STAR Collaboration

Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC

L. Adamczyk AGH University of Science and Technology, Cracow, Poland J. K. Adkins University of Kentucky, Lexington, Kentucky, 40506-0055, USA G. Agakishiev Joint Institute for Nuclear Research, Dubna, 141 980, Russia M. M. Aggarwal Panjab University, Chandigarh 160014, India Z. Ahammed Variable Energy Cyclotron Centre, Kolkata 700064, India I. Alekseev Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia J. Alford Kent State University, Kent, Ohio 44242, USA C. D. Anson Ohio State University, Columbus, Ohio 43210, USA A. Aparin Joint Institute for Nuclear Research, Dubna, 141 980, Russia D. Arkhipkin Brookhaven National Laboratory, Upton, New York 11973, USA E. C. Aschenauer Brookhaven National Laboratory, Upton, New York 11973, USA G. S. Averichev Joint Institute for Nuclear Research, Dubna, 141 980, Russia J. Balewski Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA A. Banerjee Variable Energy Cyclotron Centre, Kolkata 700064, India Z. Barnovska Nuclear Physics Institute AS CR, 250 68 Řež/Prague, Czech Republic D. R. Beavis Brookhaven National Laboratory, Upton, New York 11973, USA R. Bellwied University of Houston, Houston, TX, 77204, USA A. Bhasin University of Jammu, Jammu 180001, India A. K. Bhati Panjab University, Chandigarh 160014, India P. Bhattarai University of Texas, Austin, Texas 78712, USA H. Bichsel University of Washington, Seattle, Washington 98195, USA J. Bielcik Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic J. Bielcikova Nuclear Physics Institute AS CR, 250 68 Řež/Prague, Czech Republic L. C. Bland Brookhaven National Laboratory, Upton, New York 11973, USA I. G. Bordyuzhin Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia W. Borowski SUBATECH, Nantes, France J. Bouchet Kent State University, Kent, Ohio 44242, USA A. V. Brandin Moscow Engineering Physics Institute, Moscow Russia S. G. Brovko University of California, Davis, California 95616, USA S. Bültmann Old Dominion University, Norfolk, VA, 23529, USA I. Bunzarov Joint Institute for Nuclear Research, Dubna, 141 980, Russia T. P. Burton Brookhaven National Laboratory, Upton, New York 11973, USA J. Butterworth Rice University, Houston, Texas 77251, USA H. Caines Yale University, New Haven, Connecticut 06520, USA M. Calderón de la Barca Sánchez University of California, Davis, California 95616, USA D. Cebra University of California, Davis, California 95616, USA R. Cendejas Pennsylvania State University, University Park, Pennsylvania 16802, USA M. C. Cervantes Texas A&M University, College Station, Texas 77843, USA P. Chaloupka Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic Z. Chang Texas A&M University, College Station, Texas 77843, USA S. Chattopadhyay Variable Energy Cyclotron Centre, Kolkata 700064, India H. F. Chen University of Science & Technology of China, Hefei 230026, China J. H. Chen Shanghai Institute of Applied Physics, Shanghai 201800, China L. Chen Central China Normal University (HZNU), Wuhan 430079, China J. Cheng Tsinghua University, Beijing 100084, China M. Cherney Creighton University, Omaha, Nebraska 68178, USA A. Chikanian Yale University, New Haven, Connecticut 06520, USA W. Christie Brookhaven National Laboratory, Upton, New York 11973, USA J. Chwastowski Cracow University of Technology, Cracow, Poland M. J. M. Codrington University of Texas, Austin, Texas 78712, USA R. Corliss Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA J. G. Cramer University of Washington, Seattle, Washington 98195, USA H. J. Crawford University of California, Berkeley, California 94720, USA X. Cui University of Science & Technology of China, Hefei 230026, China S. Das Institute of Physics, Bhubaneswar 751005, India A. Davila Leyva University of Texas, Austin, Texas 78712, USA L. C. De Silva University of Houston, Houston, TX, 77204, USA R. R. Debbe Brookhaven National Laboratory, Upton, New York 11973, USA T. G. Dedovich Joint Institute for Nuclear Research, Dubna, 141 980, Russia J. Deng Shandong University, Jinan, Shandong 250100, China A. A. Derevschikov Institute of High Energy Physics, Protvino, Russia R. Derradi de Souza Universidade Estadual de Campinas, Sao Paulo, Brazil S. Dhamija Indiana University, Bloomington, Indiana 47408, USA B. di Ruzza Brookhaven National Laboratory, Upton, New York 11973, USA L. Didenko Brookhaven National Laboratory, Upton, New York 11973, USA C. Dilks Pennsylvania State University, University Park, Pennsylvania 16802, USA F. Ding University of California, Davis, California 95616, USA P. Djawotho Texas A&M University, College Station, Texas 77843, USA X. Dong Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA J. L. Drachenberg Valparaiso University, Valparaiso, Indiana 46383, USA J. E. Draper University of California, Davis, California 95616, USA C. M. Du Institute of Modern Physics, Lanzhou, China L. E. Dunkelberger University of California, Los Angeles, California 90095, USA J. C. Dunlop Brookhaven National Laboratory, Upton, New York 11973, USA L. G. Efimov Joint Institute for Nuclear Research, Dubna, 141 980, Russia J. Engelage University of California, Berkeley, California 94720, USA K. S. Engle United States Naval Academy, Annapolis, MD 21402, USA G. Eppley Rice University, Houston, Texas 77251, USA L. Eun Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA O. Evdokimov University of Illinois at Chicago, Chicago, Illinois 60607, USA R. Fatemi University of Kentucky, Lexington, Kentucky, 40506-0055, USA S. Fazio Brookhaven National Laboratory, Upton, New York 11973, USA J. Fedorisin Joint Institute for Nuclear Research, Dubna, 141 980, Russia P. Filip Joint Institute for Nuclear Research, Dubna, 141 980, Russia E. Finch Yale University, New Haven, Connecticut 06520, USA Y. Fisyak Brookhaven National Laboratory, Upton, New York 11973, USA C. E. Flores University of California, Davis, California 95616, USA C. A. Gagliardi Texas A&M University, College Station, Texas 77843, USA D. R. Gangadharan Ohio State University, Columbus, Ohio 43210, USA D. Garand Purdue University, West Lafayette, Indiana 47907, USA F. Geurts Rice University, Houston, Texas 77251, USA A. Gibson Valparaiso University, Valparaiso, Indiana 46383, USA M. Girard Warsaw University of Technology, Warsaw, Poland S. Gliske Argonne National Laboratory, Argonne, Illinois 60439, USA D. Grosnick Valparaiso University, Valparaiso, Indiana 46383, USA Y. Guo University of Science & Technology of China, Hefei 230026, China A. Gupta University of Jammu, Jammu 180001, India S. Gupta University of Jammu, Jammu 180001, India W. Guryn Brookhaven National Laboratory, Upton, New York 11973, USA B. Haag University of California, Davis, California 95616, USA O. Hajkova Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic A. Hamed Texas A&M University, College Station, Texas 77843, USA L-X. Han Shanghai Institute of Applied Physics, Shanghai 201800, China R. Haque National Institute of Science Education and Research, Bhubaneswar 751005, India J. W. Harris Yale University, New Haven, Connecticut 06520, USA J. P. Hays-Wehle Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA S. Heppelmann Pennsylvania State University, University Park, Pennsylvania 16802, USA A. Hirsch Purdue University, West Lafayette, Indiana 47907, USA G. W. Hoffmann University of Texas, Austin, Texas 78712, USA D. J. Hofman University of Illinois at Chicago, Chicago, Illinois 60607, USA S. Horvat Yale University, New Haven, Connecticut 06520, USA B. Huang Brookhaven National Laboratory, Upton, New York 11973, USA H. Z. Huang University of California, Los Angeles, California 90095, USA P. Huck Central China Normal University (HZNU), Wuhan 430079, China T. J. Humanic Ohio State University, Columbus, Ohio 43210, USA G. Igo University of California, Los Angeles, California 90095, USA W. W. Jacobs Indiana University, Bloomington, Indiana 