Beam-Energy Dependence of the Directed Flow of Deuterons in Au+Au Collisions
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, 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, 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, Y. Hu, H. Z. Huang, et al. (264 additional authors not shown)
BBeam-Energy Dependence of the Directed Flow of Deuterons in Au+Au Collisions
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 ,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 , 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 , 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. Kikoła , C. Kim , B. Kimelman , D. Kincses ,T. A. Kinghorn , I. Kisel , A. Kiselev , M. Kocan , L. Kochenda , L. K. Kosarzewski , L. Kramarik , P. Kravtsov ,K. Krueger , N. Kulathunga Mudiyanselage , L. Kumar , S. 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 , N. G. Minaev , S. Mioduszewski , B. Mohanty , 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 , 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 , A. I. Sheikh , 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 , C. Zhang , 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 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 ] J u l 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 (STAR Collaboration) (Dated: July 10, 2020)We present a measurement of the first-order azimuthal anisotropy, v , of deuterons from Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV recorded with the STAR experiment at the Relativistic Heavy IonCollider (RHIC). The energy dependence of the v ( y ) slope, dv /dy | y =0 , for deuterons, where y is the rapidity,is extracted for semi-central collisions (10-40% centrality) and compared to that of protons. While the v ( y ) slopes of protons are generally negative for √ s NN >
10 GeV, those for deuterons are consistent with zero, astrong enhancement of the v ( y ) slope of deuterons is seen at the lowest collision energy (the largest baryondensity) at √ s NN = v for protonsand deuterons. The experimental results are compared with transport and coalescence models. I. INTRODUCTION
One of the main goals of high-energy heavy-ion collisionexperiments is to explore the state and evolution of nuclearmatter under extreme conditions. These experiments measurethe multiplicities of many different particle species and thecorrelations between these particles. The correlations betweenthe azimuthal angles of these particles are particularly infor-mative. The directed flow, v , and the elliptic flow, v , arethe first and second harmonic coefficients of the Fourier ex-pansion of the particle azimuthal distributions in momentumspace relative to the reaction-plane [1]. The reaction-plane isdefined by the beam direction and the impact parameter. Thedirected flow has two components: a rapidity-even function, v even1 , and a rapidity-odd function, v odd1 . The values of v even1 represent the contribution from event-by-event initial nucleigeometry fluctuations [2, 3]. This work will focus on therapidity-odd component. The values of v as a function ofrapidity, y , are sensitive to the amount of expansion the colli-sion system goes through during the early collision stages [4].The RHIC has completed the first phase of the BeamEnergy Scan (BES) program [5]. The directed flow v ( y ) asa function of rapidity, y , for different mesons and baryonshas been measured in Au+Au collisions over the range ofbeam energies of √ s NN = dv /dy | y =0 at mid-rapidity for net-protons and net- Λ hyperons as a function of collision energy show a min-imum around √ s NN = 10-20 GeV. According to a hydro-dynamic model [8], a minimum dv /dy | y =0 of net-baryonsas a function of collision energy is a signature of a first-order phase transition between hadronic matter and the quarkgluon plasma. However, no existing hydrodynamic modelcan quantitatively reproduce the measured magnitudes of themeson and baryon directed flow [6, 7].Besides the charged hadrons, a large number of light nucleiare produced in heavy-ion collisions. Their production issensitive to the properties of cluster formation and fireballevolution [9–13]. There are two commonly-used and verydifferent phenomenological pictures for the mechanisms gov-erning the production of light nuclei. The thermal modeldescribes deuteron production as occurring throughout thewhole time evolution of the fireball up to chemical freeze-out via elementary nucleon-nucleon and/or parton-parton in-teractions [10, 14, 15]. Such models are able to reproduce theobserved deuteron multiplicities [16, 17]. It is, however, dif-ficult to understand how deuterons formed in the intermediatestages of the collisions can survive the subsequent evolution,as their binding energy (2 MeV) is so small compared tothe fireball temperature ( ∼
