Flow and interferometry results from Au+Au collisions at s NN − − − − √ = 4.5 GeV
STAR Collaboration, J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, D. M. Anderson, A. Aparin, E. C. Aschenauer, M. U. Ashraf, F. G. Atetalla, A. Attri, G. S. Averichev, V. Bairathi, K. Barish, A. Behera, R. Bellwied, A. Bhasin, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, J. D. Brandenburg, A. V. Brandin, J. Butterworth, H. Caines, M. Calderón de la Barca Sánchez, J. M. Campbell, D. Cebra, I. Chakaberia, P. Chaloupka, B. K. Chan, F-H. Chang, Z. Chang, N. Chankova-Bunzarova, A. Chatterjee, D. Chen, J. H. Chen, X. Chen, Z. Chen, J. Cheng, M. Cherney, M. Chevalier, S. Choudhury, W. Christie, X. Chu, H. J. Crawford, M. Csanád, M. Daugherity, T. G. Dedovich, I. M. Deppner, A. A. Derevschikov, L. Didenko, X. Dong, J. L. Drachenberg, J. C. Dunlop, T. Edmonds, N. Elsey, J. Engelage, G. Eppley, R. Esha, S. Esumi, O. Evdokimov, A. Ewigleben, O. Eyser, R. Fatemi, S. Fazio, P. Federic, J. Fedorisin, C. J. Feng, Y. Feng, P. Filip, E. Finch, Y. Fisyak, A. Francisco, L. Fulek, C. A. Gagliardi, T. Galatyuk, F. Geurts, A. Gibson, K. Gopal, D. Grosnick, W. Guryn, A. I. Hamad, A. Hamed, S. Harabasz, J. W. Harris, S. He, W. He, X. H. He, S. Heppelmann, S. Heppelmann, N. Herrmann, E. Hoffman, L. Holub, Y. Hong, S. Horvat, et al. (268 additional authors not shown)
FFlow and interferometry results from Au+Au collisions at √ s NN = 4.5 GeV J. Adam , L. Adamczyk , J. R. Adams , J. K. Adkins , G. Agakishiev , M. M. Aggarwal , Z. Ahammed ,I. Alekseev , , D. M. Anderson , A. Aparin , E. C. Aschenauer , M. U. Ashraf , F. G. Atetalla , A. Attri ,G. S. Averichev , V. Bairathi , K. Barish , A. Behera , R. Bellwied , A. Bhasin , J. Bielcik , J. Bielcikova ,L. C. Bland , I. G. Bordyuzhin , J. D. Brandenburg , , A. V. Brandin , J. Butterworth , H. Caines ,M. Calder´on de la Barca S´anchez , J. M. Campbell , D. Cebra , I. Chakaberia , , P. Chaloupka , B. K. Chan ,F-H. Chang , Z. Chang , N. Chankova-Bunzarova , A. Chatterjee , D. Chen , J. H. Chen , X. Chen ,Z. Chen , J. Cheng , M. Cherney , M. Chevalier , S. Choudhury , W. Christie , X. Chu , H. J. Crawford ,M. Csan´ad , M. Daugherity , T. G. Dedovich , I. M. Deppner , A. A. Derevschikov , L. Didenko , X. Dong ,J. L. Drachenberg , J. C. Dunlop , T. Edmonds , N. Elsey , J. Engelage , G. Eppley , R. Esha ,S. Esumi , O. Evdokimov , A. Ewigleben , O. Eyser , R. Fatemi , S. Fazio , P. Federic , J. Fedorisin ,C. J. Feng , Y. Feng , P. Filip , E. Finch , Y. Fisyak , A. Francisco , L. Fulek , C. A. Gagliardi ,T. Galatyuk , F. Geurts , A. Gibson , K. Gopal , D. Grosnick , W. Guryn , A. I. Hamad , A. Hamed ,S. Harabasz , J. W. Harris , S. He , W. He , X. He , S. Heppelmann , S. Heppelmann , N. Herrmann ,E. Hoffman , L. Holub , Y. Hong , S. Horvat , Y. Hu , H. Z. Huang , S. L. Huang , T. Huang ,X. Huang , T. J. Humanic , P. Huo , G. Igo , D. Isenhower , W. W. Jacobs , C. Jena , A. Jentsch , Y. Ji ,J. Jia , , K. Jiang , S. Jowzaee , X. Ju , E. G. Judd , S. Kabana , M. L. Kabir , S. Kagamaster ,D. Kalinkin , K. Kang , D. Kapukchyan , K. Kauder , H. W. Ke , D. Keane , A. Kechechyan , M. Kelsey ,Y. V. Khyzhniak , D. P. Kiko(cid:32)la , C. Kim , B. Kimelman , D. Kincses , T. A. Kinghorn , I. Kisel ,A. Kiselev , A. Kisiel , M. Kocan , L. Kochenda , L. K. Kosarzewski , L. Kozyra , L. Kramarik ,P. Kravtsov , K. Krueger , N. Kulathunga Mudiyanselage , L. Kumar , R. Kunnawalkam Elayavalli ,J. H. Kwasizur , R. Lacey , S. Lan , J. M. Landgraf , J. Lauret , A. Lebedev , R. Lednicky , J. H. Lee ,Y. H. Leung , C. Li , W. Li , W. Li , X. Li , Y. Li , Y. Liang , R. Licenik , T. Lin , Y. Lin , M. A. Lisa ,F. Liu , H. Liu , P. Liu , P. Liu , T. Liu , X. Liu , Y. Liu , Z. Liu , T. Ljubicic , W. J. Llope ,R. S. Longacre , N. S. Lukow , S. Luo , X. Luo , G. L. Ma , L. Ma , R. Ma , Y. G. Ma , N. Magdy ,R. Majka , D. Mallick , S. Margetis , C. Markert , H. S. Matis , J. A. Mazer , K. Meehan , N. G. Minaev ,S. Mioduszewski , B. Mohanty , M. M. Mondal , I. Mooney , Z. Moravcova , D. A. Morozov , M. Nagy ,J. D. Nam , Md. Nasim , K. Nayak , D. Neff , J. M. Nelson , D. B. Nemes , M. Nie , G. Nigmatkulov ,T. Niida , L. V. Nogach , T. Nonaka , A. S. Nunes , G. Odyniec , A. Ogawa , S. Oh , V. A. Okorokov ,B. S. Page , R. Pak , A. Pandav , Y. Panebratsev , B. Pawlik , D. Pawlowska , H. Pei , C. Perkins ,L. Pinsky , R. L. Pint´er , J. Pluta , J. Porter , M. Posik , N. K. Pruthi , M. Przybycien , J. Putschke ,H. Qiu , A. Quintero , S. K. Radhakrishnan , S. Ramachandran , R. L. Ray , R. Reed , H. G. Ritter ,J. B. Roberts , O. V. Rogachevskiy , J. L. Romero , L. Ruan , J. Rusnak , N. R. Sahoo , H. Sako ,S. Salur , J. Sandweiss , S. Sato , W. B. Schmidke , N. Schmitz , B. R. Schweid , F. Seck , J. Seger ,M. Sergeeva , R. Seto , P. Seyboth , N. Shah , E. Shahaliev , P. V. Shanmuganathan , M. Shao , F. Shen ,W. Q. Shen , S. S. Shi , Q. Y. Shou , E. P. Sichtermann , R. Sikora , M. Simko , J. Singh , S. Singha ,N. Smirnov , W. Solyst , P. Sorensen , H. M. Spinka , B. Srivastava , T. D. S. Stanislaus , M. Stefaniak ,D. J. Stewart , M. Strikhanov , B. Stringfellow , A. A. P. Suaide , M. Sumbera , B. Summa ,X. M. Sun , X. Sun , Y. Sun , Y. Sun , B. Surrow , D. N. Svirida , P. Szymanski , A. H. Tang ,Z. Tang , A. Taranenko , T. Tarnowsky , J. H. Thomas , A. R. Timmins , D. Tlusty , M. Tokarev ,C. A. Tomkiel , S. Trentalange , R. E. Tribble , P. Tribedy , S. K. Tripathy , O. D. Tsai , Z. Tu , T. Ullrich ,D. G. Underwood , I. Upsal , , G. Van Buren , J. Vanek , A. N. Vasiliev , I. Vassiliev , F. Videbæk ,S. Vokal , S. A. Voloshin , F. Wang , G. Wang , J. S. Wang , P. Wang , Y. Wang , Y. Wang , Z. Wang ,J. C. Webb , P. C. Weidenkaff , L. Wen , G. D. Westfall , H. Wieman , S. W. Wissink , R. Witt , Y. Wu ,Z. G. Xiao , G. Xie , W. Xie , H. Xu , N. Xu , Q. H. Xu , Y. F. Xu , Y. Xu , Z. Xu , Z. Xu ,C. Yang , Q. Yang , S. Yang , Y. Yang , Z. Yang , Z. Ye , Z. Ye , L. Yi , K. Yip , H. Zbroszczyk ,W. Zha , D. Zhang , S. Zhang , S. Zhang , X. P. Zhang , Y. Zhang , Y. Zhang , Z. J. Zhang ,Z. Zhang , Z. Zhang , J. Zhao , C. Zhong , C. Zhou , X. Zhu , Z. Zhu , M. Zurek , M. Zyzak (STAR Collaboration) Abilene Christian University, Abilene, Texas 79699 AGH University of Science and Technology, FPACS, Cracow 30-059, Poland Alikhanov Institute for Theoretical and Experimental Physics NRC ”Kurchatov Institute”, Moscow 117218, Russia Argonne National Laboratory, Argonne, Illinois 60439 a r X i v : . [ nu c l - e x ] A ug American University of Cairo, New Cairo 11835, New Cairo, Egypt Brookhaven National Laboratory, Upton, New York 11973 University of California, Berkeley, California 