Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory

Title Measurements of phi production in relativistic heavy-ion collisions at RHIC

Permalink https://escholarship.org/uc/item/7df6h06g

Authors Abelev, B.I. STAR Collaboration

Publication Date 2009-08-28

eScholarship.org Powered by the California Digital Library University of California Measurements of production in relativistic heavy-ion collisions at RHIC

B. I. Abelev,1 M. M. Aggarwal,2 Z. Ahammed,3 B. D. Anderson,4 D. Arkhipkin,5 G. S. Averichev,6 Y. Bai,7 J. Balewski,8 O. Barannikova,1 L. S. Barnby,9 J. Baudot,10 S. Baumgart,11 D. R. Beavis,12 R. Bellwied,13 F. Benedosso,7 R. R. Betts,1 S. Bhardwaj,14 A. Bhasin,15 A. K. Bhati,2 H. Bichsel,16 J. Bielcik,17 J. Bielcikova,17 B. Biritz,18 L. C. Bland,12 M. Bombara,9 B. E. Bonner,19 M. Botje,7 J. Bouchet,4 E. Braidot,7 A. V. Brandin,20 S. Bueltmann,12 T. P. Burton,9 M. Bystersky,17 X. Z. Cai,21 H. Caines,11 M. Calder´on de la Barca S´anchez,22 J. Callner,1 O. Catu,11 D. Cebra,22 R. Cendejas,18 M. C. Cervantes,23 Z. Chajecki,24 P. Chaloupka,17 S. Chattopadhyay,3 H. F. Chen,25 J. H. Chen,21 J. Y. Chen,26 J. Cheng,27 M. Cherney,28 A. Chikanian,11 K. E. Choi,29 W. Christie,12 S. U. Chung,12 R. F. Clarke,23 M. J. M. Codrington,23 J. P. Coffin,10 T. M. Cormier,13 M. R. Cosentino,30 J. G. Cramer,16 H. J. Crawford,31 D. Das,22 S. Dash,32 M. Daugherity,33 M. M. de Moura,30 T. G. Dedovich,6 M. DePhillips,12 A. A. Derevschikov,34 R. Derradi de Souza,35 L. Didenko,12 T. Dietel,36 P. Djawotho,37 S. M. Dogra,15 X. Dong,38 J. L. Drachenberg,23 J. E. Draper,22 F. Du,11 J. C. Dunlop,12 M. R. Dutta Mazumdar,3 W. R. Edwards,38 L. G. Efimov,6 E. Elhalhuli,9 M. Elnimr,13 V. Emelianov,20 J. Engelage,31 G. Eppley,19 B. Erazmus,39 M. Estienne,10 L. Eun,40 P. Fachini,12 R. Fatemi,41 J. Fedorisin,6 A. Feng,26 P. Filip,5 E. Finch,11 V. Fine,12 Y. Fisyak,12 C. A. Gagliardi,23 L. Gaillard,9 D. R. Gangadharan,18 M. S. Ganti,3 E. Garcia-Solis,1 V. Ghazikhanian,18 P. Ghosh,3 Y. N. Gorbunov,28 A. Gordon,12 O. Grebenyuk,7 D. Grosnick,42 B. Grube,29 S. M. Guertin,18 K. S. F. F. Guimaraes,30 A. Gupta,15 N. Gupta,15 K. Kajimoto,33 K. Kang,27 J. Kapitan,17 M. Kaplan,43 D. Keane,4 A. Kechechyan,6 D. Kettler,16 V. Yu. Khodyrev,34 J. Kiryluk,38 A. Kisiel,24 S. R. Klein,38 A. G. Knospe,11 A. Kocoloski,8 D. D. Koetke,42 T. Kollegger,36 M. Kopytine,4 L. Kotchenda,20 V. Kouchpil,17 P. Kravtsov,20 V. I. Kravtsov,34 K. Krueger,44 C. Kuhn,10 A. Kumar,2 L. Kumar,2 P. Kurnadi,18 M. A. C. Lamont,12 J. M. Landgraf,12 S. Lange,36 S. LaPointe,13 F. Laue,12 J. Lauret,12 A. Lebedev,12 R. Lednicky,5 C-H. Lee,29 M. J. LeVine,12 C. Li,25 Y. Li,27 G. Lin,11 X. Lin,26 S. J. Lindenbaum,45 M. A. Lisa,24 F. Liu,26 J. Liu,19 L. Liu,26 T. Ljubicic,12 W. J. Llope,19 R. S. Longacre,12 W. A. Love,12 Y. Lu,25 T. Ludlam,12 D. Lynn,12 G. L. Ma,21 J. G. Ma,18 Y. G. Ma,21 D. P. Mahapatra,32 R. Majka,11 L. K. Mangotra,15 R. Manweiler,42 S. Margetis,4 C. Markert,33 H. S. Matis,38 Yu. A. Matulenko,34 T. S. McShane,28 A. Meschanin,34 J. Millane,8 M. L. Miller,8 N. G. Minaev,34 S. Mioduszewski,23 A. Mischke,7 J. Mitchell,19 B. Mohanty,3 D. A. Morozov,34 M. G. Munhoz,30 B. K. Nandi,46 C. Nattrass,11 T. K. Nayak,3 J. M. Nelson,9 C. Nepali,4 P. K. Netrakanti,47 M. J. Ng,31 L. V. Nogach,34 S. B. Nurushev,34 G. Odyniec,38 A. Ogawa,12 H. Okada,12 V. Okorokov,20 D. Olson,38 M. Pachr,17 S. K. Pal,3 Y. Panebratsev,6 T. Pawlak,48 T. Peitzmann,7 V. Perevoztchikov,12 C. Perkins,31 W. Peryt,48 S. C. Phatak,32 M. Planinic,49 J. Pluta,48 N. Poljak,49 N. Porile,47 A. M. Poskanzer,38 M. Potekhin,12 B. V. K. S. Potukuchi,15 D. Prindle,16 C. Pruneau,13 N. K. Pruthi,2 J. Putschke,11 I. A. Qattan,37 R. Raniwala,14 S. Raniwala,14 R. L. Ray,33 A. Ridiger,20 H. G. Ritter,38 J. B. Roberts,19 O. V. Rogachevskiy,6 J. L. Romero,22 A. Rose,38 C. Roy,39 L. Ruan,12 M. J. Russcher,7 V. Rykov,4 R. Sahoo,39 I. Sakrejda,38 T. Sakuma,8 S. Salur,38 J. Sandweiss,11 M. Sarsour,23 J. Schambach,33 R. P. Scharenberg,47 N. Schmitz,50 J. Seger,28 I. Selyuzhenkov,37 P. Seyboth,50 A. Shabetai,10 E. Shahaliev,6 M. Shao,25 M. Sharma,13 S. S. Shi,26 X-H. Shi,21 E. P. Sichtermann,38 F. Simon,50 R. N. Singaraju,3 M. J. Skoby,47 N. Smirnov,11 R. Snellings,7 P. Sorensen,12 J. Sowinski,37 H. M. Spinka,44 B. Srivastava,47 A. Stadnik,6 T. D. S. Stanislaus,42 D. Staszak,18 R. Stock,36 M. Strikhanov,20 B. Stringfellow,47 A. A. P. Suaide,30 M. C. Suarez,1 N. L. Subba,4 M. Sumbera,17 X. M. Sun,38 Y. Sun,25 Z. Sun,51 B. Surrow,8 T. J. M. Symons,38 A. Szanto de Toledo,30 J. Takahashi,35 A. H. Tang,12 Z. Tang,25 T. Tarnowsky,47 D. Thein,33 J. H. Thomas,38 J. Tian,21 A. R. Timmins,9 S. Timoshenko,20 M. Tokarev,6 V. N. Tram,38 A. L. Trattner,31 S. Trentalange,18 R. E. Tribble,23 O. D. Tsai,18 J. Ulery,47 T. Ullrich,12 D. G. Underwood,44 G. Van Buren,12 N. van der Kolk,7 M. van Leeuwen,7 A. M. Vander Molen,52 R. Varma,46 G. M. S. Vasconcelos,35 I. M. Vasilevski,5 A. N. Vasiliev,34 F. Videbaek,12 S. E. Vigdor,37 Y. P. Viyogi,32 S. Vokal,6 S. A. Voloshin,13 M. Wada,33 W. T. Waggoner,28 F. Wang,47 G. Wang,18 J. S. Wang,51 Q. Wang,47 X. Wang,27 X. L. Wang,25 Y. Wang,27 J. C. Webb,42 G. D. Westfall,52 C. Whitten Jr.,18 H. Wieman,38 S. W. Wissink,37 R. Witt,11 J. Wu,25 Y. Wu,26 N. Xu,38 Q. H. Xu,38 Y. Xu,25 Z. Xu,12 P. Yepes,19 I-K. Yoo,29 Q. Yue,27 M. Zawisza,48 H. Zbroszczyk,48 W. Zhan,51 H. Zhang,12 S. Zhang,21 W. M. Zhang,4 Y. Zhang,25 Z. P. Zhang,25 Y. Zhao,25 C. Zhong,21 J. Zhou,19 R. Zoulkarne ev,5 Y. Zoulkarneeva,5 and J. X. Zuo21 (STAR Collaboration) June 16, 2009

