v2 in the measured pT range. When comparing the by convoluting the v2(pT ) with the respective pT spectrum φ meson nuclear modification factor Rcp (0–5%/40–60%) and for four centrality bins. It should be noted that the centrality elliptic flow v2 to those of the similar mass baryon, and to dependence of the v of the φ meson is consistent with that 0 2 the lighter KS meson, we see that the φ meson clearly behaves of the charged hadrons [67]. 0 more like the KS meson than the baryon. Therefore, the processes relevant to Rcp and v2 at intermediate pT are driven not by the mass of the particle, but rather by the type of the IV. CONCLUSION particle, i.e., number of constituent quarks (NCQ) scaling. The In conclusion, STAR has measured φ meson production for coalescence/recombination model provides a fairly consistent 62.4, 130, 200 GeV Au + Au, 200 GeV d + Au, and NSD picture to describe particle production in the intermediate pT p + p collisions at RHIC. Details of the analysis method region over a broad range of collision energies and system sizes at RHIC. for φ meson are presented. The respective energy and Npart dependence of the φ meson production, as well as the pT spectra for five collision systems, are reported. The φ spectra in central Au + Au 200 GeV collisions are ACKNOWLEDGMENTS described well by an exponential function. The spectra for p + p, d + Au, and the most peripheral Au + Au 200 GeV We thank the RHIC Operations Group and RCF at BNL, the collisions are better described by a Levy function due to the NERSC Center at LBNL, and the resources provided by the high-pT power-law tails. This change of spectra shape from Open Science Grid consortium for their support. This work was p + p, d + Au, and peripheral Au + Au to central Au + Au supported in part by the Offices of NP and HEP within the US collisions is most likely due to a change of the dominant φ DOE Office of Science, the US NSF, the Sloan Foundation, the production mechanism in the different collision environments. DFG Excellence Cluster EXC153 of Germany, CNRS/IN2P3, The yield of φ mesons per participant pair increases and RA, RPL, and EMN of France, STFC and EPSRC of the United saturates with the increase of Npart. It is found that the pT of Kingdom, FAPESP of Brazil, the Russian Ministry of Sci. and φ,,, and does not follow the pT vs hadron mass trend Tech., the NNSFC, CAS, MoST, and MoE of China, IRP and determined by the π −,K−, and p¯. This may be due to their GA of the Czech Republic, FOM of the Netherlands, DAE, small hadronic cross sections, which indicates that the φ and DST, and CSIR of the Government of India, Swiss NSF, the strange hadrons can retain more information about the early Polish State Committee for Scientific Research, and the Korea state of the collision system. Sci. & Eng. Foundation.

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