150 MeV [18]). Another modeldescribes deuteron production as occurring much later in the collision, near kinetic freeze-out, when the temperatures aremuch lower [19–23]. This is the coalescence model, in whichtwo nucleons that are near each other in space and travelingwith similar velocities, can form a deuteron. Thus, themomentum distribution of these formed deuterons is stronglyrelated to that of protons. The comparison of light nucleusdirected flow with that of protons can provide additionalinformation to understand the mechanisms involved in lightnucleus production in high-energy heavy-ion collisions.Both the EOS and FOPI collaborations observed energydependence of the directed flow for protons and deuteronsfrom Au+Au collisions for lab kinetic energies of . A GeVto . A GeV [24–26]. These observations suggest that thedirected flow of deuterons has a more pronounced energydependence than that of protons. Thus, the light nucleusdirected flow may provide a more sensitive measure of thecollective motion than the lighter hadrons.In this paper, we present the measurement of the directedflow for deuterons in Au+Au collisions at √ s NN = 7.7,11.5, 14.5, 19.6, 27, and 39 GeV from the STAR experi-ment. The results are discussed and compared with AMPT (AMulti-Phase Transport) calculation and a simple coalescencemodel [27]. II. EXPERIMENT AND DATA ANALYSIS
The data used here are for Au+Au collisions at beamenergies of √ s NN = 7.7, 11.5, 14.5, 19.6, 27, and 39 GeVcollected by the STAR experiment [28] at the RHIC facility.A minimum bias trigger was used. The 7.7, 11.5, and 39GeV data were recorded in 2010. The 19.6 and 27 GeV datawere recorded in 2011, and the 14.5 GeV data were recordedin 2014. The STAR experiment consists of a solenoidalmagnet and different detectors for tracking, triggering, andparticle identification (PID). The Time Projection Chamber(TPC) [29] is a charged-particle tracking device which coversthe full azimuth and a pseudo-rapidity range | η | < . Chargedparticle trajectories are reconstructed with the TPC, and themomentum components are obtained from the curvature ofthe helical path in the 0.5 Tesla magnetic field. The twomomentum components in the plane transverse to the beam-line define the azimuthal angle of each track. The maindetectors used for PID are the TPC and the Time-of-Flightsystem (TOF) [30]. The details of other STAR detectors aredescribed elsewhere [28]. A. Event and Track Selection
For each event, the location of the primary vertex can bereconstructed in three dimensions by extrapolating the TPCtrack segments to the beam-axis. The primary vertex isrequired to be within certain distances of the center of STARin the directions along the beam axis, v z , and transverse to it, v r , as listed in Table I. TABLE I. The event selection quality cuts v z and v r (see text), thenumber of events, and the baryon chemical potential, µ B [31], ateach of the different collision energies studied here. The center oftransverse radial position is located at ( v x , v y ) = (0, -0.89 cm) for14.5 GeV. √ s NN (GeV) | v z | (cm) v r (cm) Events( × ) µ B (MeV)7.7 70 2 4 42011.5 50 2 12 31514.5 50 1 11 26019.6 50 2 36 20527 50 2 70 15539 40 2 130 115 The reconstructed tracks used in this analysis were requiredto pass basic quality cuts, including having at least 15 TPCspace points assigned to them. Each track is also requiredto extrapolate to within 1 cm of the primary vertex location(distance of closest approach DCA), and has assigned to itat least half of the possible number of TPC space points(maximum 45) for its trajectory.The centrality of each event is determined by comparingthe charged particle multiplicity measured in the event to aMonte-Carlo Glauber reference [32]. The results presentedin this paper use the 10-40% intermediate centrality regionwhere the v ( y ) measurements are the most significant. Thefirst-order event plane resolution, and v itself, in more centralcollisions are relatively smaller, while the deuteron yields arealso relatively smaller in more peripheral collisions. B. Particle Identification