This work was supported by the Director, Office of Science, Office of Nuclear Science of the U.S. Department of Energy under Contract No. DE-AC02- 05CH11231. arXiv:0809.4737v2 [nucl-ex] 16 Jun 2009 .H Tang, H. A. .Poljak, N. .Liu, F. .Didenko, L. .Wieman, H. .Manweiler, R. .D Tsai, D. O. .Benedosso, F. .E Vigdor, E. S. .Kuhn, C. .Schmitz, N. .S Wang, S. J. .I Abelev, I. B. .Lednicky, R. .Cherney, M. .Staszak, D. .V Rogachevskiy, V. O. .S Ganti, S. M. .Igo, G. .Hirsch, A. .Haag, B. .Kabana, S. .Daugherity, M. .Okorokov, V. .Lynn, D. .Snellings, R. .Biritz, B. .A Morozov, A. D. .Y.Khodyrev, Yu. V. .A afse,Jr., Vanfossen, A. J. .Feng, A. esrmnsof Measurements .Millane, J. .Engelage, J. .Sakrejda, I. .Grosnick, D. .Yue, Q. .Chajecki, Z. .R ut Mazumdar, Dutta R. M. .S Shi, S. S. .Balewski, J. .P Coffin, P. J. Tlusty, .Kopytine, M. .M Sun, M. X. .Peitzmann, T. Netrakanti, K. P. .Cle´nd aBraS´anchez, Barca la Calder´on de M. .P Zhang, P. Z. .V Brandin, V. A. 50 .Raniwala, R. 6 .Liu, H. 17 52 .Iordanova, A. 5 3 6 33 3 50 3 43 11 22 24 .J Hallman, J. T. 6 21 .Kumar, L. 6 .M Poskanzer, M. A. 40 .L Ma, L. G. .Ulery, J. .Djawotho, P. 16 .Tang, Z. 10 13 9 46 50 45 28 .C Bland, C. L. 23 .M Hoffman, M. A. .Strikhanov, M. .Filip, P. .Zawisza, M. .Tokarev, M. 28 .W Wissink, W. S. .Seger, J. .Wang, Q. 26 .M Aggarwal, M. M. .Kajimoto, K. 22 .P Viyogi, P. Y. 22 4 5 .Chikanian, A. 29 -.Lee, C-H. .Garcia-Solis, E. -.Shi, X-H. 23 .Margetis, S. .R Betts, R. R. 45 17 .L Miller, L. M. 42 .Sorensen, P. .Eppley, G. .Liu, J. .Olson, D. 38 19 .Sakuma, T. 32 .Sun, Y. .Chaloupka, P. .Barannikova, O. .Grube, B. .M Cormier, M. T. 28 .D Silva, De C. 35 .Zhao, Y. 32 .Kotchenda, L. 26 .G Munhoz, G. M. 12 33 38 .Perevoztchikov, V. 13 33 30 39 .Raniwala, S. 10 19 .Kiryluk, J. 9 .Bruna, E. .L Romero, L. J. 36 33 .Ullrich, T. .Tarnowsky, T. .Finch, E. .J Ng, J. M. .Kurnadi, P. .Jacobs, P. .G Ma, G. J. 39 34 .Selyuzhenkov, I. .Varma, R. 16 38 47 3 12 .Liu, L. 3 .Wang, X. φ 22 -.Blyth, S-L. .J LeVine, J. M. 36 .P Sichtermann, P. E. 19 .Hamed, A. 9 42 .M Dogra, M. S. 14 .Sun, Z. 46 .Zbroszczyk, H. 26 34 .A Trainor, A. T. 3 38 16 22 23 eo rdcini eaiitchayincliin tRHIC at collisions heavy-ion relativistic in production meson 23 23 51 .Pachr, M. .Bhardwaj, S. .Markert, C. .Erazmus, B. .Sowinski, J. .Kang, K. .Vokal, S. 49 .R Edwards, R. W. .Stringfellow, B. 9 .M Guertin, M. S. .Witt, R. .V .S Potukuchi, S. K. V. B. .Zhong, C. .G Minaev, G. N. 30 .Salur, S. .W Hoffmann, W. G. .E Choi, E. K. 11 50 51 .Ghazikhanian, V. 51 22 .G Dedovich, G. T. 49 3 4 .Ahammed, Z. 6 26 22 9 .Chattopadhyay, S. 35 .Ljubicic, T. .Bueltmann, S. 21 15 37 43 .G Underwood, G. D. .V Nogach, V. L. .G Ma, G. Y. 6 .Fine, V. .Kisiel, A. .S Barnby, S. L. .R Cosentino, R. M. .Kouchpil, V. 5 .W Jacobs, W. W. .L Ray, L. R. .A .Lamont, C. A. M. 33 .Surrow, B. .M .Vasconcelos, S. M. G. .L Wang, L. X. .K Nandi, K. B. 22 41 5 .Rose, A. 11 12 43 44 3 22 .Callner, J. .Thein, D. 18 .Bombara, M. .W Harris, W. J. 16 39 3 .S Page, S. B. .Perkins, C. 42 .A Voloshin, A. S. 16 .Kapitan, J. .Wu, Y. 35 40 48 .Sandweiss, J. 47 34 .Li, C. .Dong, X. .Seyboth, P. .Zhou, J. 3 .S Matis, S. H. .M Spinka, M. H. .Bhasin, A. .Estienne, M. .N Tram, N. V. 29 SA Collaboration) (STAR 6 .Zhan, W. 32 .Christie, W. .Fisyak, Y. 39 33 22 3 22 22 .S .F Guimaraes, F. F. S. K. 46 .R Klein, R. S. 42 .J Llope, J. W. .Mioduszewski, S. .P Mahapatra, P. D. 38 23 42 .A .Suaide, P. A. A. .Simon, F. 12 50 11 3 .G Efimov, G. L. 32 2 .Roy, C. 42 6 .D Anderson, D. B. 38 9 .Reed, R. 15 .P Burton, P. T. .Li, Y. .J .Symons, M. J. T. .Baudot, J. .J Hofman, J. D. 16 .Ghosh, P. .DePhillips, M. .Xu, N. .Kravtsov, P. 36 22 .B Nurushev, B. S. .Catu, O. .H Thomas, H. J. 16 4 .Wang, Y. 46 11 37 .Nattrass, C. 18 1 2 51 .Jakl, P. .Peryt, W. .L Drachenberg, L. J. .Zoulkarneev, R. 21 24 .K Pal, K. S. .VnBuren, Van G. 18 3 .F Chen, F. H. .E Bonner, E. B. 51 .Kaplan, M. .G Cramer, G. J. 3 .Prindle, D. 22 49 .He, W. 43 .M Landgraf, M. J. 22 40 .Zhang, H. 17 3 .A Gagliardi, A. C. .Shabetai, A. .K Bhati, K. A. 1 .Sarsour, M. 24 22 u .Matulenko, A. Yu. .Wada, M. 5 .U Chung, U. S. 22 7 .Lin, G. .Ruan, L. .L Trattner, L. A. .Srivastava, B. 36 .Eun, L. 51 .Ridiger, A. .H Xu, H. Q. .N Singaraju, N. R. .M Vasilevski, M. I. 46 11 17 .G Knospe, G. A. 43 .S Longacre, S. R. 12 16 .Cebra, D. .N Gorbunov, N. Y. 47 26 .Jin, F. .Baumgart, S. 2 37 .C Webb, C. J. 46 41 9 51 .Elhalhuli, E. 14 3 19 .Heinz, M. .Bystersky, M. 22 51 .C Phatak, C. S. .I Kravtsov, I. V. 48 .S Hollis, S. R. 8 3 38 .C Suarez, C. M. .Pandit, Y. 31 .Mischke, A. .A Derevschikov, A. A. 32 .K Nayak, K. T. .Majka, R. 3 22 .Arkhipkin, D. .Keane, D. 42 .Zhang, S. .Tian, J. .Lin, X. 36 .Pruneau, C. 3 48 41 17 37 .H Chen, H. J. 30 13 .J Russcher, J. M. .Fachini, P. .Odyniec, G. 39 22 .Sat eToledo, de Szanto A. .vnLeeuwen, van M. .T Waggoner, T. W. .Botje, M. 26 3 .J Crawford, J. H. .Schambach, J. 3 .Shahaliev, E. .Gupta, A. .Bichsel, H. .Zoulkarneeva, Y. 41 5 .G Jones, G. P. .Xu, Y. 41 33 .F Clarke, F. R. .LaPointe, S. .G Ritter, G. H. 4 .Cendejas, R. .E Draper, E. J. 51 .Gaillard, L. 50 .Stadnik, A. 51 45 .Trentalange, S. 39 32 13 46 51 3 19 2 51 39 .Heppelmann, S. 19 .J Lindenbaum, J. S. 9 .Kocoloski, A. .D Westfall, D. G. 28 .A Love, A. W. .R Timmins, R. A. .S McShane, S. T. .Elnimr, M. .N Vasiliev, N. A. .J Skoby, J. M. 38 .R Beavis, R. D. 11 14 10 .Panebratsev, Y. .Z Huang, Z. H. 3 9 .I Mall, I. M. .M Zhang, M. W. 46 28 .Kechechyan, A. 39 49 32 .Mitchell, J. 13 22 18 .Fatemi, R. .L Subba, L. N. .Xu, Z. .Z Cai, Z. X. .Planinic, M. .Gordon, A. 48 .M Nelson, M. J. .Bouchet, J. .K Pruthi, K. N. .Y Chen, Y. J. .Krueger, K. .S Averichev, S. G. .Ogawa, A. .Gupta, N. 2 12 28 .Bielcik, J. 49 42 41 .Joseph, J. 32 12 22 2 6 4 28 .Shao, M. .Rykov, V. 10 5 .Lauret, J. 3 .P Scharenberg, P. R. .J .Codrington, M. J. M. .R Gangadharan, R. D. .C Cervantes, C. M. .Das, D. 13 .Draid Souza, de Derradi R. .D .Stanislaus, S. D. T. .Du, F. .B Roberts, B. J. 49 .M adrMolen, Vander M. A. .Yepes, P. .Wang, F. 3 6 5 37 n .X Zuo X. J. and 23 33 39 .Lu, Y. 20 36 .E Tribble, E. R. .Emelianov, V. 3 .K Mangotra, K. L. 6 25 31 3 32 .Takahashi, J. .D Koetke, D. D. 10 2 19 52 .Bellwied, R. 19 19 18 .J Humanic, J. T. .Smirnov, N. 50 3 .Caines, H. .Fedorisin, J. .Mohanty, B. 11 .Grebenyuk, O. 1 12 12 .WitnJr., Whitten C. 51 .Timoshenko, S. .Hippolyte, B. .Videbaek, F. 27 38 2 19 5 30 .Okada, H. .Meschanin, A. .Zhang, Y. .Pluta, J. .Braidot, E. .Sumbera, M. .Guryn, W. .Krus, M. .Cheng, J. 19 .Bielcikova, J. 3 .Nepali, C. .Dash, S. .Pawlak, T. 38 .Kettler, D. .C Dunlop, C. J. .A Lisa, A. M. .Sharma, M. .G Judd, G. E. .Putschke, J. 36 33 .Lebedev, A. .Sahoo, R. 12 .Ludlam, T. -.Yoo, I-K. .Wang, G. .Bai, Y. 36 51 39 41 47 11 41 14 49 51 3 26 43 38 7 33 12 46 3 45 19 28 3 45 6 18 47 48 17 29 22 40 11 41 29 7 28 49 4 11 25 34 32 26 51 6 3 6 3 3 2

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,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, 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 48University of Washington, Seattle, Washington 98195, USA 49Wayne State University, Detroit, Michigan 48201, USA 50Institute of Physics, CCNU (HZNU), Wuhan 430079, China 51Yale University, New Haven, Connecticut 06520, USA 52University of Zagreb, Zagreb, HR-10002, Croatia We present results for the measurement of φ meson production via its charged decay channel + − φ K K in Au+Au collisions at √s = 62.4, 130, and 200 GeV, and in p + p and d+Au → NN 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 Ω/φ yield ratio as a function of pT is consistent with a model based on the recombination of thermal s up to pT 4 GeV/c, but disagrees at higher transverse momenta. The measured nuclear ∼ 3

modification factor, RdAu, for the φ meson increases above unity at intermediate pT , similar to that for and , while RAA is suppressed due to the energy loss effect in central Au+Au collisions. Number of constituent scaling of both Rcp and v2 for the φ meson with respect

to other in Au+Au collisions 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.