47408, USA H. Jang Korea Institute of Science and Technology Information, Daejeon, Korea E. G. Judd University of California, Berkeley, California 94720, USA S. Kabana SUBATECH, Nantes, France D. Kalinkin Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia K. Kang Tsinghua University, Beijing 100084, China K. Kauder University of Illinois at Chicago, Chicago, Illinois 60607, USA H. W. Ke Central China Normal University (HZNU), Wuhan 430079, China D. Keane Kent State University, Kent, Ohio 44242, USA A. Kechechyan Joint Institute for Nuclear Research, Dubna, 141 980, Russia A. Kesich University of California, Davis, California 95616, USA Z. H. Khan University of Illinois at Chicago, Chicago, Illinois 60607, USA D. P. Kikola Purdue University, West Lafayette, Indiana 47907, USA I. Kisel Frankfurt Institute for Advanced Studies FIAS, Germany A. Kisiel Warsaw University of Technology, Warsaw, Poland D. D. Koetke Valparaiso University, Valparaiso, Indiana 46383, USA T. Kollegger Frankfurt Institute for Advanced Studies FIAS, Germany J. Konzer Purdue University, West Lafayette, Indiana 47907, USA I. Koralt Old Dominion University, Norfolk, VA, 23529, USA W. Korsch University of Kentucky, Lexington, Kentucky, 40506-0055, USA L. Kotchenda Moscow Engineering Physics Institute, Moscow Russia P. Kravtsov Moscow Engineering Physics Institute, Moscow Russia K. Krueger Argonne National Laboratory, Argonne, Illinois 60439, USA I. Kulakov Frankfurt Institute for Advanced Studies FIAS, Germany L. Kumar National Institute of Science Education and Research, Bhubaneswar 751005, India R. A. Kycia Cracow University of Technology, Cracow, Poland M. A. C. Lamont Brookhaven National Laboratory, Upton, New York 11973, USA J. M. Landgraf Brookhaven National Laboratory, Upton, New York 11973, USA K. D. Landry University of California, Los Angeles, California 90095, USA J. Lauret Brookhaven National Laboratory, Upton, New York 11973, USA A. Lebedev Brookhaven National Laboratory, Upton, New York 11973, USA R. Lednicky Joint Institute for Nuclear Research, Dubna, 141 980, Russia J. H. Lee Brookhaven National Laboratory, Upton, New York 11973, USA W. Leight Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA M. J. LeVine Brookhaven National Laboratory, Upton, New York 11973, USA C. Li University of Science & Technology of China, Hefei 230026, China W. Li Shanghai Institute of Applied Physics, Shanghai 201800, China X. Li Purdue University, West Lafayette, Indiana 47907, USA X. Li Temple University, Philadelphia, Pennsylvania, 19122, USA Y. Li Tsinghua University, Beijing 100084, China Z. M. Li Central China Normal University (HZNU), Wuhan 430079, China L. M. Lima Universidade de Sao Paulo, Sao Paulo, Brazil M. A. Lisa Ohio State University, Columbus, Ohio 43210, USA F. Liu Central China Normal University (HZNU), Wuhan 430079, China T. Ljubicic Brookhaven National Laboratory, Upton, New York 11973, USA W. J. Llope Rice University, Houston, Texas 77251, USA R. S. Longacre Brookhaven National Laboratory, Upton, New York 11973, USA X. Luo Central China Normal University (HZNU), Wuhan 430079, China G. L. Ma Shanghai Institute of Applied Physics, Shanghai 201800, China Y. G. Ma Shanghai Institute of Applied Physics, Shanghai 201800, China D. M. M. D. Madagodagettige Don Creighton University, Omaha, Nebraska 68178, USA D. P. Mahapatra Institute of Physics, Bhubaneswar 751005, India R. Majka Yale University, New Haven, Connecticut 06520, USA S. Margetis Kent State University, Kent, Ohio 44242, USA C. Markert University of Texas, Austin, Texas 78712, USA H. Masui Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA H. S. Matis Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA D. McDonald Rice University, Houston, Texas 77251, USA T. S. McShane Creighton University, Omaha, Nebraska 68178, USA N. G. Minaev Institute of High Energy Physics, Protvino, Russia S. Mioduszewski Texas A&M University, College Station, Texas 77843, USA B. Mohanty National Institute of Science Education and Research, Bhubaneswar 751005, India M. M. Mondal Texas A&M University, College Station, Texas 77843, USA D. A. Morozov Institute of High Energy Physics, Protvino, Russia M. G. Munhoz Universidade de Sao Paulo, Sao Paulo, Brazil M. K. Mustafa Purdue University, West Lafayette, Indiana 47907, USA B. K. Nandi Indian Institute of Technology, Mumbai, India Md. Nasim National Institute of Science Education and Research, Bhubaneswar 751005, India T. K. Nayak Variable Energy Cyclotron Centre, Kolkata 700064, India J. M. Nelson University of Birmingham, Birmingham, United Kingdom L. V. Nogach Institute of High Energy Physics, Protvino, Russia S. Y. Noh Korea Institute of Science and Technology Information, Daejeon, Korea J. Novak Michigan State University, East Lansing, Michigan 48824, USA S. B. Nurushev Institute of High Energy Physics, Protvino, Russia G. Odyniec Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA A. Ogawa Brookhaven National Laboratory, Upton, New York 11973, USA K. Oh Pusan National University, Pusan, Republic of Korea A. Ohlson Yale University, New Haven, Connecticut 06520, USA V. Okorokov Moscow Engineering Physics Institute, Moscow Russia E. W. Oldag University of Texas, Austin, Texas 78712, USA R. A. N. Oliveira Universidade de Sao Paulo, Sao Paulo, Brazil M. Pachr Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic B. S. Page Indiana University, Bloomington, Indiana 47408, USA S. K. Pal Variable Energy Cyclotron Centre, Kolkata 700064, India Y. X. Pan University of California, Los Angeles, California 90095, USA Y. Pandit University of Illinois at Chicago, Chicago, Illinois 60607, USA Y. Panebratsev Joint Institute for Nuclear Research, Dubna, 141 980, Russia T. Pawlak Warsaw University of Technology, Warsaw, Poland B. Pawlik Institute of Nuclear Physics PAN, Cracow, Poland H. Pei Central China Normal University (HZNU), Wuhan 430079, China C. Perkins University of California, Berkeley, California 94720, USA W. Peryt Warsaw University of Technology, Warsaw, Poland A. Peterson Ohio State University, Columbus, Ohio 43210, USA P. Pile Brookhaven National Laboratory, Upton, New York 11973, USA M. Planinic University of Zagreb, Zagreb, HR-10002, Croatia J. Pluta Warsaw University of Technology, Warsaw, Poland D. Plyku Old Dominion University, Norfolk, VA, 23529, USA N. Poljak University of Zagreb, Zagreb, HR-10002, Croatia J. Porter Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA A. M. Poskanzer Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA N. K. Pruthi Panjab University, Chandigarh 160014, India M. Przybycien AGH University of Science and Technology, Cracow, Poland P. R. Pujahari Indian Institute of Technology, Mumbai, India H. Qiu Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA A. Quintero Kent State University, Kent, Ohio 44242, USA S. Ramachandran University of Kentucky, Lexington, Kentucky, 40506-0055, USA R. Raniwala University of Rajasthan, Jaipur 302004, India S. Raniwala University of Rajasthan, Jaipur 302004, India R. L. Ray University of Texas, Austin, Texas 78712, USA C. K. Riley Yale University, New Haven, Connecticut 06520, USA H. G. Ritter Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA J. B. Roberts Rice University, Houston, Texas 77251, USA O. V. Rogachevskiy Joint Institute for Nuclear Research, Dubna, 141 980, Russia J. L. Romero University of California, Davis, California 95616, USA J. F. Ross Creighton University, Omaha, Nebraska 68178, USA A. Roy Variable Energy Cyclotron Centre, Kolkata 700064, India L. Ruan Brookhaven National Laboratory, Upton, New York 11973, USA J. Rusnak Nuclear Physics Institute AS CR, 250 68 Řež/Prague, Czech Republic N. R. Sahoo Variable Energy Cyclotron Centre, Kolkata 700064, India P. K. Sahu Institute of Physics, Bhubaneswar 751005, India I. Sakrejda Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA S. Salur Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA A. Sandacz Warsaw University of Technology, Warsaw, Poland J. Sandweiss Yale University, New Haven, Connecticut 06520, USA E. Sangaline University of California, Davis, California 95616, USA A. Sarkar Indian Institute of Technology, Mumbai, India J. Schambach University of Texas, Austin, Texas 78712, USA R. P. Scharenberg Purdue University, West Lafayette, Indiana 47907, USA A. M. Schmah Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA W. B. Schmidke Brookhaven National Laboratory, Upton, New York 11973, USA N. Schmitz Max-Planck-Institut für Physik, Munich, Germany J. Seger Creighton University, Omaha, Nebraska 68178, USA P. Seyboth Max-Planck-Institut für Physik, Munich, Germany N. Shah University of California, Los Angeles, California 90095, USA E. Shahaliev Joint Institute for Nuclear Research, Dubna, 141 980, Russia P. V. Shanmuganathan Kent State University, Kent, Ohio 44242, USA M. Shao University of Science & Technology of China, Hefei 230026, China B. Sharma Panjab University, Chandigarh 160014, India W. Q. Shen Shanghai Institute of Applied Physics, Shanghai 201800, China S. S. Shi Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Q. Y. Shou Shanghai Institute of Applied Physics, Shanghai 201800, China E. P. Sichtermann Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA R. N. Singaraju Variable Energy Cyclotron Centre, Kolkata 700064, India M. J. Skoby Indiana University, Bloomington, Indiana 47408, USA D. Smirnov Brookhaven National Laboratory, Upton, New York 11973, USA N. Smirnov Yale University, New Haven, Connecticut 06520, USA D. Solanki University of Rajasthan, Jaipur 302004, India P. Sorensen Brookhaven National Laboratory, Upton, New York 11973, USA U. G. deSouza Universidade de Sao Paulo, Sao Paulo, Brazil H. M. Spinka Argonne National Laboratory, Argonne, Illinois 60439, USA B. Srivastava Purdue University, West Lafayette, Indiana 47907, USA T. D. S. Stanislaus Valparaiso University, Valparaiso, Indiana 46383, USA J. R. Stevens Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA R. Stock Frankfurt Institute for Advanced Studies FIAS, Germany M. Strikhanov Moscow Engineering Physics Institute, Moscow Russia B. Stringfellow Purdue University, West Lafayette, Indiana 47907, USA A. A. P. Suaide Universidade de Sao Paulo, Sao Paulo, Brazil M. Sumbera Nuclear Physics Institute AS CR, 250 68 Řež/Prague, Czech Republic X. Sun Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA X. M. Sun Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Y. Sun University of Science & Technology of China, Hefei 230026, China Z. Sun Institute of Modern Physics, Lanzhou, China B. Surrow Temple University, Philadelphia, Pennsylvania, 19122, USA D. N. Svirida Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia T. J. M. Symons Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA A. Szanto de Toledo Universidade de Sao Paulo, Sao Paulo, Brazil J. Takahashi Universidade Estadual de Campinas, Sao Paulo, Brazil A. H. Tang Brookhaven National Laboratory, Upton, New York 11973, USA Z. Tang University of Science & Technology of China, Hefei 230026, China T. Tarnowsky Michigan State University, East Lansing, Michigan 48824, USA J. H. Thomas Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA A. R. Timmins University of Houston, Houston, TX, 77204, USA D. Tlusty Nuclear Physics Institute AS CR, 250 68 Řež/Prague, Czech Republic M. Tokarev Joint Institute for Nuclear Research, Dubna, 141 980, Russia S. Trentalange University of California, Los Angeles, California 90095, USA R. E. Tribble Texas A&M University, College Station, Texas 77843, USA P. Tribedy Variable Energy Cyclotron Centre, Kolkata 700064, India B. A. Trzeciak Warsaw University of Technology, Warsaw, Poland O. D. Tsai University of California, Los Angeles, California 90095, USA J. Turnau Institute of Nuclear Physics PAN, Cracow, Poland T. Ullrich Brookhaven National Laboratory, Upton, New York 11973, USA D. G. Underwood Argonne National Laboratory, Argonne, Illinois 60439, USA G. Van Buren Brookhaven National Laboratory, Upton, New York 11973, USA G. van Nieuwenhuizen Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA J. A. Vanfossen, Jr Kent State University, Kent, Ohio 44242, USA R. Varma Indian Institute of Technology, Mumbai, India G. M. S. Vasconcelos Universidade Estadual de Campinas, Sao Paulo, Brazil A. N. Vasiliev Institute of High Energy Physics, Protvino, Russia R. Vertesi Nuclear Physics Institute AS CR, 250 68 Řež/Prague, Czech Republic F. Videbæk Brookhaven National Laboratory, Upton, New York 11973, USA Y. P. Viyogi Variable Energy Cyclotron Centre, Kolkata 700064, India S. Vokal Joint Institute for Nuclear Research, Dubna, 141 980, Russia A. Vossen Indiana University, Bloomington, Indiana 47408, USA M. Wada University of Texas, Austin, Texas 78712, USA M. Walker Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA F. Wang Purdue University, West Lafayette, Indiana 47907, USA G. Wang University of California, Los Angeles, California 90095, USA H. Wang Brookhaven National Laboratory, Upton, New York 11973, USA J. S. Wang Institute of Modern Physics, Lanzhou, China X. L. Wang University of Science & Technology of China, Hefei 230026, China Y. Wang Tsinghua University, Beijing 100084, China Y. Wang University of Illinois at Chicago, Chicago, Illinois 60607, USA G. Webb University of Kentucky, Lexington, Kentucky, 40506-0055, USA J. C. Webb Brookhaven National Laboratory, Upton, New York 11973, USA G. D. Westfall Michigan State University, East Lansing, Michigan 48824, USA H. Wieman Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA S. W. Wissink Indiana University, Bloomington, Indiana 47408, USA R. Witt United States Naval Academy, Annapolis, MD 21402, USA Y. F. Wu Central China Normal University (HZNU), Wuhan 430079, China Z. Xiao Tsinghua University, Beijing 100084, China W. Xie Purdue University, West Lafayette, Indiana 47907, USA K. Xin Rice University, Houston, Texas 77251, USA H. Xu Institute of Modern Physics, Lanzhou, China N. Xu Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Q. H. Xu Shandong University, Jinan, Shandong 250100, China Y. Xu University of Science & Technology of China, Hefei 230026, China Z. Xu Brookhaven National Laboratory, Upton, New York 11973, USA W. Yan Tsinghua University, Beijing 100084, China C. Yang University of Science & Technology of China, Hefei 230026, China Y. Yang Institute of Modern Physics, Lanzhou, China Y. Yang Central China Normal University (HZNU), Wuhan 430079, China Z. Ye University of Illinois at Chicago, Chicago, Illinois 60607, USA P. Yepes Rice University, Houston, Texas 77251, USA L. Yi Purdue University, West Lafayette, Indiana 47907, USA K. Yip Brookhaven National Laboratory, Upton, New York 11973, USA I-K. Yoo Pusan National University, Pusan, Republic of Korea Y. Zawisza University of Science & Technology of China, Hefei 230026, China H. Zbroszczyk Warsaw University of Technology, Warsaw, Poland W. Zha University of Science & Technology of China, Hefei 230026, China J. B. Zhang Central China Normal University (HZNU), Wuhan 430079, China S. Zhang Shanghai Institute of Applied Physics, Shanghai 201800, China X. P. Zhang Tsinghua University, Beijing 100084, China Y. Zhang University of Science & Technology of China, Hefei 230026, China Z. P. Zhang University of Science & Technology of China, Hefei 230026, China F. Zhao University of California, Los Angeles, California 90095, USA J. Zhao Shanghai Institute of Applied Physics, Shanghai 201800, China C. Zhong Shanghai Institute of Applied Physics, Shanghai 201800, China X. Zhu Tsinghua University, Beijing 100084, China Y. H. Zhu Shanghai Institute of Applied Physics, Shanghai 201800, China Y. Zoulkarneeva Joint Institute for Nuclear Research, Dubna, 141 980, Russia M. Zyzak Frankfurt Institute for Advanced Studies FIAS, Germany