94720 University of California, Davis, California 95616 University of California, Los Angeles, California 90095 University of California, Riverside, California 92521 Central China Normal University, Wuhan, Hubei 430079 University of Illinois at Chicago, Chicago, Illinois 60607 Creighton University, Omaha, Nebraska 68178 Czech Technical University in Prague, FNSPE, Prague 115 19, Czech Republic Technische Universit¨at Darmstadt, Darmstadt 64289, Germany ELTE E¨otv¨os Lor´and University, Budapest, Hungary H-1117 Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany Fudan University, Shanghai, 200433 University of Heidelberg, Heidelberg 69120, Germany University of Houston, Houston, Texas 77204 Huzhou University, Huzhou, Zhejiang 313000 Indian Institute of Science Education and Research (IISER), Berhampur 760010 , India Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India Indian Institute Technology, Patna, Bihar 801106, India Indiana University, Bloomington, Indiana 47408 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu 730000 University of Jammu, Jammu 180001, India Joint Institute for Nuclear Research, Dubna 141 980, Russia Kent State University, Kent, Ohio 44242 University of Kentucky, Lexington, Kentucky 40506-0055 Lawrence Berkeley National Laboratory, Berkeley, California 94720 Lehigh University, Bethlehem, Pennsylvania 18015 Max-Planck-Institut f¨ur Physik, Munich 80805, Germany Michigan State University, East Lansing, Michigan 48824 National Research Nuclear University MEPhI, Moscow 115409, Russia National Institute of Science Education and Research, HBNI, Jatni 752050, India National Cheng Kung University, Tainan 70101 Nuclear Physics Institute of the CAS, Rez 250 68, Czech Republic Ohio State University, Columbus, Ohio 43210 Institute of Nuclear Physics PAN, Cracow 31-342, Poland Panjab University, Chandigarh 160014, India Pennsylvania State University, University Park, Pennsylvania 16802 NRC ”Kurchatov Institute”, Institute of High Energy Physics, Protvino 142281, Russia Purdue University, West Lafayette, Indiana 47907 Rice University, Houston, Texas 77251 Rutgers University, Piscataway, New Jersey 08854 Universidade de S˜ao Paulo, S˜ao Paulo, Brazil 05314-970 University of Science and Technology of China, Hefei, Anhui 230026 Shandong University, Qingdao, Shandong 266237 Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 Southern Connecticut State University, New Haven, Connecticut 06515 State University of New York, Stony Brook, New York 11794 Instituto de Alta Investigaci´on, Universidad de Tarapac´a, Chile Temple University, Philadelphia, Pennsylvania 19122 Texas A&M University, College Station, Texas 77843 University of Texas, Austin, Texas 78712 Tsinghua University, Beijing 100084 University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan United States Naval Academy, Annapolis, Maryland 21402 Valparaiso University, Valparaiso, Indiana 46383 Variable Energy Cyclotron Centre, Kolkata 700064, India Warsaw University of Technology, Warsaw 00-661, Poland Wayne State University, Detroit, Michigan 48201 and Yale University, New Haven, Connecticut 06520 (Dated: August 10, 2020)The Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) was ex-tended to energies below √ s NN = 7 . mode of operation in the STAR (Solenoidal Track At RHIC) experiment. In the fixed-target mode,ions circulate in one ring of the collider and interact with a stationary target at the entrance of theSTAR Time Projection Chamber. The first results for Au+Au collisions at √ s NN = 4 . √ s NN = 3 . PACS numbers: 25.75.-q, 25.75.Ag, 25.75.Dw, 25.75.Gz, 25.75.Ld, 25.75.Nq
I. INTRODUCTION
The BES program at RHIC was undertaken to studythe nature of the Quantum Chromodynamics (QCD)phase diagram in the plane of temperature versus baryonchemical potential, which is explored by varying the col-lision energy. The phase diagram region of current in-terest, at relatively high baryon chemical potential, isnot accessible so far by first-principle lattice QCD calcu-lations, and there is a wide-ranging international effortto investigate it experimentally [1]. The BES-II program,begun in 2019, covers collision energies at and below 19.6GeV. The lowest energy which is accessible at RHIC withadequate luminosity is 7.7 GeV in the collider mode ofoperation. Therefore a fixed-target (FXT) program hasbeen developed to allow the STAR experiment to accessenergies below 7.7 GeV. In this paper, results are pre-sented from a first run using a single RHIC beam atinjection energy incident on a gold target inside STARbeam-pipe, providing Au+Au collisions at √ s NN = 4 . √ s NN ) of 4.9 GeV.The present measurements of heavy-ion collisions at4.5 GeV with STAR in fixed-target mode provide com-plementary views of the phase diagram to those from col-lider mode data, and extend the systematics of the worlddata on a number of observables at these energies. Char-acteristics of quark-gluon plasma (QGP), including thenature of the transition between QGP and hadronic mat-ter [3–9], can be explored via measurements of azimuthalanisotropy with respect to the collision reaction plane(defined by the beam axis and the vector connecting thecenters of the two colliding nuclei). This anisotropy ischaracterized by a series of Fourier coefficients [10–13]: v n = (cid:104) cos n ( φ − Ψ R ) (cid:105) , (1)where the angle brackets indicate an average over allevents and particles of interest, φ denotes the azimuthalangle of each particle, Ψ R is the azimuthal angle of thereaction plane, and n denotes the harmonic number. Thepresent study explores the first two harmonics: directedflow ( v ) and elliptic flow ( v ). II. PERFORMANCE IN FIXED TARGET MODE charged