PACS numbers: 25.75.Dw

I. INTRODUCTION (e+ + e−) from the KEK experiment [22, 23]. In STAR, we measure the φ meson mass and width to compare with The φ(1020) ’s properties and its trans- these predictions/measurements, using the decay channel port in the nuclear medium have been of interest since φ K+K−. its discovery [1]. The proper lifetime of the φ meson is → From phenomenological analysis, it is suggested that about 45 fm/c and it decays into charged K+K− the φ meson mean free path in hadronic media is large with a branching ratio of 49.2%, and more rarely into the because of its small cross section of scattering with dilepton pairs e+e− (B. R. of 2.97 10−4) and µ+µ− (B. hadrons [5]. Many other calculations also indicate that R. of 2.86 10−4). × the φ meson has small rescattering cross sections with The mechanism× for φ meson production in high en- hadronic [19, 20]. However, after including three- ergy collisions has remained an open issue. As the and four-vector meson vertices into their hidden local lightest of strange quarks (ss¯) with hidden symmetry model, Alvarez-Ruso and Koch [24] found that , φ meson production is suppressed in elemen- the φ meson mean free path in nuclear media is smaller tary collisions because of the Okubo-Zweig-Iizuka (OZI) than that usually estimated. Ishikawa et al. [25] pre- rule [2, 3, 4]. The OZI rule states that processes with dis- sented new data on near-threshold φ photoproduction on connected quark lines in the initial and final state are sup- several nuclear targets. They found that the cross sec- pressed. In an environment with many strange quarks, φ tion between φ meson and a , σ , is equal to can be produced readily through coalescence, by- φN 35+17 mb, which appears to be much larger than previ- passing the OZI rule [5]. The φ meson has been predicted −11 ous expectations although the experimental uncertainty to be a probe of the quark- plasma (QGP) formed is very large [26]. Meanwhile, Sibirtsev et al. [27] pre- in ultrarelativistic heavy-ion collisions [6, 7, 8, 9, 10, 11]. sented a new analysis of existing φ photoproduction data On the other hand, a naive interpretation of φ meson and found σ 10 mb. Thus, σ in heavy-ion colli- enhancement in heavy-ion collisions would be that the φ φN φN sions is still unclear.∼ meson is produced via KK¯ φ in the hadronic rescat- tering stage. Models that include→ hadronic rescatterings The measurement of collective radial flow (represented by p ) probes the equation of state of matter produced such as RQMD [12] and UrQMD [13] have predicted an h T i increase of the φ to K− production ratio at midrapid- in nuclear collisions [28, 29]. Strong radial flow has been ity as a function of the number of participant nucle- observed for many such as π, K, and p(¯p) [30]. ons. This prediction was disproved in Au+Au collisions If the φ meson has indeed small hadronic rescattering cross sections and decouples early from the collision sys- at √sNN = 200 GeV, from STAR year 2001 data [14]. With the higher statistics data newly recorded from the tem, contributions to the radial flow of the φ meson will Solenoidal Tracker at RHIC (STAR) experiment [15], a be mostly from the partonic stage instead of the hadronic precise measurement of the φ/K− ratio as a function of stage. Thus the φ meson may have a significantly smaller beam energy and collision centrality is presented to con- radial flow than other hadrons with similar mass, such firm this finding in this paper. as the , especially in central heavy-ion collisions. The in-medium properties of vector mesons in the hot Therefore, φ mesons may carry information about the and dense environment are also interesting [11]. The conditions of nuclear collisions before chemical freeze-out. mass and width of the φ meson were predicted to change Thus it is important to experimentally measure and com- because of the partial restoration of chiral symmetry in pare the freeze-out properties of the φ to other hadrons the nuclear medium. Asakawa and Ko [16] and Song [17] as a function of centrality and collision species. A com- predicted that the φ mass decreases as a result of many- prehensive set of measurements will shed light on the body effects in a hadronic medium. A double φ peak characteristics of φ meson production and the evolution structure in the dilepton spectrum from of the collision system. relativistic heavy-ion collisions was proposed as a sig- The elliptic flow parameter v2 is a good tool for study- nature of a phase transition from the QGP to hadronic ing the system formed in the early stages of high energy matter [18]. Other calculations have predicted that the φ collisions at RHIC. It has been found that at low pT meson width can be widened significantly due to nuclear (0 < pT < 2 GeV/c), the dependence of v2 on particle medium effects [19, 20, 21]. Recently, an interesting φ mass [31, 32, 33] is consistent with hydrodynamic cal- mass modification at normal nuclear density in 12 GeV culations in which local thermal equilibrium of partons p + A interactions was observed in the dilepton channel is assumed [34, 35, 36, 37, 38]. This observation indi- 4 cates that thermally equilibrated partonic matter may direction. Radial-drift TPCs (FTPCs) [53] are also in- have been created at RHIC. However, at intermediate stalled to extend particle tracking into the forward and pT (2 < pT < 5 GeV/c), the measured v2 for various backward regions (2.5 < η < 4.0). Surrounding the hadrons seems to depend on the number of constituent TPC is the central trigger| barrel| (CTB) [54], which is a quarks in the rather than its mass, consistent scintillator counter array whose analog signal is sensitive with the results from coalescence/recombination mod- to the total charged particle multiplicity with coverage els [39, 40, 41, 42, 43, 44]. Since φ is a meson but has a η 1.0. A pair of beam-beam counters (BBCs) at mass close to that of the proton and Λ, the measurement 3| .3| ≤< η < 5.0 and a pair of zero degree calorimeters of the φ meson elliptic flow will provide a unique tool for (ZDCs) [55] at θ < 2 mrad are located on either side testing the above statement. of the collision region along the beam line, and are used Current measurements of various hadrons by STAR to provide event triggers for data taking. A more de- 0 ∗ ± (Λ, p, KS, K(892) , h , etc.) show that the nuclear tailed description of the STAR detector can be found in modification factor Rcp for differs from that of Ref. [15] and references therein. mesons [45, 46], consistent with the prediction of quark coalescence/recombination models [42, 43, 47, 48]. Be- B. Event selection cause of the value of the φ meson mass, a comparison of 1. T rigger selection Rcp for the φ with these previous measurements will con- clusively determine if the observed difference is driven by The Au+Au data used in this analysis were taken with particle mass or particle type. two different trigger conditions. One was a minimum-bias In previous studies, the production of the φ meson (MB) trigger requiring only a coincidence between both has been measured in Au+Au collisions at √sNN = ZDCs. The other was a central trigger additionally re- 130 GeV [49] and in Au+Au and p + p collisions at quiring both a large analog signal in the CTB indicating

√sNN = 200 GeV [14] at RHIC. The Au+Au 200 GeV a high charged particle multiplicity at midrapidity and data presented in this paper were taken from the year a small ZDC signal. The ZDCs measure beam-velocity 2004 run, where the number of events is approximately from the fragmentation of colliding nuclei and ten times larger than the previously reported number for were used as the experimental level-0 trigger for select- the Au+Au run in year 2001 [14]. The data from the ing d+Au and Au+Au collisions for their respective runs. year 2004 run contain the data reported in ref. [50, 51]. For p + p data taking, the BBCs were used as trigger It has been found that the results from the two runs are detectors. The central trigger corresponds to approxi- consistent with each other. In this paper, we present mately the top 15% and 12% of the measured cross sec- systematic measurements of φ meson production over a tion for Au+Au collisions at 130 GeV and 200 GeV, re- broad range of collision energies and system sizes, in- spectively. Data from both the MB and central triggers cluding Au+Au collisions at √sNN = 62.4, 130 [49], were used for this analysis. For the Au+Au 62.4 GeV and 200 GeV, and p + p [14] and d+Au collisions at data set, only MB triggered events were used. For p + p

√sNN = 200 GeV from the STAR experiment. In Sec. collisions at 200 GeV, the MB trigger was used in the II, we briefly introduce the STAR detector and discuss analysis. It was based on a coincidence between the two our analysis method (event-mixing technique) in detail. BBCs. The BBCs are sensitive only to the non-single In Sec. III, we present the measurement of φ meson in- diffractive (NSD) part (30 mb) of the p+p total inelastic variant mass distributions (III A), transverse mass mT ) cross section (42 mb) [14]. spectra (III B, particle ratios (III C), nuclear modifica- 2. tion factors (III D) and the elliptic flow parameter v2 V ertex cuts and centrality selection (III E); we also discuss the physics implication of each of The longitudinal z position of the interaction point is these results. A summary and conclusions are presented in Sec. IV. determined on-line by the measured time difference of the two ZDCs’s signals. A cut on the z position of the in- II. DATA ANALYSIS teraction point is applied on-line for all data sets (except p + p) in order to maximize the amount of useful data for A. Experimental Setup physics analysis, since events with primary vertices far away from the center of the TPC have a significant non- The STAR detector [15] consists of several subsystems uniform acceptance. In the off-line data analysis further in a large solenoidal analyzing magnet. We discuss here cuts are applied on the z position of the reconstructed the subdetectors used in the analyses relevant to this pa- primary vertex (VZ ), to ensure nearly uniform detector per. With its axis aligned along the beam direction, the acceptance. These cuts are listed in Table I. time projection chamber (TPC) [52] is the main tracking To define the collision centrality for the Au+Au data, device for charged particles, covering a pseudorapidity the raw charged hadron multiplicity distribution in the range η 1.8 and providing complete azimuthal cover- TPC within a pseudo-rapidity window η 0.5 ( η age. The| | ≤ entire TPC is located inside a solenoidal mag- 0.75 was used for the Au+Au 130 GeV| | data) ≤ was| | di- ≤ net, and data are taken at the maximum magnetic field vided into several bins. Each bin corresponds to a cer- B = 0.5 Tesla, where the z axis is parallel to the beam tain fraction of the total inelastic cross section [56]. For | z| 5

System √s Trigger VZ Centrality Events Year -6 NN | | ×10 (GeV) (cm) 10 6 Au+Au 62.4 MB 0 3 0-80% 60.2 1 2004 9 - + ≤ × p K K p Au+Au 130 MB 0 8 0-85% 70.6 1 5 2000 ≤ × 8 Au+Au 130 Central 0 8 0-11% 80.8 1 5 2000 ≤ × - + Au+Au 200 MB 0 3 0-80% 10.4 1 7 2004 7 π π ≤ × 6