(July 28, 2025)

Abstract

We report the beam energy ( $\sqrt{s_{\mathrm{NN}}}$ = 7.7 - 200 GeV) and collision centrality dependence of the mean ( $M$ ), standard deviation ( $\sigma$ ), skewness ( $S$ ), and kurtosis ( $\kappa$ ) of the net-proton multiplicity distributions in Au+Au collisions. The measurements are carried out by the STAR experiment at midrapidity ( $|y|<0.5$ ) and within the transverse momentum range 0.4 $<$ $p_{\rm T}$ $<$ 0.8 GeV/ $c$ in the first phase of the Beam Energy Scan program at the Relativistic Heavy Ion Collider. These measurements are important for understanding the Quantum Chromodynamic (QCD) phase diagram. The products of the moments, $S\sigma$ and $\kappa\sigma^{2}$ , are sensitive to the correlation length of the hot and dense medium created in the collisions and are related to the ratios of baryon number susceptibilities of corresponding orders. The products of moments are found to have values significantly below the Skellam expectation and close to expectations based on independent proton and anti-proton production. The measurements are compared to a transport model calculation to understand the effect of acceptance and baryon number conservation, and also to a hadron resonance gas model.

pacs:

25.75.Gz,12.38.Mh,21.65.Qr,25.75.-q,25.75.Nq

The Beam Energy Scan (BES) program at the Relativistic Heavy-Ion Collider (RHIC) facility aims at studying in detail the QCD phase structure. This enables us to map the phase diagram, temperature ( $T$ ) versus baryonic chemical potential ( $\mu_{\rm B}$ ), of strong interactions. Important advancements have been made towards the understanding of the QCD phase structure at small $\mu_{\rm B}$ . Theoretically, it has been found that at high temperatures, there occurs a cross-over transition from hadronic matter to a de-confined state of quarks and gluons at $\mu_{\rm B}$ = 0 MeV Aoki:2006we . Experimental data from RHIC and the Large Hadron Collider have provided evidence of the formation of QCD matter with quark and gluon degrees of freedom starwhitepaper . Several studies have been done to estimate the quark-hadron transition temperature at $\mu_{\rm B}$ = 0 transitiontemp . Interesting features of the QCD phase structure are expected to appear at larger $\mu_{\rm B}$ Fukushima:2010bq . These include the QCD critical point (CP) qcp ; qcp1 and a first order phase boundary between quark-gluon and hadronic phases firstorder .