N110 c ha r ged d N / d N P il e U pTop % Top % Top % Top % Top % Top % = 4.5 GeV NN sSTAR FXT MC GlauberPile Up FIG. 1: (Color online) Centrality selection for STAR FXT √ s NN = 4.5 GeV Au+Au collisions. The centrality variable N charged is the number of tracks that pass the basic trackcuts. The black points are the data, the thin red curve is thecombined Monte-Carlo Glauber and negative binomial fit tothe data, and the thick blue line is a Monte-Carlo model ofpile-up events [14]. Vertical lines indicate the minimum num-ber of tracks required for an event to be in the correspondingcentrality bin. Events with multiplicity greater than 240 aredominated by pile-up, and are excluded from all analyses. For the results reported in this paper, RHIC provided asingle beam of gold ions with a kinetic energy of 8.9 GeVper nucleon in the laboratory frame. In this paper, therapidity of a particle, y , is always given in the collisioncenter-of-momentum frame, not the laboratory frame.The beam was incident on a gold target of thickness1.93 g/cm (1 mm), corresponding to a 1.7% interactionprobability. The target was installed inside the vacuumpipe, below its center and 211 cm to the west of the cen-ter of the STAR detector. Central Au+Au events wererecorded by requiring a coincidence between the down-stream trigger detector, an arrangement of scintillatortiles called the Beam-Beam Counter (BBC) [15], and ahigh multiplicity signal in the time-of-flight (TOF) bar-rel [16]. About 1.3 million events with centrality 0-30% TABLE I: The centrality selection used in the analyses.Included are the average number of participating nucleons( N part ) estimated for the data for each centrality, the valuesof N part predicted from a Glauber model for a minimum-biastrigger, the percentage of triggers corresponding to pile-upof two lower-multiplicity collisions, and the total number ofevents recorded. Each centrality corresponds to 5% of thetotal cross section.Centrality (cid:104) N part (cid:105) (cid:104) N part (cid:105) Pile-up Events(% of σ total ) (Estimated) (Min bias) (%)0 - 5 341 ± ± ± ± ± ± were recorded.The distribution of charged particle multiplicities isshown in Fig. 1. Also shown in the figure are the central-ity selection criteria. The centrality class and the averagenumber of participating nucleons, labeled (cid:104) N part (cid:105) (mini-mum bias) in Table I, were estimated using a Monte CarloGlauber model [17] assuming a negative binomial distri-bution for charged particle production. Comparison ofthe Glauber Monte Carlo and the data indicates that thetrigger efficiency approaches unity for the most centralcollisions, and therefore we take this as an assumptionand estimate the trigger efficiencies for less central col-lisions from the ratio of the number of recorded eventsover 267,000 (the average number of events for the twomost central bins). For the 0-5%, 5-10%, 10-15%, 15-20%, 20-25% and 25-30% bins, the efficiencies are 100%,100%, 97%, 76%, 47% and 26%, respectively. The esti-mated (cid:104) N part (cid:105) for each bin is then determined by takinga weighted average of N part , with weights equal to thenumber of recorded events for a given N charged , calcu-lated as a function of N charged from the Glauber model.Also shown in Fig. 1 is the estimated contributionof events which were the result of the pile-up of twominimum-bias collisions in the target from the samebunch. Due to the momentum resolution of the tracksand the projection distance back to the target (0.5 to3.0 meters), the average distance of closest approach ofa primary track to its vertex of origin is several millime-ters. Thus, tracks from two separate collisions within thetarget would be reconstructed as emerging from a singlevertex.The location of the target along the beam axis waschosen to be z = 211 cm (where z = 0 corresponds tothe center of the detector) in order to maximize the ac-ceptance of the STAR Time Projection Chamber (TPC)[18] for fixed-target events. Protons and pions were se-lected from all charged tracks within a 2 σ band centeredon the Bichsel prediction for dE/dx [19]. The acceptanceis illustrated in Fig. 2 by the distribution of the measured p T and rapidity for protons and pions. FIG. 2: Negative pion and proton relative yield versus ra-pidity and transverse momentum for STAR FXT √ s NN = 4.5GeV Au + Au collisions. The black line indicates the locationof midrapidity. The target (beam) rapidity in the center ofmass frame is at +1.52 (-1.52). III. DIRECTED FLOWA. Proton and pion v All directed flow analyses in this paper pertain only torapidity-odd v ( y ), which is a measure of the collectivesideward deflection of emitted particles. The rapidity-even correlation v even1 ( y ) [20, 21] is not related to the re-action plane in mass-symmetric collisions, and originatesfrom initial-state event-by-event fluctuations.We consider three distinct analysis methods: first, theTPC event plane (EP) approach with random sub-eventsfor EP resolution correction [10–12]; second, a methodbased on the use of the Beam Beam Counter (BBC) de-tector for event plane determination [22–24]; and third,a direct calculation of multi-particle cumulants (the Q-cumulant method) [13]. Both the first and second meth-ods use equation (1) to calculate the directed flow withthe value of Ψ R and its resolution estimated from a sub-event calculation based on information from either theTPC or the BBC [12]. The first method is less favoreddue in part to its susceptibility to bias from non-flow (cor-relations unrelated to the initial geometry of the collision)[13], but is investigated in the present proton directedflow study because that was the method used in 2000 bythe E895 collaboration [25]. However, due to momentum - - - y - - - v p 10-25% slope near mid-rapidity: 0.002 – Open symbols are reflected = 4.5 GeV NN sSTAR FXT Au+Au{Q cumulant} v {BBC east} vFit FIG. 3: Rapidity dependence of directed flow, v ( y ), forprotons with transverse momentum 0 . < p T < . c from events with 10-25% centrality. Two analysis methods,as discussed in the text, are compared. Plotted error bars arestatistical only, and systematic errors are of comparable size.The curve is a cubic fit to the data. conservation effects [26], this first method suffers froma relatively large departure from the v ( y ) odd functionbehavior required by symmetry, and only the second andthird methods are presented in Fig. 3.More specifically, the red star markers in Fig. 3 presentproton v ( y ) based on a 4th-order direct Q-cumulantcalculation [13], which suppresses the contribution fromnon-flow. The tracks included in the analysis have trans-verse momentum 0 . < p T < . c , which matchesthe selection used by E895 at √ s NN = 4.3 GeV [25] andby STAR in collider mode at √ s NN = 7.7 - 200 GeV[24]. Our centrality selection is 10-25%, which is consis-tent with the centrality reported by the E895 collabora-tion [25]. Due to the restricted acceptance and particleidentification performance of the STAR detector in FXTmode (see Fig. 2), measurements are reported for onlyone side of midrapidity, and the odd-function behaviorof directed flow is used to reflect points to the missingrapidity region.The east-west asymmetry of FXT mode requires usto rely on the east BBC detector for the event planeestimation. Sub-event correlations between the east innerBBC (covering pseudorapidity 3.3 to 5) and the TPC[12] are used to correct for event plane resolution. Theaveraged east BBC event plane resolution for the slightlywider 10-30% centrality bin used in the pion