We use a combination of the TPC and the TOF for theidentification of charged particles. Figure 1(a) shows the av-erage dE/dx distribution of measured charged tracks versusmomentum at √ s NN = (cid:104) dE/dx B (cid:105) , for each species [33].For each track, the particle speed divided by the speedof light, β = v/c , can be measured by the combinationof the TPC and TOF systems. The TOF thus provides ameasurement of the track mass-squared, m , according to m = p (cid:18) β − (cid:19) , (1)where p is the track momentum measured in the TPC. Fig-ure 1(b) shows the m distribution as a function of momentum p (GeV/c) ( ke V / c m ) æ d E / d x Æ (a) + p + K p d p (GeV/c) ) / c ( G e V m (b) + p + K p d
FIG. 1. (a) The (cid:104) dE/dx (cid:105) of charged tracks versus momentum inAu+Au collisions at √ s NN = m versus momentum at √ s NN = π + , K + , protons, and deuterons, respectively. at √ s NN = / c < m < / c .The selection of deuteron tracks using the TPC (cid:104) dE/dx (cid:105) proceeds via the variable z , defined as [34], z = ln (cid:18) (cid:104) dE/dx (cid:105)(cid:104) dE/dx B (cid:105) (cid:19) . (2)When using the Bichsel prediction, (cid:104) dE/dx B (cid:105) , for deuteronsin Eq. 2 ( cf. Fig. 1), the deuterons are those tracks with valuesof z near zero. Figure 2 shows the z distributions in different p T ranges at √ s NN = | z | < z - - - C oun t s
10 < 1.0 GeV/c T z - - - C oun t s
10 < 1.5 GeV/c T z - - - C oun t s
10 < 2.5 GeV/c T z - - - C oun t s
10 < 4.0 GeV/c T FIG. 2. The z distribution for deuteron in various p T ranges inAu+Au collisions at √ s NN = π + , K + ,and protons. In Ref. [6], the v ( y ) of protons was measured over therange of 0.4 GeV/ c < p T < c . For the deuterons inthis analysis, the transverse momentum range is restricted tothe same range in terms of p T /A, or 0.8 GeV/ c < p T < c . The default rapidity window for extracting the v ( y ) slope is | y | < . . C. Event Plane
The reaction-plane angle, Ψ R , is the azimuth of the planespanned by the beam direction and the impact parameter vec-tor. The v of the produced particles with respect to Ψ R can bemeasured as v = (cid:104) cos( φ − Ψ R ) (cid:105) , where φ is the azimuthalangle of the produced particle and the angle brackets implyaveraging over all the particles in all events. As the reaction-plane angle, Ψ R , cannot be measured directly, we will usethe event-plane angle [1] to estimate the reaction-plane angle Ψ R . The event-plane was estimated using the v informationof the final-state particles, and hence is called the first-orderevent-plane ( Ψ ). The self-correlations were eliminated withthe large acceptance gap between the TPC, where the deuterondirected flow was measured, and the detectors measuring thefinal-state particles used to calculate Ψ .Two beam-beam counters (BBCs) [35] were used to re-construct the values of Ψ . The distribution of reconstructed Ψ values is not uniform due to imperfections in the BBCs.Therefore, a shifting method [1] was applied to flatten thedistributions. The finite multiplicity of particles in each eventlimits the precision of estimating the true reaction-plane viathe reconstructed Ψ , so the values of v have been correctedfor the event plane resolution : v = (cid:104) cos( φ − Ψ ) (cid:105) /R .The resolution correction factor, R , is determined by thesub-event plane correlation method [1], where the sub-eventplanes are reconstructed separately in the east and west BBCs.Figure 3 shows the R values as a function of the collisioncentrality at each collision energy. The resolution peaksin mid-central collisions. The resolution improves as thecollision energy decreases due to the stronger directed flowat the rapidity ranges covered by the BBC detectors. D. Systematic Uncertainties