Previous studies of net-proton multiplicity distributions suggest that the possible CP region is unlikely to be below $\mu_{\rm B}$ = 200 MeV starkurtosisprl . The versatility of the RHIC machine has permitted the center of mass energy ( $\sqrt{s_{\mathrm{NN}}}$ ) to be varied below the injection energy ( $\sqrt{s_{\mathrm{NN}}}$ = 19.6 GeV), thereby providing the possibility to scan the QCD phase diagram above $\mu_{\rm B}$ $\sim$ 250 MeV. The $\mu_{\rm B}$ value is observed to increase with decreasing $\sqrt{s_{\mathrm{NN}}}$ cleymans . The goal of the BES program at RHIC is to look for the experimental signatures of a first order phase transition and the critical point by colliding Au ions at various $\sqrt{s_{\mathrm{NN}}}$ bes .

Non-monotonic variations of observables related to the moments of the distributions of conserved quantities such as net-baryon, net-charge, and net-strangeness volker number with $\sqrt{s_{\mathrm{NN}}}$ are believed to be good signatures of a phase transition and a CP. The moments are related to the correlation length ( $\xi$ ) of the system stephanovmom . The signatures of phase transition or CP are detectable if they survive the evolution of the system survival . Finite size and time effects in heavy-ion collisions put constraints on the significance of the desired signals. A theoretical calculation suggests a non-equilibrium $\xi$ $\approx$ 2-3 fm for heavy-ion collisions krishnaxi . Hence, it is proposed to study the higher moments (like skewness, ${\it{S}}$ = $\left\langle(\delta N)^{3}\right\rangle/\sigma^{3}$ and kurtosis, $\kappa$ = [ $\left\langle(\delta N)^{4}\right\rangle/\sigma^{4}$ ] – 3 with $\delta N$ = $N$ – $\langle N\rangle$ ) of distributions of conserved quantities due to a stronger dependence on $\xi$ stephanovmom . Both the magnitude and the sign of the moments asakawa , which quantify the shape of the multiplicity distributions, are important for understanding phase transition and CP effects. Further, products of the moments can be related to susceptibilities associated with the conserved numbers. The product $\kappa$ $\sigma^{2}$ of the net-baryon number distribution is related to the ratio of fourth order ( $\chi^{(4)}_{\mathrm{B}}$ ) to second order ( $\chi^{(2)}_{\mathrm{B}}$ ) baryon number susceptibilities latticesus ; Gavai:2010zn . The ratio $\chi^{(4)}_{\mathrm{B}}$ / $\chi^{(2)}_{\mathrm{B}}$ is expected to deviate from unity near the CP. It has different values for the hadronic and partonic phases Gavai:2010zn .

This Letter reports measurements of the energy dependence of higher moments of the net-proton multiplicity ( $N_{p}-N_{\bar{p}}$ = $\Delta N_{p}$ ) distributions from Au+Au collisions. The aim is to search for signatures of the CP over a broad range of $\mu_{B}$ in the QCD phase diagram. Theoretical calculations have shown that $\Delta N_{p}$ fluctuations reflect the singularity of the charge and baryon number susceptibility, as expected at the CP hatta . The measurements presented here are within a finite acceptance range and only use the protons among the produced baryons. Refs. Kitazawa:2012at ; Bzdak:2012ab discuss the advantages of using net-baryon measurements and effects of acceptance on which the measurements depend intrinsically (e.g. conservation laws and other finite statistical fluctuations dominate near full and small acceptance respectively).

Refer to caption — Figure 1: (Color online) $\Delta N_{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_{\mathrm{NN}}}$ for 0-5%, 30-40% and 70-80% collision centralities at midrapidity. The statistical errors are small and within the symbol size. The lines are the corresponding Skellam distributions. The distributions are not corrected for the finite centrality width effect and $N_{p}$ ( $N_{\bar{p}}$ ) reconstruction efficiency.

The data presented in the paper were obtained using the Time Projection Chamber (TPC) of the Solenoidal Tracker at RHIC (STAR) star . The event-by-event proton ( $N_{p}$ ) and anti-proton ( $N_{\bar{p}}$ ) multiplicities are measured for Au+Au minimum-bias events at $\sqrt{s_{\mathrm{NN}}}$ = 11.5, 19.6, 27, 39, 62.4, and 200 GeV for collisions occurring within $\Delta Z$ = 30 cm from the TPC center along the beam line. For 7.7 GeV, $\Delta Z$ is 50 cm. The 19.6 and 27 GeV data were collected in the year 2011 and the other energies were taken in 2010. Interactions of the beam with the beam pipe are rejected by choosing events with a radial vertex position in the transverse plane of less than 2 cm. The numbers of events analyzed are 3 $\times 10^{6}$ , 6.6 $\times 10^{6}$ , 15 $\times 10^{6}$ , 30 $\times 10^{6}$ , 86 $\times 10^{6}$ , 47 $\times 10^{6}$ , and 238 $\times 10^{6}$ for $\sqrt{s_{\mathrm{NN}}}$ = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV, respectively. Similar studies have also been carried out in $p$ + $p$ collisions with 0.6 $\times 10^{6}$ and 7 $\times 10^{6}$ events at $\sqrt{s_{\mathrm{NN}}}$ = 62.4 and 200 GeV, respectively. The centrality selection utilizes the uncorrected charged particle multiplicity other than identified protons and anti-protons within pseudorapidity $|\eta|$ $<$ 1.0 measured by the TPC. It is found that the measured net-proton moment values depend on the choice of the pseudorapidity range for the centrality selection. However the values of the moments do not change if the centrality selection range is further increased to the full acceptance of the TPC (which leads to a 15% increase in charged particle multiplicity). In the UrQMD urqmd studies, after increasing the $\eta$ range used for centrality selection to two units, it is observed that the maximum decrease of moments is $\sim$ 2.5% and 35% for $\sqrt{s_{\mathrm{NN}}}$ = 200 and 7.7 GeV, respectively Luo:2013bmi . There is minimal change for central collisions compared to other centralities. For each centrality, the average number of participants ( $\langle N_{\mathrm{part}}\rangle$ ) is obtained by Glauber model calculations. The $\Delta N_{p}$ measurements are carried out at midrapidity ( $|y|$ $<$ 0.5) in the range 0.4 $<$ $p_{\mathrm{T}}$ $<$ 0.8 GeV/ $c$ . Ionization energy loss ( $dE/dx$ ) of charged particles in the TPC is used to identify the inclusive $p$ ( $\bar{p}$ ) starprc . The minimum $p_{\rm T}$ cut and a maximum distance of closest approach (DCA) to the collision vertex of 1 cm for each $p(\bar{p})$ candidate track suppress contamination from secondaries starprc . To have a good purity of the proton sample (better than 98%) for all beam energies, the maximum $p_{\mathrm{T}}$ is taken to be 0.8 GeV/ $c$ . This $p_{\mathrm{T}}$ interval accounts for approximately 50% of the total uncorrected $p+\bar{p}$ multiplicity at midrapidity. The average proton reconstruction efficiency for the $p_{\mathrm{T}}$ range studied is between 70-78% and 83-86%, for central and peripheral collisions, respectively, at different $\sqrt{s_{\mathrm{NN}}}$ .