directed flowanalysis is 41 . ± . v ( y ) at √ s NN = 4.5 GeV is describedquite well by a cubic function F y + F y , where F and F are constants extracted from a fit to the data. In order tostudy trends in proton directed flow as a function of beamenergy, we take the linear term, F = dv /dy | y =0 , to char-acterize the overall strength of the directed flow signalat each energy. This is the same procedure as used at - - - y - - v - p slope near mid-rapidity: 0.004 – -0.005 Open symbols are reflected = 4.5 GeV NN s STAR FXT Au+AuFit - - - y - - - v + p slope near mid-rapidity: 0.004 – -0.024 Open symbols are reflected = 4.5 GeV NN s STAR FXT Au+AuFit FIG. 4: Upper panel: Rapidity dependence of directed flow, v ( y ), for negative pions with transverse momentum p T > . c and total momentum magnitude | p | < . c fromevents within 10-30% centrality. Here, the BBC-based EventPlane method is used. Plotted error bars are statistical only,and systematic errors are of comparable size. The solid curveis a cubic fit to the data. Lower panel: The same for positivepions. higher beam energies by STAR in collider mode [24] andat lower beam energies by E895 [25]. The curve in Fig. 3shows the fit with F and F as free parameters. The ex-tracted proton slope is dv /dy | y =0 = F = 0 . ± . √ s NN = 7.7 to 200GeV. As some of the species in Ref. [27] have relativelypoor statistics, a more stable fit of the directed flow slopesin that analysis was obtained after requiring F = 0. Forthe purpose of a consistent comparison with the slopesreported in Ref. [27], we also report the extracted pro-ton slope with F = 0 in the present analysis, namely F = 0 . ± .
002 based on a fit over 0 ≤ y ≤ . v ( y ) for negative (upper panel) andpositive (lower panel) pions using the BBC-based methodreferenced above. The 4th-order direct Q-cumulantmethod, as employed in Fig. 3, provides consistent re-sults, but in the context of the relatively poor statisticsfor charged pions in FXT mode at √ s NN = 4.5 GeV,the statistical errors on the BBC-based method are sig-nificantly smaller. No E895 v measurements for pionswere published, so the only available experimental datafor comparison are STAR collider-mode measurements at √ s NN = 7.7 GeV and above [24]. While track selectionsof transverse momentum p T > . c and total mo-mentum magnitude | p | < . c match the measure-ments at higher energies, the limited centrality range ofour 2015 FXT test run restricts the centrality in Fig. 4to 10-30%, and does not fully match the 10-40% cen-trality already published at √ s NN = 7.7 GeV and above[24]. The blue line in Fig. 4 shows the fit with F and F as free parameters. The extracted negative pion slopeis dv /dy | y =0 = F = − . ± .
004 and positive pionslope is dv /dy | y =0 = F = − . ± .
004 For the pur-pose of a consistent comparison with slopes reported inRef. [27], we also report the extracted negative and pos-itive slopes with F = 0 in the present analysis, namely F = − . ± .
003 and F = − . ± . ≤ y ≤ . π + and π − directedflow becomes larger as we scan down from STAR colliderenergies to the present FXT energy point. This obser-vation is consistent with isospin or Coulomb dynamicsbecoming more prominent at lower beam energies, and isqualitatively consistent with measurements at even lowerenergies reported by the FOPI collaboration [28].Systematic errors arising from event-vertex cuts, par-ticle ID cuts, and from contamination by other particlespecies, all make small to negligible contributions. Sys-tematic errors arising from a cut on global distance ofclosest approach to the collision vertex, from the mini-mum number of hits required for dE/dx calculation, fromthe sensitivity to the fit range used when determining dv /dy , and from a correction for a region of diminishingproton acceptance near midrapidity, contribute at a levelthat is comparable to statistical errors. B. Lambda and Kaon v Standard topological cuts on π + π − and pπ − pairs wereutilized to identify K mesons and Λ baryons, respec-tively. Events with 10-30% centrality were selected forthis analysis. The statistics of both K and Λ candidatesare sufficient for the BBC or TPC event plane methodwith η -separated sub-events where the directed flow iscalculated using Eq. (1). Two sub-event methods areused in this analysis. First, the event plane is recon-structed using BBC information (BBC event plane), andsecond, the event plane is reconstructed using primaryprotons and deuterons measured in the TPC with labo-ratory pseudorapidity − . < η lab < K or Λcandidate (TPC event plane). In the TPC event planemethod, protons originating from Λ candidates are ex-cluded from the event plane estimation in order to elimi- nate self-correlation between Λ candidates and the eventplane. Both TPC and BBC event plane resolutions areestimated using the method of three subevents [12]. TheTPC event plane resolution is estimated to be 67 . ± . . ± . v and multiplicity of protonsand deuterons that are used to reconstruct the eventplane. With an assumption that v for deuterons is twiceas large as for protons [29], the calculated resolution is70.2%. - - - y - - - - v L slope near mid-rapidity: 0.011 – Open symbols are reflected = 4.5 GeV NN sSTAR FXTFit FIG. 5: The rapidity dependence of the directed flow for theΛ using the TPC event plane. Open symbols are the reflectionof the solid symbols. The solid blue line is a cubic fit to themeasured data. Plotted error bars are statistical only, whilesystematic errors are ± . × − . - - y - - - v S0 K slope near mid-rapidity: 0.01 – - Open symbols are reflected = 4.5 GeV NN sSTAR FXTFit FIG. 6: The rapidity dependence of the directed flow forthe K using the TPC event plane. Open symbols are thereflection of the solid symbols. The solid blue line is a cubicfit to the measured data. Plotted error bars are statisticalonly, while systematic errors are ± . × − . The directed flow of Λ or K candidates is a super-position of a signal v ( y ) and a background v B ( y ). Thecombination is v tot1 ( y ) = v ( y )∆ S + v B ( y )∆ B , where ∆ S is the fraction (relative to the total) of the Λ or K signaland ∆ B is the fraction of the combinatorial backgroundaccompanying the signal. ∆ S and its invariant mass res-olution, σ M , is calculated in every rapidity bin using thePearson VII [30] function fit to the invariant mass spec-trum of either Λ or K candidates after the combinato-rial background, whose yield is reconstructed using themomentum rotation technique [31], is subtracted. Usingequation (1), the flow of the combinatorial background, v B ( y ), is calculated from particle pairs outside the massregion of the