Au+Au 200 Central 0 3 0-5% 40.8 1 2004 dE/dx (GeV/cm) ≤ × 6 p + p 200 MB 0 5 MB (NSD) 60.5 1 6 2002 ≤ × d+Au 200 MB 0 5 MB 10.4 1 7 2003 5 ≤ × 4 - + TABLE I: Data sets used in the analysis. Cuts on VZ , the e e selected centrality ranges and the final number of events in- 3 cluded in the analysis after all cuts/selections are also shown. 2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 momentum × charge (GeV/c) the d+Au data, the raw charged hadron multiplicity in FIG. 1: (Color online) Measured dE/dx vs momentum charge the east (Au-direction) FTPC (-3.8 < η < -2.8) was used h i × for the centrality definition to avoid auto-correlation be- of reconstructed tracks in the TPC. The figure is generated from tween centrality and the measurements of charged par- Au+Au 62.4 GeV data. ticles at midrapidity in the TPC [56]. We defined four centrality bins for the Au+Au 62.4 GeV data (0-20%, GeV/c were not used, as their combined acceptance and 20-40%, 40-60%, 60-80%), three centrality bins for the efficiency becomes very small. Each track included in the Au+Au 130 GeV data (0-11%, 11-26%, 26-85%), nine φ analysis was required to have at least 15 hit points out centrality bins for the Au+Au 200 GeV data (0-5%, 0- of 45 used in the fitting of the tracks helix parameters. 10%, 10-20%, 20-30%, 30-40%, 40-50%, 50-60%, 60-70%, The ratio of the number of space points used in the track 70-80%) and three centrality bins for the d+Au 200 GeV reconstruction to the maximum possible number of hit data (0-20%, 20-40%, 40-100%). The 80-100% most pe- points was required to be greater than 55% to avoid split ripheral Au+Au collision data were not used because of tracks where a real track is reconstructed in two or more the rapidly decreasing trigger and vertex finding efficien- segments. A pseudo-rapidity cut η < 1.0 ( η < 1.1 for cies for low multiplicity events. Table I lists the data sets Au+Au 130 GeV data) was applied| | to select| tracks| that used along with centrality selections and final numbers are well within the TPC acceptance. of events after these cuts. Note that the elliptic flow (v2) measurement only from 200 GeV MB Au+Au data is pre- 2. Kaon selection sented in this paper, as the statistics for the v2 analysis is not sufficient for the 62.4 and 130 GeV Au+Au data. Particle identification (PID) was achieved by correlat- ing the ionization energy loss (dE/dx) of charged par- C. Track selection and particle identification ticles in the TPC gas with their measured momentum. The measurement of mean dE/dx was achieved by aver- 1. T rack selection aging the measured dE/dx samples along the track after truncating the top 30%. The measured dE/dx ver- Several quality cuts were applied to ensure selection sus momentum curve is reasonably well describedh byi the of good tracks. During the TPC track reconstruction, a Bethe-Bloch function [57] smeared with the detector’s charged track was extrapolated back to the beam line by resolution (note that the Bichsel function was used to fit using the reconstructed helix parameters. If the distance the dE/dx plot in Au+Au 200 GeV from the year 2004 of closest approach (DCA) of the track to the event ver- h i run [58]). The nσ values for kaons are calculated via tex was less than 3 cm and the track had at least ten hit points in the TPC, the reconstructed track was labeled 1 dE/dx measured nσ = log h i , (1) as a primary track. The helix parameters for primary R dE/dxexpected tracks were then refitted by requiring that the helix pass through the primary vertex location. This procedure im- where dE/dx measured and dE/dxexpected are dE/dx proved the momentum resolution of tracks. Since the measuredh by TPCi and calculated analytically,h respec-i φ meson has a very short lifetime, it decays at the pri- tively, and R denotes the dE/dx resolution of the track mary vertex position. Thus only primary tracks were which is found to range between 6% and 10%. R is de- used for the φ meson analysis. As a systematic check, termined experimentally and depends on the event multi- the DCA selection for primary tracks was changed from plicity and the number of dE/dx samples from the track 3 cm to 1 cm. The differences in the results were small used to calculate the mean value. Tracks within 2σ of and were included in the estimate of systematic uncer- the kaon Bethe-Bloch curve were selected as kaon can- tainties. Tracks with transverse momentum less than 0.1 didates. Figure 1 presents the measured dE/dx versus h i 6 momentum charge in Au+Au collisions at 62.4 GeV. would lead to a mismatch between the mixed-event and Table II lists× all the track cuts applied in the analysis. same-event invariant mass distributions. This mismatch would prevent the proper extraction of the φ meson sig- Cut parameter Value nal. By sorting events according to their primary ver- tex V position and performing event-mixing only among Track DCA (cm) < 3 Z events in the same vertex bin, the mismatching effect is Track NF it 15 ≥ minimized. In this analysis, events were divided into VZ Track NF it/NMax > 0.55 bins that were 6 cm wide (VZ resolution is 0.3 mm) Track momentum (GeV/c) 0.1 < p < 10 for event-mixing. To further improve the description∼ of Track transverse momentum (GeV/c) 0.1 < pT < 10 the background, two events were only mixed if they had Kaon dE/dx nσ < 2.0 (for kaon) similar event multiplicities. These requirements ensure | | φ candidate’s δ dip angle (radians) > 0.04 that the two events used in mixing have similar event − − φ candidate’s rapidity y < 0.5 (for spectra) structures, so the mixed-event invariant mass distribu- | | tion can better represent the combinatorial background y < 1.0 (for v2) | | in the same-event invariant mass distribution. Consis- tent results were obtained when we constructed the back- TABLE II: Track cuts used in the analysis, where NF it and ground distribution using like-sign pairs from the same NMax represent the number of fitted hits and the maximum number of hits for TPC tracks, respectively. event. To reduce statistical uncertainty in the mixed event, each event was mixed with five to ten other events (de- Note that from the dE/dx measurement, kaons can- pending on the collision system). To extract the φ meson not be clearly separatedh fromi pions above p 0.6 GeV/c signal, the mixed-event and same-event K+K− invari- and from protons/ above p 1.1∼ GeV/c. Also ant mass distributions were accumulated and the mixed- note that the and dE/dx∼ bands cross event distribution normalized to the same-event distribu- the bands for pions, kaons, and protons/antiprotons. tion in the region above the φ mass, 1.04 < m < 1.06 Therefore selected kaon candidates are contaminated by inv GeV/c2, and subtracted in each p and y (rapidity) bin /, pions and protons/antiprotons vary- T for every collision centrality. We varied the normalization ing with p. Contamination by these charged particles region and normalization factor to estimate the system- in the kaon sample brings in additional real correlations atic uncertainty on the normalization, and the estimated (such as particle decays) which cannot be subtracted by uncertainty was included in the quoted total systematic the event-mixing method. We have varied the n cut σ uncertainty. for kaon to investigate the efficiency and combinatorial Despite the requirements for mixing events described background dependence of the φ signal extraction on this above, a residual background remains over a broad mass cut. The resulting systematic uncertainties have been in- region in the subtracted invariant mass distribution. This cluded in the estimate of the total systematic errors. is due to an imperfect description of the combinatorial background and the fact that the mixed event cannot D. Event mixing and raw yield extraction account for the real correlated background from decay pairs due to Coulomb interactions, conversions The φ meson signal was generated by pairing all (γ e+e−), and particle decays such as K0∗ K+π−, K+K− tracks from the same event that passed the selec- ρ0 → π+π−, K0 π+π−, and Λ pπ− [61].→ For exam- tion criteria and by then calculating the invariant mass S ple,→ when both pions→ from a K0 decay→ are misidentified m for all possible K+K− pairs. As random combina- S inv as kaons, the real correlation from decay will remain in tions of K+K− pairs are dominant in this process, the the same-event as a broad distribution, but will not be resulting same-event invariant mass distribution contains reproduced by the event-mixing method. the φ meson signal on top of a large combinatorial back- Due to contamination of electrons/positrons in the se- ground. An event-mixing technique [59, 60] was applied lected kaon sample, the K+K− invariant mass distri- to calculate the shape of the combinatorial background, bution contains residual background near the threshold where the invariant mass was calculated by pairing two from correlated e+e− pairs, mainly from photon conver- kaons from two different events with same primary vertex sions (γ e+ +e−). The δ-dip-angle between the photon and multiplicity bins (mixed event). Ideally, since it com- converted→ electron and positron is usually quite small. bines two different events, the mixed-event distribution The δ-dip-angle is calculated from contains everything except the real same-event correla- tions. −1 pT 1pT 2 + pz1pz2 The STAR TPC has symmetric coverage about the δ dip angle = cos [ ], (2) − − p1p2 center of the collision region. However, variations in the acceptance occur, since the collision vertex position may where p1, p2, pT 1, pT 2, pz1, pz2 are momentum and trans- change considerably event-by-event. This variation in the verse and longitudinal momentum components of the two collision vertex position gives rise to a nonstatistical vari- tracks; this represents the opening angle of a pair in the ation in the single-particle phase-space acceptance, which pz-pT plane. We required the δ-dip-angle to be greater 7

a dot-dashed line in Fig. 3(f)] residual background func- 1400 tion. The parameters p0, p1 and p2 of B(minv) and A, d+Au 200 GeV (0-100%) m0 and Γ are free parameters. 1200 0.4

×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 T T T 2000 500 p+p 200 GeV Au+Au 62.4 GeV (60-80%) 2000 Au+Au 200 GeV (0-10%) 0 0 0 0.98(b) 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 15000.98(d) 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 0.98(f) 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 Entries/2MeV Entries/2MeV 1500 Entries/2MeV 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 < pT < 1.2 GeV/c in Au+Au 62.4 GeV collisions (60-80%) (c) and 0.8 < pT < 1.2 GeV/c in Au+Au 200 GeV collisions (0-10%) (e). Lower panels: the corresponding φ meson mass peaks after subtracting the background. Dashed curves show a Breit-Wigner + linear background function fit in (b), (d). In (f), both linear and quadratic backgrounds are shown as dashed and dot-dashed lines, respectively.

spect to the reaction plane angle, that is

∞ d3N 1 d2N 0.5 E = 1 + 2v cos[n(ϕ Ψ )] , d3p 2π p d dy n − r t t n=1 ! X 0.4 (4) where Ψr is the real reaction plane angle and ϕ is the par- ticle’s azimuthal angle. The coefficient v in the second- 0.3 2 Acceptance order term of the expansion is the dominant part and is × p+p 200 GeV called the second harmonic anisotropic flow parameter, 0.2 d+Au 200 GeV (40-100%) or elliptic flow. Au+Au 200 GeV (70-80%) The real reaction plane angle Ψ is not known, but Au+Au 200 GeV (30-40%) r 0.1 Efficiency Au+Au 200 GeV (10-20%) can be estimated experimentally [67]. In our analysis, Au+Au 200 GeV (0-5%) the estimated reaction plane angle from the second-order 0 harmonic (Ψ2) was used. This has a finite resolution 0 1 2 3 4 5 6 p (GeV/c) due to a limited number of particles available in each T event and a different event-by-event v2, which is used for the estimation. The estimated reaction plane resolution obs FIG. 4: (Color online) Reconstruction efficiency including accep- was used to correct the observed v2 to obtain the final tance of φ meson as a function of pT in several centrality bins of estimation of v2. Au+Au, d+Au and p + p 200 GeV collisions. The event plane angle Ψ2 was calculated by the equa- tion 1 w sin(2ϕ ) Ψ = tan−1 i i i , (5) 2 2 w cos(2ϕ )  Pi i i  where the sums are over allP charged particles used for We employed the STAR standard reaction plane reaction plane determination, wi and ϕi are the weight method as described in Refs. [65, 66], which uses a and azimuthal angle for the ith particle in a given event, Fourier expansion to describe particle emission with re- respectively. The weights include both a pT weight and 9