$\Delta N_{p}$ distributions from 70-80%, 30-40%, and 0-5% Au+Au collision centralities are shown in Fig. 1. The $\Delta N_{p}$ is not corrected for reconstruction efficiency. The distributions are also not corrected for the finite centrality width effect Luo:2013bmi . The subsequent analysis in this Letter is corrected for the centrality width effect. The corresponding Skellam distributions are also shown, $P(N)=\left(\frac{M_{p}}{M_{\bar{p}}}\right)^{N/2}{{I_{N}(2\sqrt{M_{p}M_{\bar{p}}}~)}~{\exp[-(M_{p}+{M_{\bar{p}}})]}}\;$ , where $I_{N}(x)$ is a modified Bessel function of the first kind, and $M_{p}$ and $M_{\bar{p}}$ are the measured mean multiplicities of proton and anti-protons BraunMunzinger:2011dn . The data seems to closely follow the Skellam distributions. To study the detail shape of the distribution, we discuss the various order cumulants ( $C_{n}$ ), where $C_{1}$ = $M$ , $C_{2}$ = $\sigma^{2}$ , $C_{3}$ = $S\sigma^{3}$ and $C_{4}$ = $\kappa\sigma^{4}$ . For both proton and anti-proton distributions being Poissonian, the $\Delta N_{\mathrm{p}}$ distribution will be a Skellam and have $C_{3}/C_{2}$ = $(M_{p}-M_{\bar{p}})/(M_{p}+M_{\bar{p}})$ and $C_{4}/C_{2}$ = 1.

The four cumulants that describe the shape of $\Delta N_{p}$ distributions at various collision energies are plotted as a function of $\langle N_{\mathrm{part}}\rangle$ in Fig. 2. We use the Delta theorem approach to obtain statistical errors Luo:2011tp . The typical statistical error values for $C_{2}$ , $C_{3}$ , and $C_{4}$ for central Au+Au collisions at 7.7 GeV are 0.3%, 2.5% and 2.5% respectively, and those for high statistics 200 GeV results are 0.04%, 1.2% and 2.0% respectively. Most of the cumulant values show a linear variation with $\langle N_{\mathrm{part}}\rangle$ . The $C_{1}$ values increase as $\sqrt{s_{\mathrm{NN}}}$ decreases, in accordance with the energy and centrality dependence of baryon transport. $C_{2}$ and $C_{4}$ have similar values as a function of $\langle N_{\mathrm{part}}\rangle$ for a given $\sqrt{s_{\mathrm{NN}}}$ . $C_{1}$ and $C_{3}$ follow each other closely as a function of $\langle N_{\mathrm{part}}\rangle$ at any given $\sqrt{s_{\mathrm{NN}}}$ . The differences between these groupings decrease as $\sqrt{s_{\mathrm{NN}}}$ decreases. The decrease in the $C_{3}$ values with increasing beam energy indicates that the distributions become symmetric for the higher beam energies. The particle production at any given centrality can be considered a superposition of several identically distributed independent sources the number of which is proportional to $N_{\mathrm{part}}$ starkurtosisprl . For the cumulants, this means a linear increase with $\langle N_{\mathrm{part}}\rangle$ as the system volume increases. This reflects that the cumulants are extensive quantities that are proportional to system volume. The lines in Fig. 2 are linear fits to the cumulants, which provide a reasonable description of the centrality dependence. This indicates that the volume effect dominates the measured cumulants values. The $\chi^{2}/\rm{ndf}$ between the linear fit and data are smaller than 3.2 for all cumulants presented. The slight deviation of some cumulants in most central collisions from the fit line are due to the corresponding proton distributions.

In order to cancel the volume effect to first order and to understand the collision dynamics, we present the ratios of the cumulants $C_{3}/C_{2}$ (= ${\it{S}}$ $\sigma$ ) and $C_{4}/C_{2}$ (= $\kappa$ $\sigma^{2}$ ) as a function of $\langle N_{\mathrm{part}}\rangle$ for all collision energies, in Fig. 3. The ${\it{S}}$ $\sigma$ are normalized to the corresponding Skellam expectations. Results with correction for the $p(\bar{p})$ reconstruction efficiency are presented. The correction for a finite track reconstruction efficiency is done by assuming a binomial distribution for the probability to reconstruct $n$ particles out of $N$ produced eff ; Bzdak:2012ab . These observables are related to the ratio of baryon number susceptibilities ( $\chi_{\mathrm{B}}$ ) at a given temperature ( $T$ ) computed in QCD motivated models as: ${\it{S}}$ $\sigma$ = $(\chi^{(3)}_{\mathrm{B}}/T)/(\chi^{(2)}_{\mathrm{B}}/T^{2})$ and $\kappa$ $\sigma^{2}$ = $(\chi^{(4)}_{\mathrm{B}})/(\chi^{(2)}_{\mathrm{B}}/T^{2})$ latticesus ; Gavai:2010zn . Close to the CP, QCD based calculations predict the net-baryon number distributions to be non-Gaussian and susceptibilities to diverge, causing ${\it{S}}$ $\sigma$ and $\kappa$ $\sigma^{2}$ to have non-monotonic variations with $\langle N_{\mathrm{part}}\rangle$ and/or $\sqrt{s_{\mathrm{NN}}}$ qcp1 ; stephanovmom .