K or Λ.Figure 5 shows the directed flow of Λ hyperons. Thehorizontal positions of the data points are corrected forthe width of the bin. Six different sets of topological cutsare employed, varying the total number of pπ − pairs from ∼ ∼ ± σ M and ± . σ M are studiedseparately to vary the signal-to-background ratio, as wellas the choice of either TPC or BBC event plane, to checkif the event planes are consistent with each other. v B ( y )is calculated in both cases in the 2 < | σ M | < F , representingthe directed flow at midrapidity. Statistical errors on v come from the upper and lower limit of slopes calculatedusing the covariance matrices of the cubic fits to the di-rected flow data. The weighted average from these 24fits is (10 . ± . × − for Λ hyperons. The systematicuncertainty, calculated as the average of the differencesbetween the mean value of 10 . × − and the nominalvalues from the fits, is 0 . × − .The directed flow of K mesons was treated similarly,except wider binning was used and three invariant masswindows ± σ M , ± σ M , and ± . σ M . v B ( y ) is calculatedin all three cases in the 2 < | σ M | < K peak. In total, ∼ π + π − pairspass the tightest topological cuts, while ∼ F is ( − . ± . × − for K and the systematic uncertainty is 1 . × − . Thedata points corrected for the bin widths are shown inFig. 6. C. Beam Energy Dependence
Figure 7 presents slopes dv /dy | y =0 , based on theabove-described cubic fits, for five species ( p , Λ, K , π + and π − ) measured in Au+Au collisions in FXT mode at √ s NN = 4.5 GeV. Error bars show statistical uncertain-ties and shaded bands show systematic errors. The latterones include factors already noted, as well as allowancefor the rapidity range used in slope fitting.Liu et al. [25] reported proton directed flow at central-ity 12-25% from the AGS E895 experiment, in the form ofmean in-plane p T and v ( y ) at √ s NN = 4 . (GeV) NN s - · y = (cid:231) / d y d v (STAR FXT) L (STAR BES) L p (STAR FXT) p (STAR BES)p (E895) Au+Au (GeV) NN s - - - · y = (cid:231) / d y d v STAR BES 10-40%STAR FXT 10-25%E895 12-25% (STAR BES) + p (STAR BES) + K (STAR BES) - p (STAR BES) - K (STAR FXT) + p (STAR BES) S0 K (STAR FXT) - p (STAR FXT) S0 K FIG. 7: (Color online) Beam energy dependence of the di-rected flow slope dv /dy at midrapidity for baryons (upperplot) and mesons (lower plot) measured by STAR (this paperand Refs. [24, 27]) and by AGS experiment E895 [25, 32].Some points are slightly offset horizontally. low. In order to compare dv /dy | y =0 between STAR andE895, it is necessary to carry out a cubic fit to E895 v ( y )for protons using similar criteria as for STAR v ( y ). TheE895 fitted slopes in the upper plot of Fig. 7 show sta-tistical and systematic errors, where the latter arise fromdetails of the fit. The E895 proton slopes reproducedin Ref. [24] are different, although consistent within er-rors, in part because Ref. [24] assumed errors on E895 v ( y ) points that were equal to the marker size in caseswhere the actual errors were smaller than the publishedmarkers.Note that the new proton v ( y ) slope measurement at √ s NN = 4.5 GeV lies within errors on an interpolationbetween the same observable from STAR’s published re-sults for collider mode [24, 27] and E895 [25]. The highestE895 energy point at √ s NN = 4.3 GeV agrees with thecurrent FXT measurement within the uncertainties. Pro-ton and Λ directed flow agree within errors at √ s NN =4.5 GeV. The Λ directed flow results fit into a patternthat was observed by STAR at √ s NN = 7.7 GeV andabove [27], but not at E895 energy points for √ s NN =3.8, 3.3 and 2.7 GeV [32].Positively charged pions, negative pions, and neutralkaons all show directed flow ( v ) signals in the oppositedirection from that of the baryons, continuing trends ob-served at higher energies. The difference between π + and π − flow becomes stronger as the collision energy isreduced, which might be caused by isospin or Coulombdynamics. IV. ELLIPTIC FLOW OF PROTONS ANDPIONS
The second term in the Fourier decomposition of theazimuthal distribution, an elliptic flow v , of identifiedparticles (protons and pions) measured in Au+Au colli-sions at √ s NN = 4.5 GeV, is discussed in this section.Elliptic flow of protons is compared with the earlier AGSdata, while elliptic flow of pions had not been measuredat this beam energy before. The appearance of num-ber of constituent quark (NCQ) scaling, i.e. the collapseof quark-number-scaled flow strengths for mesons andbaryons onto a single curve, is considered to be evidenceof QGP formation [33, 34]. Further and more detailed ex-ploration of the energy region where NCQ scaling is notpresent is very interesting, as it might provide characteri-sation of relevant observables at the lower energies, wherecreation of QGP is in question. Protons, which have beenanalyzed at a similar energy by the E895 experiment atthe AGS [35], are compared to the previously publishedresults from this experiment, while pions could only becompared to the results at higher energies. (Note thatthe results for protons at higher energies are published[36, 37]). Both positively and negatively charged pionsare investigated separately in this analysis and it is foundthat they show the same behavior within uncertainties.Therefore, in the final plots positive and negative pionsare presented together to improve the statistical signifi-cance of the result.In this analysis of elliptic flow, two methods are used:(1) the event plane method using TPC information [10–12] and (2) the two-particle cumulants method [13]. Theevent plan resolution is about 20 %. Resonance decaysgenerate unrelated correlations of particles in the finalstate. Such correlations are a non-flow contribution andthey bias the elliptic flow measurement. Since particlesfrom resonance decays are correlated both in η and φ ,we can reduce the non-flow contribution caused by res-onances by measuring elliptic flow using particles whichare not correlated in η . The implementation of this ideais different in each method. For the event plane method,we divide each event into two sub-events. For the cu-mulant method, we require a 0.1 gap in η between allconsidered pairs. Both methods give results which areconsistent within their uncertainties. Figure 8 shows the elliptic flow v as functions of trans-verse kinetic energy m T − m for pions and protons ob-tained with the event plane method, where m is mass and m T = (cid:112) m + p is transverse mass. It is compared toE895 results [35] obtained using the same method. Weanalyze the 0-30% most central events. For pions andprotons, we require | y | < .