ϕ weight. The pT weight was taken to be the particle result for the Au+Au data at 200 GeV is presented in pT up to 2.0 GeV/c and constant (2.0) above that [66]. Fig. 6. The ϕ weight was taken to be the reciprocal of the ϕ distribution (normalized by the average entries) for all selected tracks. The autocorrelations were eliminated by ×103 π 380 excluding all kaon tracks used in the φ invariant mass χ2 / ndf 1.898 / 3 5 calculation from the reaction plane angle estimation [64]. 360 A 2.943×10 ± 4442 obs ± v2 0.07392 0.01018 340 Entries/0.2 Au+Au 200 GeV (0-80%) 0.9 320 1.5 < p < 2.0 GeV/c T 0.8 300

resolution 280 2 0.7 Ψ 260 0.6 Au+Au 200 GeV 240 0 0.5 1 1.5 2 2.5 3 0.5 ϕ - Ψ (rad) 2 0.4 Central Peripheral FIG. 6: ϕ Ψ2 distribution for φ meson at 1.5 < pT < 2.0 GeV/c − 0.3 in Au+Au collisions (0-80%) at 200 GeV. The line is the fitting 0 10 20 30 40 50 60 70 80 result. Error bars are statistical only. Most Central (%)

obs The measured v2 was then divided by the reaction FIG. 5: Event plane Ψ2 resolution as a function of centrality in plane resolution to obtain the final v2, i.e., Au+Au 200 GeV collisions, where the vertical axis starts from 0.3 for clarity. vobs v = 2 . (8) 2 cos[2(Ψ Ψ )] The reaction plane resolution was then calculated by h 2 − r i

a Simulation studies have found that the measured v2 is cos[2(Ψ2 Ψr)] = C cos[2(Ψ2 Ψr)] , (6) h − i h − i about 7% (relative to the real v2) lower than the real v2 a due to binning effects (five bins in ϕ Ψ2); a correction where Ψ2 is the calculated reaction plane angle of the − subevent, and C is a constant calculated from the known has been made to the measured v2 to account for this multiplicity dependence of the resolution [66]. This reso- effect. lution was determined by dividing each event into two random subevents, a and b, with equal multiplicities. 2. Invariant mass method The reaction plane resolution therefore corresponds to how accurately the event plane angle represents the real A new method, namely, the invariant mass method, reaction plane; due to its the definition in Eq. (6), a value was also used to extract the elliptic flow v2 of the φ me- of unity indicates ideal resolution. Figure 5 presents the son. The method was proposed in Ref. [68], which de- reaction plane resolutions in different centrality bins for composes the anisotropic flow vn of a short-lived particle Au+Au 200 GeV collisions. from that of all possible daughter pairs as a function of The combinatorial background in the φ invariant mass invariant mass. For extracting the v2 of the φ meson, it + − distribution was also calculated by an event-mixing tech- utilizes the fact that the v2 of K K pairs is composed nique as described above. To guarantee the mixed-event of the v2 of the combinatorial background and the v2 sample would represent the combinatorial background, of the φ meson. Following the mixed-event background- an additional cut, the reaction plane angle difference be- subtraction procedure described in Sec. II D, the number + − tween two mixed events, was required to be less than of K K pairs in each invariant-mass bin were counted, 0.1π rad in the event-mixing procedure. After back- irrespective of the pair azimuth. Then ground subtraction, φ meson yield was extracted in each (p , ϕ Ψ ) bin. The yield distribution as a function of NK+K− (minv) = Nφ(minv) + NB(minv), (9) T − 2 ϕ Ψ2 was fitted by the function − where Nφ and NB are from the φ signal and the back- ground, respectively. Once N has been extracted via A 1 + 2vobs cos[2(ϕ Ψ )] , (7) φ 2 − 2 event-mixing and fitting the φ mass peak with Eq. (3)   for each pT bin as discussed in Section II D, NB can be obs to extract the v2 value, where A is a constant. A typical obtained from Eq. (9). 10

+ − The same-event v2 for K K pairs vs. invariant mass 〉 can be described by the function 〉 )

0.04 0.02 ) 2 2 Ψ Ψ - - - - K v2(minv) = a(minv)v2S + [1 a(minv)]v2B (minv), (10) K + + K − 0.035 0.015 K φ φ + − where v2(minv) is the v2 of same-event K K pairs, sin2( cos2( v2S v2φ is the v2 of the φ meson, v2B is the effec- 〈 ≡ 〈 0.03 0.01 tive v2 of the combinatorial background and a(minv) = Au+Au 200 GeV (0-80%) − Nφ(minv)/NK+K (minv) is the ratio of the φ signal to 0.5 < p < 1.0 GeV/c the sum of the background and φ signal. The reaction 0.025 T 0.005 plane angle Ψ2 was estimated in the same way as for the reaction plane method described in the previous section. 0.02 0 Therefore the two methods are not completely indepen- dent. v2(minv) can then be calculated from the following 0.015 -0.005 equation [66] for each minv bin 1 1.02 1.04 1.06 1.08 1.1 Invariant Mass (GeV/c2) v (m ) = cos[2(ϕ Ψ )] , (11) 2 inv h KK − 2 i + − where ϕKK is the azimuthal angle of the K K pair. FIG. 7: (Color online) cos[2(ϕ + − Ψ2)] (full red points) and h K K − i Under the assumption that the background contribu- sin[2(ϕK+K− Ψ2)] (open blue points) as a function of minv h + − − i of K K pairs at 0.5 < pT < 1.0 GeV/c in Au+Au 200 GeV tion to v2(minv) [the second part on right side of equa- collisions (0-80%), where the solid curve is the result of fitting by tion (10)] is smooth as a function of minv [68], a poly- Equation (10). The arrow shows the position of φ invariant mass 2 nomial function, p0+p1minv+p2minv, can be used to peak. The dash line shows zero horizontal line. parametrize the background v2B vs minv. v2S is then ob- tained by fitting v2 by Eq. (10) in each pT bin, with v2S as a free parameter. Figure 7 shows cos[2(ϕK+K− Ψ2)] mass or transverse momentum distributions. The sys- h − i [i.e. v2 in Equation 11] vs minv for 0.5 < pT < 1.0 GeV/c tematic uncertainty in the overall normalization for the in Au+Au 200 GeV collisions (0-80%), where the solid p + p 200 GeV data was found to be 15% for dN/dy and curve is the result of fitting Eq. (10). At the same time, 5% for p , including uncertainties due to vertex finding h T i sin[2(ϕK+K− Ψ2)] vs minv (open points) is found, as and trigger inefficiency for low multiplicity events. h − i expected, to be consistent with zero due to collisional ge- Systematic uncertainties for the v2 measurement from obs ometry symmetry [66]. The v2S value [i.e., v2 in Eq. (7)] the two different v2 extraction methods show pT and cen- determined by the fit was corrected for the reaction plane trality dependences, which mainly result from the de- resolution to obtain the final v2 for the φ meson. The fi- termination of S/(S+B) ratios for the invariant mass nal v2 results and related discussions will be presented in method and from the removal of residual background in Sec. III E. the reaction plane method, respectively. In our analysis, the point-to-point systematic errors included contribu- H. Systematic uncertainties tions from the following:

Major contributions to the systematic uncertainties (i) Difference in finding the φ-meson signal via bin-by- come from variations in the procedure used for extract- bin counting or Breit-Wigner function fitting meth- ing the yields from the K+K− invariant mass distribu- ods; tions and from variations in the determination of tracking and particle identification efficiencies. Different residual (ii) Difference due to the residual background fitting background functions (first-order vs. third-order poly- function: first- or third-order polynomial functions; nomial curves) were used to estimate the uncertainty of (iii) Difference in combinatorial background determina- the raw yield extraction in each bin, and it was found to tion: rotation of the background (the mixed event be of the order of 4.5%. The uncertainty due to dif- ∼ is from the azimuthal angle rotation of all tracks ferent mixed-event normalization factors was estimated from the same event) or event-mixing (the current to be 2.1% by varying the normalization region in the method); mixed-event∼ background distribution. The uncertainty from tracking and PID efficiencies was estimated to be (iv) Difference in v2 calculation: centrality-by- 8%, by varying the kinematic and PID cuts on the centrality v calculation and then weighting to ∼ 2 daughter tracks. get the final MB v2 or direct calculation of the v2 The overall systematic uncertainty was estimated to through MB raw yield fitting. be approximately 10% for the yield (dN/dy), and 10% for pT for the Au+Au and the d+Au data. It includes III. RESULTS an additionalh i contribution from the difference between exponential and Levy function fittings of the transverse A. Mass and width 11 ) ) 2 1.022 (a) 2 1.022 (c) 1.02 1.02 1.018 1.018

Mass (GeV/c 1.016 Mass (GeV/c 1.016 full: experimental data open: MC data full: experimental data open: MC data 1.014 1.014 p+p 200 GeV Au+Au 200 GeV 1.012 d+Au 200 GeV 1.012 Au+Au 62.4 GeV 1.01 PDG value 1.01 PDG value

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

) 14 (b) ) 14 (d) 2 2 12 12 10 10 8 8 6 6 4 4 Width (MeV/c Width (MeV/c 2 2 full: experimental data open: MC data full: experimental data open: MC data 0 0 p+p 200 GeV Au+Au 200 GeV -2 d+Au 200 GeV -2 Au+Au 62.4 GeV -4 PDG value -4 PDG value -6 -6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 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.

Figure 8 shows the φ invariant mass peak position and differences in mass and width of φ mesons between real width (FWHM) as a function of pT for Au+Au 200 GeV data and simulations have limited our sensitivity to pos- (0-5%), Au+Au 62.4 GeV (0-20%), d+Au 200 GeV (0- sible small modifications of φ meson properties in the 20%) and p + p 200 GeV (NSD) collisions. In the larger medium produced at RHIC collisions. It should also be pT region (> 1 GeV/c), the measured mass and width for noted that to really trace down the possible modifica- the φ meson are consistent with those from Monte Carlo tion of the φ meson mass and width in heavy-ion colli- (MC) embedding simulations in various collision systems sions, measurements through the dilepton decay channel and at different energies. At low pT (< 1 GeV/c), the are needed. An interesting excess on the low-mass side measured φ meson mass is lower and the width is larger of the φ meson invariant mass peak was observed by an than from simulation. The drop of the φ meson mass e+ + e− channel in the low βγ region (βγ < 1.25) for in both real data and simulation at low pT is due to 12 GeV p+Cu interactions from the recent KEK exper- the multiple scattering energy loss of low pT tracks in iment [22, 23]. This may indicate a vector meson mass the detector, which is not fully corrected during track modification at normal nuclear density. φ measurements reconstruction. using the dilepton channel will hopefully be addressed in STAR in year 2010 with the time-of-flight detector up- Figure 9 shows shape comparisons between experimen- grade under construction. tal and MC invariant mass distributions for the φ meson at 0.6 < pT < 1.0 GeV/c in p + p 200 GeV (NSD) and B. Spectra Au+Au 200 GeV (0-5%) collisions. The real data φ in- variant mass peak (solid circles) is wider than that from φ meson differential invariant yields were calculated standard MC data set (1) (open circles). If the momen- by correcting the extracted raw yield by tracking ef- tum resolution for low pT kaons used in the simulations ficiency, detector acceptance and the decay branching is increased by 50%, e.g., kaon momentum resolution at ratio. Figure 10 shows the φ meson transverse mass 350 MeV/c increases from 2% [MC data set (1)] to 3% (m = p 2 + m2, where m is the mass of φ meson) dis- ∼ ∼ T T 0 0 [MC data set (2)], the φ meson width from simulation re- tributions from Au+Au collisions at √sNN = 62.4, 130, produces the measured width from real data as shown by and 200p GeV and from p + p (NSD) and d+Au collisions open diamonds. This decreased momentum resolution in at √sNN = 200 GeV. All spectra are from midrapidity, MC could be possible considering uncertainties in simula- y < 0.5, with pT coverage above 0.4 GeV/c. For clarity, tions for the amount of material between the TPC active distributions| | for different centralities are scaled by fac- volume and the primary collision vertex and residual ge- tors indicated in the figure. Lines in the figure represent ometry alignment issues. These remaining issues for the fits to the transverse mass distributions for different cen- 12