We observe in Fig. 3 the $\kappa$ $\sigma^{2}$ and the ${\it{S}}$ $\sigma$ normalized to Skellam expectations are below unity for all of the Au+Au collision data sets presented. The deviations below unity of the order of 1-3% stephanovprd as seen for the central collisions for energies above 27 GeV are expected from quantum statistical effects. The measured ${\it{S}}$ $\sigma$ and $\kappa$ $\sigma^{2}$ are compared to expectations in which the cumulants of $\Delta N_{p}$ distributions are constructed by considering independent production of protons and anti-protons. For independent production, the various order ( $n$ = 1, 2, 3 and 4) net-proton cumulants are given as $C_{n}(\Delta N_{p})$ = $C_{n}(N_{p})$ + $(-1)^{n}$ $C_{n}(N_{{\bar{p}}})$ , where $C_{n}(N_{p})$ and $C_{n}(N_{{\bar{p}}})$ are cumulants of the measured distributions of $N_{\mathrm{p}}$ and $N_{{\bar{p}}}$ , respectively. This approach breaks intra-event correlations between $N_{p}$ and $N_{{\bar{p}}}$ . The results from independent production are found to be in good agreement with the data. However, for $\sqrt{s_{\mathrm{NN}}}$ $<$ 39 GeV, the $C_{n}$ of net-protons are dominated by the corresponding values from the proton distributions. The assumption that $N_{p}$ and $N_{\bar{p}}$ have independent binomial distributions Tarnowsky:2012vu also leads to a good description of the measurements (similar to independent production, but not plotted in Fig. 3).

Systematic errors are estimated by varying the following requirements for $p(\bar{p})$ tracks: DCA, track quality reflected by the number of fit points used in track reconstruction, and the $dE/dx$ selection criteria for $p(\bar{p})$ identification. The typical systematic errors are of the order 4% for $\it{M}$ and $\sigma$ , 5% for ${\it{S}}$ and 12% for $\kappa$ . A 5% uncertainty in reconstruction efficiency estimation is also considered. The statistical and systematic (caps) errors are presented separately in the figures.

Figure 4 shows the energy dependence of ${\it{S}}\sigma$ and $\kappa$ $\sigma^{2}$ for $\Delta N_{p}$ for Au+Au collisions for two collision centralities (0-5% and 70-80%), corrected for $p$ ( $\bar{p}$ ) reconstruction efficiency. The ${\it{S}}\sigma$ values normalized to the corresponding Skellam expectations are shown in the bottom panel of Fig. 4. The Skellam expectations reflect a system of totally uncorrelated, statistically random particle production. The corresponding results from the $p$ + $p$ collisions are also shown and found to be similar to peripheral Au+Au collisions for $\sqrt{s_{\mathrm{NN}}}$ = 62.4 and 200 GeV within the statistical errors. For $\sqrt{s_{\mathrm{NN}}}$ below 39 GeV, differences are observed between the 0-5% central Au+Au collisions and the peripheral collisions. The results are closer to unity for $\sqrt{s_{\mathrm{NN}}}$ = 7.7 GeV. Deviations of 0-5% Au+Au data from Skellam expectations, ( $(\mid{\rm Data}-{\rm Skellam}\mid)/\sqrt{\rm{err_{stat}}^{2}+{\rm err_{sys}}^{2}}$ ) are found to be most significant for 19.6 GeV and 27 GeV, with values of 3.2 and 3.4 for $\kappa$ $\sigma^{2}$ , and 4.5 and 5.6 for ${\it{S}}\sigma$ , respectively. The deviations for 5-10% Au+Au data are smaller for $\kappa$ $\sigma^{2}$ with values of 2.0 and 0.6 and are 5.0 and 5.4 for ${\it{S}}\sigma$ , for 19.6 GeV and 27 GeV, respectively. A reasonable description of the measurements is obtained from the independent production approach. The data also show deviations from the hadron resonance gas model Karsch:2010ck ; Garg:2013ata which predict $\kappa$ $\sigma^{2}$ and ${\it{S}}\sigma$ /Skellam to be unity. To understand the effects of baryon number conservation Bzdak:2012an and experimental acceptance, UrQMD model calculations (a transport model which does not include a CP) urqmd for 0-5% Au+Au collisions are shown in the middle and bottom panels of Fig. 4. The UrQMD model shows a monotonic decrease with decreasing beam energy Luo:2013bmi .

The current data provide the most relevant measurements over the widest range in $\mu_{B}$ (20 to 450 MeV) to date for the CP search, and for comparison with the baryon number susceptibilities computed from QCD to understand the various features of the QCD phase structure qcp1 ; latticesus ; Gavai:2010zn . The deviations of ${\it{S}}$ $\sigma$ and $\kappa$ $\sigma^{2}$ below Skellam expectation are qualitatively consistent with a QCD based model which includes a CP Stephanov:2011zz . However the UrQMD model which does not include a CP also shows deviations from the Skellam expectation. Hence conclusions on the existence of CP can be made only after comparison to QCD calculations with CP behavior which include the dynamics associated with heavy-ion collisions, such as finite correlation length and freeze-out effects.

In summary, measurements of the higher moments and their products ( ${\it{S}}$ $\sigma$ and $\kappa$ $\sigma^{2}$ ) of the net-proton distributions at midrapidity ( $|y|$ $<$ 0.5) within 0.4 $<$ $p_{\mathrm{T}}$ $<$ 0.8 GeV/ $c$ in Au+Au collisions over a wide range of $\sqrt{s_{\mathrm{NN}}}$ and $\mu_{\mathrm{B}}$ have been presented to search for a possible CP and signals of a phase transition in the collisions. These observables show a centrality and energy dependence, which are neither reproduced by non-CP transport model calculations, nor by a hadron resonance gas model. For $\sqrt{s_{\mathrm{NN}}}$ $>$ 39 GeV, ${\it{S}}$ $\sigma$ and $\kappa$ $\sigma^{2}$ values are similar for central, peripheral Au+Au collisions and $p$ + $p$ collisions. Deviations for both $\kappa$ $\sigma^{2}$ and ${\it{S}}$ $\sigma$ from HRG and Skellam expectations are observed for $\sqrt{s_{\mathrm{NN}}}$ $\leq$ 27 GeV. The measurements are reasonably described by assuming independent production of $N_{p}$ and $N_{{\bar{p}}}$ , indicating that there are no apparent correlations between the protons and anti-protons for the observable presented. However at the lower beam energies, the net-proton measurements are dominated by the shape of the proton distributions only. The data presented here also provides information to extract freeze-out conditions in heavy-ion collisions using QCD based approaches Bazavov:2012vg ; Borsanyi:2013hza .