5. In this analysis, we usetracks with 0 . < p T < . √ s NN = 4.5 GeV, we couldanalyze only protons with higher values of p T , namely p T > . v and m T − m (Fig. 8) by the number of constituent quarks (2 for pro-tons and 3 for pions). The results are presented inFig. 9. The observed scaling with the number of con-stituent quarks at 4.5 GeV is similar to what is observedfor Au+Au at higher collision energies [36, 37]. The sys-tem created for Au+Au at √ s NN = 4.5 GeV has, perhapssurprisingly, larger collectivity than expected, and thereis no significant difference in identified particle ellipticflow behavior when compared to higher energies. ] [GeV/c -m T m v STAR Au+Au 4.5 GeV pSTAR Au+Au 4.5 GeV pionsE895 Au+Au 4.3 GeV p FIG. 8: v of protons and pions from STAR FXT data analy-sis, and v of protons from E895 experiment. Blue (red) starsrepresent STAR FXT proton (pion) data (0-30% centrality),and black circles show E895 data (12-25% centrality) [35]. Figure 10 shows the beam energy dependence of v measurements, integrated over p T . The current resultsare consistent with the trends established by the previ-ously published data. V. FEMTOSCOPY OF PIONS
Two-particle correlations at low relative momentumcan be used to extract information on the space-timestructure of the particle-emitting source. Femtoscopy–the techniques of constructing and analyzing thesecorrelations– has been performed in heavy-ion experi-ments over a broad range of energies [48]. ] [GeV/c q )/n -m T (m q / n v STAR Au+Au 4.5 GeV pSTAR Au+Au 4.5 GeV pionsE895 Au+Au 4.3 GeV p FIG. 9: v scaled by the number of constituent quarks ( n q ) forcharged pions (red stars) and protons (blue stars) for 0-30%central collisions. The values of v scaled with n q for pionsand protons are consistent with each other within errors. Forcomparison, points from E895 are also shown (black circles) (GeV) NN s - - v <0.45 FOPI (Ch) 0.25 STAR FXT (p) 0-30%) 0-30% p STAR FXT ( FIG. 10: The excitation function v for all charged particlesor separately for protons and pions, measured by several ex-periments. The STAR FXT points for protons and for pionsare near the region where a change in slope occurs. Data areshown from FOPI [38, 39], E895 [35], E877 [40], CERES [41],NA49 [42], PHENIX [43], PHOBOS [44], and from the STARcollider energies [36, 37, 45–47]. A. Methodology Femtoscopic correlation functions are formed by mak-ing distributions of the relative momenta → q ≡ → p − → p of pairs of particles. A numerator distribution N ( → q ) isformed using pairs where both tracks are from the sameevent, while a denominator distribution, D ( → q ), is formedby constructing pairs where the two tracks are from sepa-rate events, but having similar multiplicity and positionsof the primary vertex; this is known as the ”mixed-event”technique [49, 50]. The shape of both distributions will bedominated by the two-particle phase space distribution, but N ( → q ) will also contain contributions from Coulombinteractions and Bose-Einstein effects. The correlationfunction is the ratio C ( → q ) = N ( → q ) D ( → q ) . (2)This ratio is sensitive to the space-time structure of thepion emitting source [48, 51]. - C ( q ) Out - Side - q [GeV/c] Long DataFit FIG. 11: Projections of the correlation functions in theLCMS frame onto the q out , q side , and q long axes for π − π − pairsfrom events in the 0-10% centrality range. Pairs are createdfrom tracks in the momentum range 0.1 < p T < c .For each projection q i shown, the other components of relativemomentum are integrated over the range | q j | < 35 MeV/c.The red curve shows the projections [48] of a 3-dimensionalfit to equation 4. Errors are statistical only. R ( f m ) out R ( f m ) HADES E895 side NN s R ( f m ) STAR E866 long FIG. 12: Excitation function of R out , R side , and R long for four experiments: HADES [52], E895 [53], STAR, andE866 [54]. STAR points show both systematic (red boxes) andstatistical errors (black lines) while errors for E895 and E866are statistical only. HADES systematic errors are roughlythe same size as the datapoints. The same momentum andcentrality selections are applied as in Fig. 11. Care must be taken to account for the effects of trackreconstruction inefficiencies on the correlation function.0Single-track inefficiencies are common to both N ( → q ) and D ( → q ) and cancel in the ratio C ( → q ). However, two-trackartifacts will affect N ( → q ) alone, distorting C ( → q ) at low | → q | . Track splitting (where hits from one charged par-ticle are reconstructed as two distinct tracks) artificiallyenhances same-event pairs at low q . To eliminate thiseffect, we required both tracks to register separate hitson a minimum number of pad rows [47, 55, 56].Track merging (where hits from two charged particlesare reconstructed as one track) suppresses same-eventlow- q pairs. These pairs cannot be recovered in the nu-merator N ( → q ), but similar pairs can be removed fromthe mixed-event distribution D ( → q ) to compensate. Tothis end, we require all pairs to have a fraction of mergedhits f MH < 10% [47, 55, 56]. All pair cuts are appliedequally to N ( → q ) and D ( → q ).The relative momentum is evaluated in the Longitudi-nally Co-Moving System (LCMS), which is chosen suchthat ( → p + → p ) · ˆ z = 0, where ˆ z is the beam direction. Therelative momentum → q is expressed in the Bertsch-Pratt[57–59] out-side-long coordinate system. The “longitu-dinal” direction, q long , is taken to be the beam direc-tion. The “out” direction, q out , is taken to be the direc-tion of the transverse component of the pair-momentum → k T = ( → p + → p ) / 2, and the “side”, q side , direction is de-fined to be perpendicular to the other two directions.We use a Gaussian parameterization of the correlationfunction [60] to relate the experimental quantity in eq.(2) to the shape of the pion emitting source. The cor-relation function that would arise solely from quantumstatistical effects is represented by the quantity C free andcan be expressed as C free ( → q ) = 1+ exp (cid:0) − R q − R q − R q − R q out q long (cid:1) . (3)Here R out , R side , and R long give the lengths of the regionsof homogeneity [61] in the out, side, and long directions,respectively. The cross term R represents a tiltof the correlation function in the q out − q long plane. Toaccount for Coulomb interactions and contributions fromhalo pions we fit the data with the Bowler-Sinyukov func-tional form [47, 62, 63]: C ( → q ) = (1 − λ ) + λK ( q inv ) C free ( → q ) , (4)where λ is the fraction of pion pairs that carry a corre-lation signal (as opposed to, for instance, non-primarypions from resonance decays which are uncorrelated withpions from the fireball, at the resolution of our measure-ment). Electromagnetic final state interactions are quan-tified by K , the spatially-integrated squared Coulombwave function. This function depends on the Lorentz in-variant q inv ≡ √− q µ q µ , where q µ = ( E − E , (cid:126)q ). Theintegral is taken over a spherical source 5 fm in radius[47, 64]. Integrating instead over a 3-fm source leads tonegligible systematic error. (GeV/c T m0.1 0.2 0.3 0.4 0.53456 ( f m ) ou t R (GeV/c T m0.1 0.2 0.3 0.4 0.53456 ( f m ) s i