from the best fits to the spectra. Overall estimated sys- tematic uncertainties on these quantities are also listed. p+p 200 GeV 0.6 < p < 1.0 GeV/c T The φ meson transverse mass spectra in central 400 Exp. data mass = 1.019 GeV Au+Au collisions can be well described by a single width = 8.28 MeV mT -exponential function, while the spectra in d+Au, MC data (1) p + p and peripheral Au+Au are better described by mass = 1.019 GeV a Levy function, due to the power-law tail at interme- 200 width = 6.15 MeV diate and high pT . Figure 11 compares the transverse momentum spectra shapes in different 200 GeV colli- sion systems (0-5% Au+Au, 0-20% d+Au, and inelas- tic p + p). The spectra are normalized by the num- 0 ber of binary collisions (Nbin) and number of partici- pant pairs (Npart/2). Nbin and Npart were determined Entries/MeV Au+Au 200 GeV 0.6 < p < 1.0 GeV/c T by Glauber model calculations [56]. We again point out Exp. data 100000 mass = 1.019 GeV that STAR only triggered on NSD p + p events (mea- width = 8.46 MeV sured σNSD = 30.0 3.5 mb) [71], while the Glauber MC data (1) model calculations use± the p + p inelastic cross section mass = 1.019 GeV width = 6.36 MeV (σinel = 42 1.0 mb). Thus the NSD p + p spectrum was 50000 ± MC data (2) normalized to the inelastic yield by a correction factor of mass = 1.019 GeV 30/42. width = 8.45 MeV A change in the shape of spectra from p + p, d+Au 0 and peripheral Au+Au collisions to central Au+Au col- lisions is clearly visible. In comparison with the fit- 1 1.02 1.04 1.06 ting result for 200 GeV p + p collisions in the high p 2 T Invariant Mass (GeV/c ) (4.0 < pT < 6.0 GeV/c) region, the Nbin normalized yield is suppressed in central Au+Au collisions at 200 GeV, while no suppression is observed for d+Au collisions at FIG. 9: (Color online) Invariant mass distributions of φ meson at 200 GeV. Since particles with high transverse momen- 0.6 < pT < 1.0 GeV/c in p + p 200 GeV (NSD) and Au+Au 200 GeV (0-5%) collisions. Solid symbols: experimental data. tum are mostly produced in hard scattering processes and Open symbols: MC simulation. Curves are the results of a Breit- modified by interactions with the medium in high energy Wigner function fit. Note: Two sets of MC data are shown for heavy-ion collisions [72, 73, 74], the change of φ spectra Au+Au 200 GeV, and see text for details. from the Levy function shape in peripheral Au+Au colli- sions to an exponential function shape in central Au+Au collisions may indicate that different physics dominates tralities. The 62.4, 130 and 200 GeV Au+Au data were the particle production in this p region. In the low p fitted by the exponential function T T (pT < 1.0 GeV/c) region, the Npart/2 normalized φ yield 1 d2N dN/dy in d+Au collisions scales with that in p + p collisions, = e−(mT −m0)/Texp , whereas it is enhanced significantly in central Au+Au 2mπ ydm d 2Tπ (m + T ) T T exp 0 exp collisions. This indicates that the hot environment cre- (12) ated by central Au+Au collisions favors the production where the slope parameter T and yield dN/dy are free exp of soft φ mesons. parameters. For p+p 200 GeV and d+Au 200 GeV data, the distributions were fitted by a Levy function [69, 70] Theoretical calculations have shown that particles with different transverse momenta (or in different collision sys- tems) are produced by or evolve with different mecha- 1 d2N dN/dy(n 1)(n 2) nisms, such as hydrodynamics [35, 36, 37, 38], coales- = − − m2π dmy d 2 πnT (nT + m (n 2)) × cence/recombination [39, 40, 41, 42, 43, 44], fragmenta- T T Levy Levy 0 − m m tion [75, 76, 77] and jet quenching [72, 73, 74] mecha- (1 + T − 0 )−n,(13) nT nisms. The observed change of the φ pT spectra shape in Levy our measurements is likely due to the change of these pro- where n, the slope parameter TLevy, and yield dN/dy, are duction mechanisms in different kinematic regions and free parameters. For the four most peripheral centrality collision systems. Further evidence of this will be dis- bins (40-50%, 50-60%, 60-70% and 70-80%) in Au+Au cussed later, based on the measurements of different ob- collisions at 200 GeV, the distributions were better fit by servables. a Levy rather than by an exponential function. In fact, Figure 12 presents the φ meson midrapidity yield per the exponential function [Eq. (12)] is the limit of the Levy participant pair (dN/dy)/(0.5Npart) as a function of function [Eq. (13)] as n approaches infinity; i.e., Texp = Npart (approximately proportional to the size of the col- TLevy(n ). Table III lists the extracted slope parame- lision system). The measured midrapidity yield per par- ter T , mean→∞ transverse momentum p , and yield dN/dy ticipant pair increases nonlinearly with N , except for h T i part 13

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

10-1 -1 0-11% dy) [(GeV/c dy) [(GeV/c 10 T T -2 dm dm 10 T T 0-80%×10 m m π π 0-20% 11-26%×0.25 (2

(2 -3

⁄ -2 ⁄ 10 20-40% 10 N N 2 2 d d 10-4 40-60% 26-85%×0.15 60-80% -5 -3 10 0 0.5 1 1.5 2 2.5 3 3.5 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2 mT-m0 (GeV/c ) mT-m0 (GeV/c )

10 ] ] 10 (d) d+Au 200 GeV -2 -2 (c) Au+Au 200 GeV ) ) 2 2 10-2 -1 0-5% 10 10-5 0-10%/10 dy) [(GeV/c dy) [(GeV/c T T 10-20%/102

3 dm -3 dm T T -8 20-30%/10 10 m m 10 4 ×

π 0-100% 500 π 30-40%/10 (2 (2 5 ×

⁄ 0-20% 50

⁄ 40-50%/10 N

N -11 6 -5 2 2 10 50-60%/10 10 d d 20-40%×10 60-70%/107 8 p+p 200 GeV (NSD) 40-100%×4 10-14 70-80%/10 10-7 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 2 m -m (GeV/c2) mT-m0 (GeV/c ) T 0

FIG. 10: (Color online) φ meson transverse mass distributions for different collision systems and different energies. For clarity, distributions for some centrality bins have been scaled by factors indicated in the figure. Curves represent the exponential (solid) and Levy (dashed) function fits to the distributions. Error bars are statistical only. Note that a scale factor of 1.09 is applied to the φ meson spectra for Au+Au collisions at 200 GeV in Ref. [50] to correct for the kaon identification efficiency effect missed previously. the largest centrality bins and the Au+Au 130 GeV re- ment of φ meson production can reflect the mechanism sults where there are only three centrality bins with big of strangeness enhancement in a dense medium formed error bars due to the limited statistics. For 200 GeV in high energy heavy-ion collisions [78]. collisions, the yield increases rapidly from p + p and The upper panel of Fig. 13 shows the N dependence d+Au to peripheral Au+Au collisions and then saturates part of φ meson p in different collision systems, where p for midcentral Au+Au collisions. For the same N , T T part is extractedh fromi the best fit to the m spectra ash de-i (dN/dy)/(0.5N ) increases with the collision energy T part scribed and shown in Table III. The measured p of of the Au+Au collisions. This is expected because of T the φ meson shows no significant centrality dependenceh i the increase of energy available to produce the φ mesons. within systematic errors. At the same N value, the φ The centrality and energy dependences of the enhance- part meson p increases slightly with collision energy from h T i 14

62.4 to 200 GeV.

The mean values of transverse momentum pT as a 0.06 function of hadron mass from 62.4 and 200 GeVh i cen- part dN/dy tral Au+Au collisions are presented in the lower panel of 0.5N 0.05 Fig. 13. These data are taken from Refs. [30, 79]. The − − pT of ordinary hadrons π , K , andp ¯ follows a trend 0.04 hthati is increasing with the mass of the hadron, as ex- pected from the dynamics of these particles coming from 0.03 a common radial velocity field shown as the hatched band [Hydro. model (1)] in the plot [80, 81]. However, heavy 0.02 such as Ξ and Ω show a deviation from the Au+Au 200 GeV trend. Their values of pT are lower than the expected 0.01 p+p 200 GeV Au+Au 130 GeV ones. The observed ph valuesi for φ meson and Λ are d+Au 200 GeV Au+Au 62.4 GeV h T i similar to those of Ξ and Ω. Meanwhile, another hydro- 0 dynamic model (2) shown by the curve [82, 83], which 0 50 100 150 200 250 300 350 400 considers possible different chemical freeze-out temper- Npart atures for ordinary and strange hadrons, gives a better description for p . This behavior can h T i FIG. 12: (Color online) Npart dependence of (dN/dy)/(0.5Npart ) be explained if strange hadrons have a smaller scattering in five different collision systems: Au+Au 62.4, 130, 200 GeV; p+p cross section than ordinary hadrons in the later hadronic 200 GeV (Inelastic); and d+Au 200 GeV. Statistical and systematic stage of the collisions. These strange particles would errors are included. then decouple earlier from the system. The collective motion of the φ meson and multistrange hadrons Ξ and in Au+Au collisions at RHIC. If radial flow is built up Ω should have been developed at the early partonic stage through the evolution of the system, the particles with a smaller hadronic cross section would have smaller radial velocity and relatively smaller p . h T i

-1 C. Ratios ] 10 Au+Au 200 GeV (0-5%) /N

-2 binary exponential fit − -2 d+Au 200 GeV (0-20%) /N The yield ratio φ/π as a function of the center-of- 10 binary Levy fit mass energy per nucleon pair (√sNN ) is presented in the

) [(GeV/c) -3 p+p 200 GeV T 10 − Levy fit upper panel of Fig. 14. The φ/π ratio increases with

dydp -4 energy in both A+A [14, 30, 49, 84, 85, 86] and p+p col- T 10 p

π lisions [87, 88, 89, 90], indicating that the yield of the φ -5 −

N/(2 10 increases faster than that of the π in A+A and p+p col- 2 )d lisions with increasing √s . The φ/π− ratio in A+A 10-6 NN binary collisions is enhanced compared to that for p + p colli-