We thank M. Asakawa, R. Gavai, S. Gupta, F. Karsch, K. Rajagopal, K. Redlich and M. A. Stephanov for discussions related to this work. We thank the RHIC Operations Group and RCF at BNL, and the NERSC Center at LBNL, the KISTI Center in Korea and the Open Science Grid consortium for providing resources and support. This work was supported in part by the Offices of NP and HEP within the U.S. DOE Office of Science, the U.S. NSF, CNRS/IN2P3, FAPESP CNPq of Brazil, Ministry of Ed. and Sci. of the Russian Federation, NNSFC, CAS, MoST, and MoE of China, the Korean Research Foundation, GA and MSMT of the Czech Republic, FIAS of Germany, DAE, DST, and CSIR of the Government of India, National Science Centre of Poland, National Research Foundation (NRF-2012004024), Ministry of Sci., Ed. and Sports of the Rep. of Croatia, and RosAtom of Russia. Finally, we gratefully acknowledge a sponsored research grant for the 2006 run period from Renaissance Technologies Corporation.

References

(1) Y. Aoki et al., Nature 443, 675 (2006).
(2) I. Arsene et al., Nucl. Phys. A 757, 1 (2005); B. B. Back et al., Nucl. Phys. A 757, 28 (2005); J. Adams et al., Nucl. Phys. A 757, 102 (2005); K. Adcox et al., Nucl. Phys. A 757, 184 (2005); S. Chatrchyan et al., JHEP 05, 063 (2012); B. Abelev et al., Phys. Rev. Lett. 109, 072301 (2012).
(3) Y. Aoki et al., Phys. Lett. B 643, 46 (2006); M. Cheng et al., Phys. Rev. D 74, 054507 (2006).
(4) K. Fukushima and T. Hatsuda, Rept. Prog. Phys. 74, 014001 (2011).
(5) M. A. Stephanov, Prog. Theor. Phys. Suppl. 153, 139 (2004) [Int. J. Mod. Phys. A 20, 4387 (2005)]; Z. Fodor and S. D. Katz, JHEP 04, 050 (2004).
(6) R. V. Gavai and S. Gupta, Phys. Rev. D 78, 114503 (2008); Phys. Rev. D 71, 114014 (2005); S. Gupta, PoS CPOD 2009, 025 (2009).
(7) S. Ejiri, Phys. Rev. D 78, 074507 (2008); E. S. Bowman and J. I. Kapusta, Phys. Rev. C 79, 015202 (2009).
(8) M. M. Aggarwal et al., Phys. Rev. Lett. 105, 022302 (2010).
(9) J. Cleymans et al., Phys. Rev. C 73, 034905 (2006).
(10) B. I. Abelev et al., Phys. Rev. C 81, 024911 (2010); STAR Internal Note - SN0493, 2009.
(11) V. Koch, A. Majumder and J. Randrup, Phys. Rev. Lett. 95, 182301 (2005); M. Asakawa, U. W. Heinz and B. Muller, Phys. Rev. Lett. 85, 2072 (2000).
(12) M. A. Stephanov, Phys. Rev. Lett. 102, 032301 (2009); C. Athanasiou et al., Phys. Rev. D 82, 074008 (2010).
(13) M. A. Stephanov, Phys. Rev. D 81, 054012 (2010).
(14) B. Berdnikov and K. Rajagopal, Phys. Rev. D 61, 105017 (2000).
(15) M. Asakawa, S. Ejiri and M. Kitazawa, Phys. Rev. Lett. 103, 262301 (2009); M. A. Stephanov, Phys. Rev. Lett. 107, 052301 (2011).
(16) S. Ejiri, F. Karsch and K. Redlich, Phys. Lett. B 633, 275 (2006); M. Cheng et al., Phys. Rev. D 79, 074505 (2009); B. Stokic et al., Phys. Lett. B 673, 192 (2009); S. Gupta et al., Science 332, 1525 (2011).
(17) R. V. Gavai and S. Gupta, Phys. Lett. B 696, 459 (2011).
(18) Y. Hatta and M. A. Stephanov, Phys. Rev. Lett. 91, 102003 (2003).
(19) M. Kitazawa and M. Asakawa, Phys. Rev. C 86, 024904 (2012) [Erratum-ibid. C 86, 069902 (2012)].
(20) A. Bzdak and V. Koch, Phys. Rev. C 86, 044904 (2012).
(21) K. H. Ackermann et al., Nucl. Instr. Meth. A 499, 624 (2003).
(22) M. Bleicher et al., J. Phys. G 25, 1859 (1999).
(23) X. Luo, J. Xu, B. Mohanty and N. Xu, J. Phys. G 40, 105104 (2013).
(24) B. I. Abelev et al., Phys. Rev. C 79, 034909 (2009); Phys. Lett. B 655, 104 (2007).
(25) P. Braun-Munzinger et al., Phys. Rev. C 84, 064911 (2011).
(26) X. Luo, J. Phys. G 39, 025008 (2012).
(27) $C_{2}^{X-Y}=({C_{2}^{x-y}+(\varepsilon-1)(\langle x\rangle+\langle y\rangle)})/{{\varepsilon^{2}}}$ ; $C_{3}^{X-Y}=(C_{3}^{x-y}+3(\varepsilon-1)(C_{2}^{x}-C_{2}^{y})+(\varepsilon-1)(\varepsilon-2)(\langle x\rangle-\langle y\rangle))/{\varepsilon^{3}}$ and ${C_{4}}(X-Y)=({C_{4}}(x-y)-2(\varepsilon-1){C_{3}}(x+y)+8(\varepsilon-1)({C_{3}}(x)+{C_{3}}(y))+(5-\varepsilon)(\varepsilon-1){C_{2}}(x+y)+8(\varepsilon-2)(\varepsilon-1)({C_{2}}(x)+{C_{2}}(y))+({\varepsilon^{2}}-6\varepsilon+6)(\varepsilon-1)(\langle x\rangle+\langle y\rangle))/{\varepsilon^{4}}$ . Where ( $X,Y$ ) and ( $x,y$ ) are the numbers of ( $p$ , $\bar{p}$ ) produced and measured respectively. $\varepsilon$ is the $p(\bar{p})$ reconstruction efficiency.
(28) M. A. Stephanov, K. Rajagopal and E. V. Shuryak, Phys. Rev. D 60, 114028 (1999).
(29) T. J. Tarnowsky and G. D. Westfall, Phys. Lett. B 724, 51 (2013).
(30) M. Gyulassy and X.-N. Wang, Comput. Phys. Commun. 83, 307 (1994).
(31) F. Karsch and K. Redlich, Phys. Lett. B 695, 136 (2011).
(32) P. Garg et al., arXiv:1304.7133 [nucl-ex].
(33) A. Bzdak, V. Koch and V. Skokov, Phys. Rev. C 87, 014901 (2013).
(34) M. A. Stephanov, J. Phys. G 38, 124147 (2011).
(35) A. Bazavov et al., Phys. Rev. Lett. 109, 192302 (2012).
(36) S. Borsanyi et al., arXiv:1305.5161 [hep-lat].