de R (GeV/c T m0.1 0.2 0.3 0.4 0.523456 ( f m ) l ong R = 4.3 GeV NN s E895 = 4.5 GeV NN s STAR = 4.9 GeV NN s E866 FIG. 13: Transverse mass dependence of R out , R side , and R long for three experiments: E895 [53], STAR, and E866 [54].Pairs for the STAR points are created from negative piontracks in the momentum range 0.15 < p T < c fromevents in the 0-15% centrality range. STAR points show bothsystematic (magenta boxes) and statistical errors (black lines)while errors for E895 and E866 are statistical only. B. Results Figure 11 shows fits of the form in Eq. 4 (red lines)to the experimental correlation function defined in Eq.2 (blue stars). The three panels show projections ofthe correlation function onto the q out , q side , and q long axes. Data here are for π − π − pairs created from trackswith transverse momentum 0 . < p T < . c , fromevents in the 0-10% centrality range. The transversemomentum of the pairs is required to be in the range0 . < k T < . c . These cuts are chosen tomatch as closely as possible those in the E895 experi-ment, which used the same p T cuts and correspondedto approximately 0-11% centrality [53]. There is a slightsuppression at q side ≈ q long ≈ s Centrality (%2.02.53.03.54.04.55.0 R ( f m ) out R side R long R FIG. 14: The centrality dependence of R out , R side , and R long .Errors are statistical only. Here π + π + and π − π − pairs in themomentum range 0.15 < p T < c are used. (fm) long R ( f m ) s i de R Fixed Target E895 STAR HADES Collider STAR ALICE FIG. 15: R side vs. R long , which measures the prolate-ness/oblateness of the pion emitting source when viewed frombeside the beam. HADES [52], ALICE [65] and STAR [66]points include systematic errors; E895 [53] show statisticalerrors only. The various centrality, p T , and k T cuts used inthe different experiments are discussed in the text. For theSTAR fixed-target point, the same momentum and centralityselection are applied as in figure 13. The grey curve indicatesthe evolution of the shape, as the collision energy is increased. Fig. 11, χ / ndf = 122272 / . 12. Fits discussedhere have χ / ndf = 1 – 2. While not perfect, these rea-sonable fits can be used to extract radii that characterizethe spacetime extent of the source.Figure 12 shows the excitation function of the threefemtoscopic radii for the HADES [52], E895 [53], STAR, and E866 [54] experiments. The comparison with datafrom E866 is complicated by several issues. Firstly, adifferent centrality definition was employed, and it is un-clear how to translate this into the more commonly-usedcharacterization of the fraction of the inelastic cross sec-tion. Secondly, the narrow spectrometer acceptance ofE866 did not cover midrapidity (it covered − . (cid:46) y (cid:46) − . 05) and has a higher transverse momentum lowerlimit. Thirdly, unlike the other results to which we com-pare (and most other measurements), the m T -dependentanalysis was not performed in the LCMS. Nevertheless,the E866 results with the closest event and track selec-tion criteria to the present results are included for con-text. The E895 and E866 points show a monotonicallydecreasing beam energy dependence. The fixed-targetSTAR points are consistent with this trend within theuncertainties.The R side radius primarily reflects the spatial extentof the pion emitting source, whereas R out convolves thiswith the emission duration of the fireball [67–69]. Figure13 shows the radii as functions of the transverse mass m T = (cid:112) m π + k , where m π is the pion mass. In or-der to match analysis cuts from the E866 data, here theSTAR points use a wider transverse momentum cut of0 . < p T < . c , and include events from the 0-15% centrality range. The decrease in R side and R out with increasing m T has been attributed to transverseflow, and the decrease in R long is attributed to longi-tudinal flow [61, 68]. High- m T pairs come from smallerregions within the source and do not reflect the system’soverall size [66]. The STAR points agree very well withthose from E895 and E866 for R side and R long , as wellas for R out at high m T . For R out the STAR points areslightly below E895 and E866 at low m T , but agree withinuncertainties.Figure 14 shows the centrality dependence of the radii.Here we combine π + π + and π − π − pairs and use the widertransverse momentum range of 0 . < p T < . c .The radii decrease for more peripheral events due to thesmaller geometric size of the initial participant region andthe subsequent emission region at freezeout.Figure 15 shows R side vs. R long for several differentdata sets: E895 Au+Au [53], STAR FXT Au+Au, STARBES-I Au+Au[66], and ALICE Pb+Pb[65]. STAR FXTand BES points use low- k T , π + π + and π − π − pion pairs,with (cid:104) k T (cid:105) ≈ (cid:104) k T (cid:105) of ≈ √ s NN ) corresponding to each ex-periment are indicated in GeV. The significantly differentacceptance and use of a different frame by E866 [54] af-fects the longitudinal radius in a way very different fromthat for the sideward. Hence, it makes little sense to in-clude E866 data in a graph which plots R side versus R long ;it is not shown in Fig. 15, which is a direct comparisonof similar measurements over three orders of magnitudein energy.2The figure indicates the prolateness/oblateness of thepion emitting source, as viewed from beside the beam. Ahigh R side and low R long indicates a very prolate source,whereas the reverse indicates an oblate source. Lower en-ergy collisions generally produce more prolate systems,and the shape of the emission region tends to becomemore oblate as the collision energy is increased. In thisrepresentation, the evolution follows a “swoosh” system-atic, indicated by the grey curve drawn to guide theeye. This trend reflects the evolution from stopping-dominated dynamics at low collision energies, to theapproximately longitudinally-boost-invariant scenario atthe highest energies. The STAR fixed-target point has R side ≈ R long ≈ . VI. SUMMARY In this first set of results from fixed-target running atthe STAR experiment, we report that the directed flow( v ) of protons and Λ baryons is in line with existingsystematics at higher and lower energy. This is criticallyimportant, as the directed flow of net baryons [24, 27]is one of the most intriguing experimental results fromthe BES program, as well as one of the most difficult formodels to explain.We have also presented the first measurements of az-imuthal anisotropy of charged pions and neutral kaonsat these energies. Both show directed flow ( v ) signalsin the direction opposite to that of the baryons, con-tinuing trends observed at higher energies. The differ-ence between π + and π − flow becomes stronger as thecollision energy is reduced, perhaps signaling importantisospin or Coulomb dynamics. Interestingly, within therelatively large statistical uncertainties, the data are con-sistent with constituent quark scaling of elliptic flow, aneffect proposed at much higher energies to arise fromquark coalescence in the QGP phase.Pion source radii based on femtoscopy agree quantita-tively with previous measurements at the AGS, and withthe broader systematic trends established at higher beamenergies. They signal a transition