(1/N 10-7 sions, which indicates that A+A collisions may provide a more advantageous environment for the production of -1 0 1 2Au+Au 3 200 4GeV (0-5%) 5 /(N /2) 6 10 part φ mesons. In fact, an enhanced production of φ meson ] exponential fit -2 -2 d+Au 200 GeV (0-20%) /(N /2) in heavy-ion environment has been predicted to be a sig- 10 part Levy fit nal of QGP formation [5]. However, no clear conclusion 10-3 p+p 200 GeV can be drawn from the experimental measurements since ) [(GeV/c)

T Levy fit the relative enhancement from p + p to A+A collisions -4

dydp 10

T does not seem to change for √sNN >10 GeV. The bot- p π 10-5 tom panel of Fig. 14 shows the Npart dependence of the − − N/(2

2 φ/π ratio in different collisions. The φ/π ratio first -6 10 increases with Npart, and then seems to be saturated in /2)]d

part the high N region. 10-7 part To further study whether φ meson production, or just [1/(N 0 1 2 3 4 5 6 that of strange particles, is enhanced in high energy A+A p (GeV/c) collisions with respect to elementary collisions, we have T − plotted the yield ratio of φ/K as a function of √sNN in A+A, e+e and p+p collisions in the top panel of Fig. 15. FIG. 11: (Color online) Comparison of transverse momentum For these collisions, at energies above the threshold for spectra shape among different 200 GeV collision systems: Au+Au φ production, the φ/K− ratio is essentially independent (0-5%), d+Au (0-20%) and p + p (inelastic)). The spectra are nor- of collision species and energy from a few GeV up to malized by Nbin (top panel) and Npart/2 (bottom panel). 200 GeV [14, 30, 49, 84, 85, 86, 87, 88, 89, 90]. The 15

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 Function χ /ndf Texp/Levy (MeV) n hpT i (MeV/c) dN/dy 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 lower panel of Fig. 15 shows that the yield ratio φ/K− cates that strangeness approaches/reaches chemical equi- from our analysis is also almost constant as a function libration for midcentral and central Au+Au collisions at of centrality. This is remarkable considering that the RHIC energies. environment created by p + p collisions is so drastically Because the mechanisms of (multi)strange particle pro- different from that of Au+Au collisions that have both duction are predicted to be very sensitive to the early partonic and hadronic interactions. phase of nuclear collisions, the ratio of Ω/φ is expected The centrality dependence of the φ/K− ratio provides to reflect the partonic nature of the thermal source that another serious test for rescattering models based on the characterizes QGP [96] and the effects of the strong color assumption that kaon coalescence is the dominant mech- field (SCF) [98]. In Fig. 16, the ratios of Ω/φ vs. pT are ¯ + anism for φ production. The KK and K- modes presented for different centrality bins. The Ω (Ω− + Ω ) are included in these rescattering models [12, 13]. They − data points are from Ref. [34] (for 0-12%) and from predict an increasing φ/K ratio vs. centrality (shown ref. [100] for the other centralities. Also shown in the by the dashed line in the lower panel of Fig. 15), which is figure are three curves from two recombination model again in contradiction with the approximately flat trend − expectations for central collisions. A model by Ko et al., of our measurements. Note also that the φ/K ratio based on the dynamical recombination of quarks [97], is from the UrQMD model is scaled by a factor of 3.4 to compared with the data and found to overpredict the match the magnitude of our measurement for peripheral ratio by a factor of about 3 over the whole pT region Au+Au collisions. The comparisons of the data to pre- (Note: the bumpy shape for this model is due to the dictions from these rescattering models including pT − h i limited statistics of their Monte Carlo simulation of the and φ/K effectively rule out kaon coalescence as the model.). Based on φ and Ω production from coalescence dominant production mechanism for the φ meson. These of thermal s quarks in the medium [96], Hwa and Yang measurements of the φ/K− ratio may point to a com- can describe the trend of the data up to pT 4 GeV/c mon underlying production mechanism for φ and strange ∼ but fail at higher pT (solid line). In the alternative SCF mesons in all collision systems. scenario [98, 99], a large string tension of κ = 3 GeV/fm In addition, statistical models [91, 92, 93, 94, 95] can reproduce the data up to pT 4.5 GeV/c in the based on the assumption that the accessible phase space framework of the HIJING/BB v2.0∼ model, but the ef- is fully saturated and thermalized can reproduce the fect of strong color electric fields remains an open issue STAR measurements of integrated hadron yield ratios and needs to be further investigated. With decreasing (including φ/π− and φ/K−) at midrapidity in p + p and centrality, the observed Ω/φ ratios seem to turn over Au+Au collisions at 200 GeV [34]. In these statisti- at successively lower values of pT , possibly indicating a cal models the strangeness phase-space occupancy factor smaller contribution from thermal quark coalescence in γs approaches unity with increasing Npart, which indi- more peripheral collisions [96]. This is also reflected in 16

1400 0.03 A + A - π

/ 0.025 p + p

1200 φ (MeV/c) φ 0.02 > T 1000

Au+Au 200 GeV -

π d+Au 200 GeV Au+Au 130 GeV

1400 / 0.035

Au+Au 62.4 GeV φ Au+Au 62.4 GeV 1200 0.03

> (MeV/c) Ω T 1000 Λ Ξ

FIG. 14: (Color online) Top panel: Energy dependence of the ratio FIG. 13: (Color online) Top panel: Npart dependence of p in − T φ φ/π in A+A (full points) and p+p (open points) collisions. Stars different collision systems; Bottom panel: Hadron mass dependenceh i are data from the STAR experiment at RHIC. Bottom panel: N of p in central Au+Au collisions at 62.4 and 200 GeV. The band part T dependence of ratio φ/π− in different collision systems. Systematic andh curvei 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 clarity, and systematic errors are included for the φ.

where Nbin is the number of binary inelastic nucleon- nucleon collisions determined from Glauber model calcu- the smooth evolution of the pT spectra shapes from the lations [71, 101]. It is obvious that these two ratios will thermal-like exponentials to Levy-like curves. be unity if nucleus-nucleus collisions are just simple su- perpositions of nucleon-nucleon collisions. Deviation of D. Nuclear modification factor these ratios from unity would imply contributions from nuclear or QGP effects. It should be mentioned that The measurement of the nuclear modification factors when using p + p collisions in the RAB ratio, inelastic Rcp and RAB provides a sensitive tool to probe the pro- collisions should be used instead of the measured NSD duction dynamics and hadronization process in relativis- collisions, therefore a correction factor 30/42, which was tic heavy-ion collisions [39, 40, 41, 42, 43, 44]. Rcp, which discussed in the above subsection B, was applied to cor- is the ratio of yields in central to peripheral heavy-ion rect the NSD yield to the inelastic yield in p+p collisions. collisions normalized by Nbin, is defined as There is a pT -dependent correction to the NSD distribu- tion from singly diffractive (SD) events, which is small in central [dN/(NbindpT )] our measured pT range, being 1.05 at pT = 0.4 GeV/c Rcp(pT ) = peripheral , (14) [N/d (NbindpT )] and unity above 1.2 GeV/c as determined from PYTHIA simulations [71]. and RAB , which is the yield ratio of nucleus (A) + nu- Figure 17 presents the pT dependence of Rcp for the cleus (B) collisions to inelastic p+p collisions normalized φ with respect to midperipheral (top panel) and most- by Nbin, is defined as peripheral (bottom panel) bins in Au+Au collisions at ¯ 0 + − 200 GeV. Results for the Λ+Λ, the KS [45], the π +π A+B [dN/(NbindpT )] and the p +p ¯ [102] particles are also shown in the figure RAB(pT ) = p+p , (15) [ dN/dpT ] for comparison. Both statistical and systematic errors 17

0.25 A + A

- 0.4

p + p φ Hwa & Yang (total) / /K

φ e + e Hwa & Yang (thermal) 0.2 Ω 0.35 Ko reco. (x1/3) 0.3 SCF (κ=3 GeV/fm) Ω/φ (0-12%) 0.15 0.25 Ω/φ (20-40%) 0.2 Ω/φ (40-60%) 0.1 0.15 0.1 0.05 2 10 10 0.05 sNN (GeV) 0 0 1 2 3 4 5 6 Au+Au 62.4 GeV p+p 200 GeV

- 0.3 p (GeV/c) Au+Au 130 GeV d+Au 200 GeV T /K φ Au+Au 200 GeV 0.25 Au+Au 200 GeV (UrQMD×3.4) FIG. 16: (Color online) The Ω/φ ratio vs. pT for three centrality bins in √sNN = 200 GeV Au+Au collisions, where the data points 0.2 for 40-60% are shifted slightly for clarity. As shown in the legend, the lines represent the results from Hwa and Yang [96], Ko et al. [97] and for SCF, Refs. [98, 99]. 0.15

0.1 φ meson for Au+Au 62.4, 200 GeV and d+Au 200 GeV collisions. For the three collision systems, the Rcp factor 0 50 100 150 200 250 300 350 400 follows Npart scaling at low pT . However, the Rcp at in- N part termediate pT is strongly suppressed in Au+Au collisions at 200 GeV, is weakly suppressed in Au+Au collisions at FIG. 15: (Color online) Top panel: Energy dependence of ratio 62.4 GeV, and shows no suppression in d+Au collisions φ/K− in A+A (full symbols) and elementary (e+e: open triangles at 200 GeV. and p + p: open circles and star) collisions. Stars are data from Our measured Rcp for the φ meson further supports the STAR experiments at RHIC. Bottom panel: Npart dependence of proposed partonic coalescence/recombination scenario at ratio φ/K− in different collision systems. The dashed line shows results from UrQMD model calculations. Systematic errors are intermediate pT [42, 43, 47, 48], where the centrality de- included for the STAR data points. pendence of particle yield depends on the number of con- stituent quarks (NCQ) rather than on the mass of the particle. Das and Hwa [47] proposed a recombination scenario to explain the leading particle effect in p+p col- are included. Most of the systematic errors cancel in the lisions, where the fragmenting partons would recombine ratios; however, the uncertainty due to particle identifi- with sea quarks to form hadrons. The resulting pT dis- cation from dE/dx remains as the dominant source and tribution for the leading particle is therefore determined varies from point to point over the range 7% 12%. ∼ − by the fragmenting quarks. In heavy-ion collisions, it is In the measured pT region, the Rcp of φ meson is con- possible that qq¯ (qqq) come together and form a meson sistent with Npart scaling at lowest pT (dot-dashed line), () due to the high density of quarks (antiquarks) in and is significantly suppressed relative to the binary col- the collision system. The abundant nearby partons give lision scale (dashed horizontal line at unity) at all pT in the recombination/coalescence mechanism a comparative Au+Au collisions at 200 GeV. When compared to the advantage over the fragmentation mechanism for particle ¯ 0 STAR measured Λ + Λ and KS data [45], the Rcp for φ production in the intermediate p region, and this suc- 0 T follows that of KS rather than that of the similarly mas- cessfully explains the relative enhancement of baryons in ¯ sive Λ (Λ), especially for the case of 0-5%/40-60%. For the intermediate p region, such as the ratios p/π and 0 T 0-5%/60-80%, the Rcp of φ sits between that for the KS 0 Λ/KS [102, 103, 104]. Recently, Hwa and Yang used and the Λ. This may be attributed to the shape change their recombination model to successfully describe the φ of the φ spectra from exponential at 40-60% centrality to meson pT spectra, but it fails to reproduce the pT de- Levy at 60-80% centrality as discussed above, which may pendence of Ω/φ at higher pT as shown in the previ- be due to the change of the φ production mechanism at ous subsection. They assumed that for the production intermediate pT in different environments with different of φ this thermal component dominates over others in- degrees of strangeness equilibration. volving jet shower contributions because of the suppres- Figure 18 presents the pT dependence of Rcp for the sion of shower s quarks in central Au+Au collisions [96]. 18