region between oblateand prolate spatial sources.Overall, while these measurements are important andof interest on their own, they also pave the way for theFXT energy scan with nominally one hundred times moreevents at each energy. The FXT energy scan is an inte-gral part of the BES-II program at RHIC which beganin early 2019. It extends the reach of the STAR experi-ment across an important energy regime of high baryonchemical potential, ranging from 420 to 720 MeV [70],corresponding to collision energies from 7.7 down to 3.0GeV. VII. ACKNOWLEDGEMENTS We acknowledge valuable discussions with YasushiNara and Horst St¨ocker. We thank the RHIC OperationsGroup and RCF at BNL, the NERSC Center at LBNL,and the Open Science Grid consortium for providing re-sources and support. This work was supported in partby the Office of Nuclear Physics within the U.S. DOE Of-fice of Science, the U.S. National Science Foundation, theMinistry of Education and Science of the Russian Fed-eration, National Natural Science Foundation of China,Chinese Academy of Science, the Ministry of Science andTechnology of China and the Chinese Ministry of Educa-tion, the Higher Education Sprout Project by Ministryof Education at NCKU, the National Research Founda-tion of Korea, Czech Science Foundation and Ministryof Education, Youth and Sports of the Czech Republic,Hungarian National Research, Development and Innova-tion Office, New National Excellency Programme of theHungarian Ministry of Human Capacities, Departmentof Atomic Energy and Department of Science and Tech-nology of the Government of India, the National ScienceCentre of Poland, the Ministry of Science, Education andSports of the Republic of Croatia, RosAtom of Russia andGerman Bundesministerium fur Bildung, Wissenschaft,Forschung and Technologie (BMBF), Helmholtz Associ-ation, Ministry of Education, Culture, Sports, Science,and Technology (MEXT) and Japan Society for the Pro-motion of Science (JSPS).3 [1] T. Galatyuk, Nucl. Phys. A982 , 163 (2019).[2] G. Rai et al. (E895 Collaboration), Nucl. Phys. A ,162 (1999).[3] J. Steinheimer, J. Auvinen, H. Petersen, M. Bleicher, andH. St¨ocker, Phys. Rev. C , 054913 (2014).[4] V. P. Konchakovski, W. Cassing, Y. B. Ivanov, and V. D.Toneev, Phys. Rev. C , 014903 (2014).[5] Y. B. Ivanov and A. A. Soldatov, Phys. Rev. C ,024915 (2015).[6] Y. Nara, H. Niemi, J. Steinheimer, and H. St¨ocker, Phys.Lett. B , 543 (2017).[7] S. Singha, P. Shanmuganathan, and D. Keane, Adv. HighEnergy Phys. , 2836989 (2016).[8] Y. Nara, H. Niemi, A. Ohnishi, J. Steinheimer, X. Luo,and H. St¨ocker, Eur. Phys. J. A , 18 (2018).[9] Y. Nara, T. Maruyama, and H. St¨ocker (2020),2004.05550.[10] J.-Y. Ollitrault, Phys. Rev. D , 229 (1992).[11] S. Voloshin and Y. Zhang, Z. Phys. C , 665 (1996).[12] A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C ,1671 (1998).[13] A. Bilandzic, R. Snellings, and S. Voloshin, Phys. Rev.C , 044913 (2011).[14] K. Meehan, Ph.D. thesis, University of California,Davis (2018), URL https://drupal.star.bnl.gov/STAR/files/FinalThesis.pdf .[15] E. G. Judd et al., Nucl. Instrum. and Meth. A , 228(2018).[16] W. Llope, Nucl. Instrum. and Meth. A , S110 (2012).[17] R. Ray and M. Daugherity, J. Phys. G , 125106 (2008).[18] M. Anderson et al., Nucl. Instrum. and Meth. A , 659(2003).[19] H. Bichsel, Nucl. Instrum. and Meth. A , 154 (2006).[20] D. Teaney and L. Yan, Phys. Rev. C , 064904 (2011).[21] M. Luzum and J.-Y. Ollitrault, Phys. Rev. Lett. ,102301 (2011).[22] C. A. Whitten, AIP Conference Proceedings , 390(2008).[23] G. Agakishiev et al. (STAR Collaboration), Phys. Rev.C , 014901 (2012).[24] L. Adamczyk et al. (STAR Collaboration), Phys. Rev.Lett. , 162301 (2014).[25] H. Liu et al. (E895 Collaboration), Phys. Rev. Lett. ,5488 (2000).[26] N. Borghini, P. M. Dinh, J.-Y. Ollitrault, A. M.Poskanzer, and S. A. Voloshin, Phys. Rev. C , 014901(2002).[27] L. Adamczyk et al. (STAR Collaboration), Phys. Rev.Lett. , 062301 (2018).[28] W. Reisdorf et al. (FOPI Collaboration), Nucl. Phys. A , 459 (2007).[29] S. Wang et al. (EOS Collaboration), Phys. Rev. Lett. ,2646 (1995).[30] K. Pearson, Philosophical Transactions of the Royal So-ciety of London. Series A, Containing Papers of a Math-ematical or Physical Character , 429 (1916).[31] B. I. Abelev et al. (STAR Collaboration), Science ,58 (2010).[32] P. Chung et al. (E895 Collaboration), Phys. Rev. Lett. , 2533 (2001).[33] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. , 052302 (2004).[34] J. Tian, J. Chen, Y. Ma, X. Cai, F. Jin, G. Ma, S. Zhang,and C. Zhong, Phys. Rev. C , 067901 (2009).[35] C. Pinkenburg et al. (E895 Collaboration), Phys. Rev.Lett. , 1295 (1999).[36] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C , 014902 (2013).[37] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C , 014907 (2016).[38] W. Reisdorf et al. (FOPI Collaboration), Nucl. Phys. A , 1 (2012).[39] A. Andronic et al. (FOPI Collaboration), Phys. Lett. B , 173 (2005).[40] P. Braun-Munzinger and J. Stachel, Nucl. Phys. A ,3c (1998).[41] H. Appelsh¨auser (CERES Collaboration), Nucl. Phys. A , 253 (2002).[42] C. Alt et al. (NA49 Collaboration), Phys. Rev. C ,034903 (2003).[43] A. Adare et al. (PHENIX Collaboration), Phys. Rev. C , 034913 (2015).[44] B. B. Back et al. (PHOBOS Collaboration), Phys. Rev.Lett. , 122303 (2005).[45] C. Adler et al. (STAR Collaboration), Phys. Rev. Lett. , 182301 (2001).[46] J. Adams et al. (STAR Collaboration), Phys. Rev. C 72 ,014904 (2005).[47] J. Adams et al. (STAR Collaboration), Phys. Rev. C ,044906 (2005).[48] M. A. Lisa, S. Pratt, R. Soltz, and U. Wiedemann, An-nual Review of Nuclear and Particle Science , 357(2005).[49] G. I. Kopylov and M. I. Podgoretsky, Sov. J. Nucl. Phys. , 219 (1972).[50] U. Heinz and B. V. Jacak, Annual Review of Nuclear andParticle Science , 529 (1999).[51] G. Goldhaber, S. Goldhaber, W. Lee, and A. Pais, Phys.Rev. , 300 (1960).[52] J. Adamczewski-Musch et al. (HADES), Phys. Lett. B , 446 (2019).[53] M. A. Lisa et al. (E895 Collaboration), Phys. Rev. Lett. , 2798 (2000).[54] L. Ahle et al. (E802 Collaboration), Phys. Rev. C ,054906 (2002).[55] C. Adler et al. (STAR Collaboration), Phys. Rev. Lett. , 082301 (2001).[56] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. , 012301 (2004).[57] S. Pratt, Phys. Rev. D , 1314 (1986).[58] G. Bertsch, M. Gong, and M. Tohyama, Phys. Rev. C , 1896 (1988).[59] S. Chapman, P. Scotto, and U. Heinz, Phys. Rev. Lett. , 4400 (1995).[60] U. Heinz, A. Hummel, M. A. Lisa, and U. A. Wiedemann,Phys. Rev. C , 044903 (2002).[61] A. Makhlin and Y. Sinyukov, Z. Phys. C , 69 (1988).[62] M. Bowler, Phys. Lett. B , 69 (1991).[63] Y. Sinyukov, R. Lednicky, S. Akkelin, J. Pluta, andB. Erazmus, Phys. Lett. B , 248 (1998).[64] B. I. Abelev et al. (STAR Collaboration), Phys. Rev. C , 024905 (2009). [65] A. Aamodt et al. (ALICE Collaboration), Phys. Lett. B , 328 (2011).[66] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C , 014904 (2015).[67] E. Mount, G. Graef, M. Mitrovski, M. Bleicher, andM. A. Lisa, Phys. Rev. C , 014908 (2011).[68] F. Reti`ere and M. A. Lisa, Phys. Rev. C , 044907 (2004).[69] D. Rischke and M. Gyulassy, Nucl. Phys. A , 479(1996).[70] J. Cleymans, H. Oeschler, K. Redlich, and S. Wheaton,Phys. Rev. C73