0

cp Λ Λ φ KS + cp R 1 R 1

Au+Au 200 GeV Scaling 0-5% binary Scaling binary participant 40-60% participant Au+Au 200 GeV Au+Au 62.4 GeV d+Au 200 GeV 10-1 0-5% 0-20% 0-20% 0 1 2 3 4 5 60-80% 60-80% 40-100% Au+Au 200 GeV 10-1 cp

R 1 0 1 2 3 4 5 p (GeV/c) 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 collisions, where rectangular bands represent the uncertainties of 0-5% : 0 Λ Λ φ 60-80% KS + binary and participant scalings (see legend). Statistical and sys- - tematic errors are included. 0-12% : π++π p+p 10-1 60-80% 0 1 2 3 4 5 p (GeV/c) T AB R

FIG. 17: (Color online) pT dependence of the nuclear modification factor Rcp in Au+Au 200 GeV collisions. The top and bottom pan- 1 els present Rcp from midperipheral and most-peripheral collisions, respectively. See legend for symbol and line designations. The rectangular bands show the uncertainties of binary and participant scalings. Statistical and systematic errors are included.

However, the partonic medium, with an intrinsic tem- Au+Au 200 GeV (0-5%): φ perature, may modify the recombination probability and + - -1 d+Au 200 GeV (0-20%): φ π +π p+p momentum distribution for the φ [42, 43, 48]. 10 0 1 2 3 4 5 Figure 19 presents the pT dependence of the nuclear modification factor RAB in Au+Au and d+Au collisions p (GeV/c) T at 200 GeV. For comparison, data points for RdAu of π+ + π− and p +p ¯ are also shown in the figure. The FIG. 19: (Color online) p dependence of the nuclear modification RdAu of φ mesons reveals a similar enhancement trend as T + − factor RAB for φ in Au+Au 200 GeV and d+Au 200 GeV collisions. those of π + π and p +p ¯ at the intermediate p , which − T For comparison, data points for π++π in d+Au 200 GeV and p+¯p was attributed to be the Cronin effect [105, 106, 107]. in d+Au 200 GeV are also shown (see legend). Rectangular bands The Cronin enhancement may result either from mo- shows the uncertainties of binary (solid line) and participant (dot- mentum broadening due to multiple soft [108] (or semi- dash line) scalings. Systematic errors are included for φ, π+ + π− hard [109, 110, 111, 112]) scattering in the initial state and p +p ¯. or from final state interactions suggested in the recom- bination model [113]. These mechanisms lead to differ- of parton-medium final state interactions in Au+Au col- ent particle type and/or mass dependence in the nuclear lisions. The two R observations in central d+Au and modification factors as a function of p . Our measure- AB T Au+Au collisions are consistent with the shape compar- ment of R of φ mesons does not have the precision dAu isons in Fig. 11 (top panel). to differentiate particle dependence scenarios [114, 115]. On the other hand, the RAA in Au+Au 200 GeV is lower E. Elliptic flow than that in d+Au 200 GeV and consistent with the bi- nary collision scaling at intermediate pT . These features Figure 20 shows the elliptic flow v2 of the φ meson are consistent with the scenario that features the onset as a function of pT in MB (0-80%) Au+Au collisions at 19 2 2 v v Au+Au 200 GeV 0.25 Au+Au 200 GeV 0.3 Λ φ 40-80% 0 10-40% 0.2 Ks AMPT (10mb) 0.2 0-5% 0.15 φ 0.1 0.1

0.05 0 NQ = 3 0 NQ = 2 -0.1

0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 p (GeV/c) p (GeV/c) T T

FIG. 20: (Color online) pT dependence of the elliptic flow v2 of φ, FIG. 21: (Color online) Elliptic flow v2 as a function of pT , v2(pT ), 0 for the φ meson from different centralities. The vertical error bars Λ, and KS in Au+Au collisions (0-80%) at 200 GeV. Data points for φ are from the reaction plane method (full up-triangles) and represent the statistical errors while the square bands represent invariant mass method (full circles), where data points from the the systematic uncertainties. For clarity, data points of 10-40% are reaction plane method are shifted slightly along the x axis for clar- shifted in the pT direction slightly. ity. Vertical error bars represent statistical errors, while the square bands represent systematic uncertainties. The magenta curved band represents the v2 of the φ meson from the AMPT model with as strongly as the lighter u and d quarks. The AMPT a string melting mechanism [116]. The dash and dot curves rep- model with string melting and parton coalescence mech- resent parametrizations inspired by number-of-quark scaling ideas from Ref. [117] for NQ=2 and NQ=3 respectively. anisms can reproduce the experimental results well up to 3 GeV/c, which favors the hadronization scenario of coalescence/recombination of quarks [116, 118]. 0 The v2 of the φ meson from other centralities are shown √sNN =200 GeV. The v2 of the KS and Λ measured by STAR [45] in Au+Au 200 GeV collisions are also shown in Fig. 21. The data are analyzed from the invariant mass method only. As expected, v2(pT ) increases with increas- for comparison. Measurements of v2 for the φ meson from both reaction plane and invariant mass methods ing eccentricity (decreasing centrality) of the initial over- are presented, and they are consistent with each other. lap region. This trend is also illustrated in Table IV which presents the p -integrated values of φ-meson ellip- The first interesting observation is that the φ meson T tic flow, v , calculated by convoluting the v (p ) with has significantly nonzero v in the measured p region. 2 2 T 2 T the respectiveh i p spectrum for four centrality bins. It If the φ meson has a small interaction cross section with T should be noted that the centrality dependence of the the evolving hot-dense matter in A+A collisions, it would v of the φ meson is consistent with that of the charged not participate in the late-stage hadronic interactions in 2 hadronsh i [67]. contrast to hadrons such as π, K, and p(¯p) which freeze- out later. This indicates that the nonzero v2 of the φ meson must have been developed in the earlier partonic TABLE IV: Integrated elliptic flow v2 for the φ meson for h i stage. In the low pT region (<2 GeV/c), the v2 value four centrality bins in Au+Au collisions at 200 GeV. 0 of φ is between that for the KS and the Λ in Au+Au Centrality (%) v2 (%) 200 GeV collisions, consistent with the expectation of a h i mass ordering for v in hydrodynamic models. These 40 – 80 8.5 1.1 (stat) 0.2 (sys) 2 ± ± observations support the hypothesis of the development 10 – 40 6.6 0.8 (stat) 0.2 (sys) ± ± of partonic collectivity and possible thermalization in the 0 – 5 2.1 1.2 (stat) 0.5 (sys) ± ± early stages of heavy-ion collisions at RHIC [34, 100], 0 – 80 5.8 0.6 (stat) 0.2 (sys) although the underlying mechanism for the equilibration ± ± process remains an open issue. In the intermediate pT region ( 2-5 GeV/c), the v2 of IV. CONCLUSION ∼ 0 the φ meson is consistent with that for the KS rather than for the Λ. When we fit the v2(pT ) of φ mesons with In conclusion, STAR has measured φ meson produc- the quark number scaling function [117], the resulting fit tion for 62.4, 130, 200 GeV Au+Au, 200 GeV d+Au, parameter NCQ (number of constitute quarks) = 2.3 and NSD p + p collisions at RHIC. Details of the analysis ± 0.4. The fact that the v2(pT ) of φ is the same as that method for φ meson are presented. The respective en- of other mesons indicates that the heavier s quarks flow ergy and Npart dependence of the φ meson production, 20 as well as the pT spectra for five collision systems, are in Au+Au 200 GeV collisions. The φ meson was found reported. to have nonzero v2 in the measured pT range. When The φ spectra in central Au+Au 200 GeV collisions comparing the φ meson nuclear modification factor Rcp are described well by an exponential function. The spec- (0-5%/40-60%) and elliptic flow v2 to those of the simi- 0 tra for p + p, d+Au and the most peripheral Au+Au lar mass Λ baryon, and to the lighter KS meson, we see 0 200 GeV collisions are better described by a Levy func- that the φ meson clearly behaves more like the KS me- tion due to the high-pT power-law tails. This change of son than the Λ baryon. Therefore, the processes relevant spectra shape from p + p, d+Au and peripheral Au+Au to Rcp and v2 at intermediate pT are driven not by the to central Au+Au collisions is most likely due to a change mass of the particle, but rather by the type of the par- of the dominant φ production mechanism in the different ticle, i.e. number of constituent quarks (NCQ) scaling. collision environments. The yield of φ mesons per par- The coalescence/recombination model provides a fairly ticipant pair increases and saturates with the increase of consistent picture to describe particle production in the N . It is found that the p of φ, Λ, Ξ, and Ω does intermediate p region over a broad range of collision part h T i T not follow the pT vs. hadron mass trend determined energies and system sizes at RHIC. by the π−, K−h, andi p ¯. This may be due to their small hadronic cross sections, which indicates that the φ and ACKNOWLEDGMENTS strange hadrons can retain more information about the early state of the collision system. The φ/K− yield ratios from p + p and A+B colli- We thank the RHIC Operations Group and RCF at sions over a broad range of collision energies above the BNL, the NERSC Center at LBNL and the resources φ threshold are remarkably close to each other, indicat- provided by the Open Science Grid consortium for their ing similar underlying hadronization processes for soft support. This work was supported in part by the Offices pairs in these collisions. The lack of a of NP and HEP within the U.S. DOE Office of Science, significant centrality dependence of the φ/K− yield ra- the U.S. NSF, the Sloan Foundation, the DFG Excellence tio and pT φ effectively rules out kaon coalescence as a Cluster EXC153 of Germany, CNRS/IN2P3, RA, RPL, dominanth productioni channel at RHIC. The trend of the and EMN of France, STFC and EPSRC of the United Ω/φ ratio is consistent with recombination models and a Kingdom, FAPESP of Brazil, the Russian Ministry of strong color field scenario up to pT 4 GeV/c in central Sci. and Tech., the NNSFC, CAS, MoST, and MoE of Au+Au collisions. ∼ China, IRP and GA of the Czech Republic, FOM of the The measurement of the φ meson nuclear modification Netherlands, DAE, DST, and CSIR of the Government factor RAB is consistent with the Cronin effect in d+Au of India, Swiss NSF, the Polish State Committee for Sci- 200 GeV collisions, and with the energy loss mechanism entific Research, and the Korea Sci. & Eng. Foundation.

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