The systematic uncertainties on the directed flow are esti-mated by varying the criteria used to select tracks and identifyparticles. The absolute difference between the results usingthe default and the varied criteria is quoted as the systematicuncertainty. The systematic uncertainty related to the trackselection procedure is estimated by varying the DCA (from1 to 0.5 and 2 cm) and the number of TPC space points(from 15 to 20). Additional systematic uncertainties arisingfrom the particle misidentification are estimated by varyingthe PID cuts on z and m . The systematic uncertainty corre-sponding to the chosen range of the dv /dy fit is estimatedby taking the difference between the best fitted slope, andthe value of the slope within | y | < . . It is the choiceof the dv /dy fit range that makes the largest contributionto the total systematic uncertainties. Non-flow contributionsto the systematic uncertainty are reduced due to the large Collision Centrality(%) R es o l u t i on Y FIG. 3. The values of the first-order event plane ( Ψ ) resolution R as a function of the centrality of Au+Au collisions at √ s NN = 7.7,11.5, 14.5, 19.6, 27, and 39 GeV. The Ψ was reconstructed withthe BBCs and its resolution is determined by the correlation of thesub-event-plane angles determined separately by the east and westBBCs. Data presented later (10-40% centrality) are indicated by thedashed-line box. pseudo-rapidity gap between the TPC and BBC detectors.The possible systematic uncertainty from the first-order event-plane resolution estimation is discussed in [6] and included inthe total systematic uncertainties. All the sources are addedin quadrature as the final total systematic uncertainties, whichare of a similar magnitude as the statistical uncertainties. III. RESULTS AND DISCUSSION
Figure 4 shows the rapidity dependence of the directedflow, v , of protons and deuterons at each of the studiedcollision energies. The v ( y ) of deuterons is antisymmetricabout y = 0 . As with the protons, the v ( y ) of deuteronsincreases monotonically with increasing rapidity at √ s NN = v dependence on rapidity fordeuterons than for protons. The limited event statistics andrelatively lower deuteron production rate at higher energiesmakes such comparisons less certain.The v ( y ) slope at mid-rapidity ( y < | . | ) is obtained byfitting the data with a straight line. For √ s NN > v ( y ) slope is mainly influenced by the twodata points at the extreme rapidity bins. Figure 5 presentsthe resulting values of the v ( y ) slope versus the collisionenergy for 10-40% central collisions. A significantly largerdeuteron v ( y ) slope with respect to protons is observed at √ s NN = v ( y ) slope is observed tobe consistent with zero at all energies above 7.7 GeV, but withlarge uncertainties.The results from the data were compared to those from theAMPT model [27]. This is a hybrid model which has beenused to describe the charged particle multiplicity, transversemomentum, and the elliptic flow of identified particles inrelativistic heavy-ion collisions. In this model, scattering Particle Rapidity (y) v - - Au+Au 10-40% - - - - - - - protondeuteron - - - - - FIG. 4. Rapidity dependence of v for protons [7] (open squares)and deuterons (solid circles) in 10-40% Au+Au collisions at √ s NN = 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV. The dot-dashed and dashedlines are fits to proton and deuteron v , respectively, at midrapidity( | y | < . ) with a linear function to extract the slopes. The plotteduncertainties are statistical only. among hadrons is described by ART (A Relativistic Trans-port) model [36]. The deuterons are produced and dissolvedwithin ART via nuclear reactions. The centrality of the simu-lated events is determined by integrating the charged particlemultiplicity distribution, as was done for the experimentaldata. The comparison between data and the AMPT modelresult can be seen in Fig. 5. A decreasing trend for increasingcollision energies is seen in the AMPT simulation, while themodel significantly overpredicts the observed magnitude ofthe deuteron directed flow slope.A commonly-applied picture for light nucleus productionin heavy-ion collisions involves the coalescence of nucleonswhich are close to each other in space and have similarvelocities. Then, the spectral distribution of a light nu-cleus, d N A /d p A , depends on the distributions of protons, d N p /d p p , and neutrons, d N n /d p n , [21], E A d N A d p A ∝ (cid:16) E p d N p d p p (cid:17) Z (cid:16) E n d N n d p n (cid:17) A − Z , (3)where A and Z are nucleus mass number and charge number,respectively. In this production mechanism, the expectedvalue of the light nucleus directed flow can be expressed asa function of the directed flow of its constituent nucleons. As-suming the protons and neutrons flow similarly, the deuteron (GeV) NN sCollision Energy y = / d y ) ( d v FIG. 5. Directed flow slope at mid-rapidity, dv /dy | y =0 , as afunction of beam energy in 10-40% Au+Au collisions. Solid circlesrepresent deuterons. Open squares are the published results in [7]for protons. The band denotes the results for deuterons from AMPTtransport model. Statistical uncertainties (bars) and systematic un-certainties (horizontal brackets) are shown separately. For visibility,the data points are staggered horizontally. v is given by [37]: v ,d ( y, p T ) = 2 v ,p ( y, p T )1 + 2 v ,p ( y, p T ) , (4)where each constituent nucleon has half the p T and the samerapidity as the deuteron. Then one can calculate the expected v for the deuterons from the measured v for protons [7],assuming as usual the (unmeasured) neutron flow is the sameas that of the (measured) protons. As the proton v (cid:28) , Eq. 4can be simplified as v ,d ( y, p T ) ≈ v ,p ( y, p T . (5)This indicates that, in the coalescence mechanism, the v ofprotons and deuterons will follow an atomic mass-numberscaling. In fact, Eq. 4 and Eq. 5 can be applied to anyanisotropy coefficient. For the elliptic flow of light nuclei,the STAR collaboration has observed such a mass-numberscaling in √ s NN = v ( y ) slope for deuteronswould have the same sign as that observed for the protonsand have a larger magnitude. In Fig. 5, within the statisticaland systematic uncertainties, the deuteron v ( y ) slope at mid-rapidity is consistent with this expectation at √ s NN = √ s NN > v ( y ) slopes have adifferent sign than the corresponding proton v ( y ) slopes withlarge uncertainties.To further test the coalescence model, we studied the p T dependence of the directed flow, v , at all measured energies,which is shown in Fig. 6. At √ s NN = v ( p T ) indicate a mass-number scaling for p T /A > GeV/ c within | y | < . , while the value of the deuteron v /A showsan enhancement towards lower p T /A . This enhancement is /A (GeV/c) T p / A v Au+Au 10-40% - -
27 GeV protondeuteron - -
39 GeV
FIG. 6. The p T dependence of v /A in | y | < . for protons (opensquares) and deuterons (solid circles) in 10-40% Au+Au collisionsat √ s NN = 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV. Statisticaluncertainties (bars) and systematic uncertainties (horizontal lines)are shown separately. not caused by the knock-out deuteron background with itsnegligible production at √ s NN = v ( p T ) of deuterons, tritons, He , and He at p T < . GeV/ c in Au+Au collisions at a beam energy of 10.8 A GeV [39]. The cause of the low p T enhancement of thedeuteron v in the √ s NN = IV. SUMMARY
In summary, we present the mid-rapidity directed flow v ( y ) of deuterons in Au+Au collisions at √ s NN = v ( y ) slope, dv /dy | y =0 ,shows a strong increase at the lowest collision energy of √ s NN = v ( y ) slopes at mostmeasured collision energies. The coalescence model fordeuteron production predicts an atomic-mass-number scalingof the proton and deuteron v . At √ s NN = v ( p T ) data at higher p T within | y | < v ( p T ) show enhancements towardsvery low p T . There is at present no explanation for thisenhancement. Stronger conclusions will be possible withthe event statistics achieved with the Beam Energy Scan IIprogram. ACKNOWLEDGEMENT
We thank the RHIC Operations Group and RCF at BNL,the NERSC Center at LBNL, and the Open Science Gridconsortium for providing resources and support. This workwas supported in part by the Office of Nuclear Physics withinthe U.S. DOE Office of Science, the U.S. National ScienceFoundation, the Ministry of Education and Science of theRussian Federation, National Natural Science Foundation ofChina, Chinese Academy of Science, the Ministry of Sci-ence and Technology of China and the Chinese Ministry ofEducation, the Higher Education Sprout Project by Ministryof Education at NCKU, the National Research Foundation ofKorea, Czech Science Foundation and Ministry of Education,Youth and Sports of the Czech Republic, Hungarian NationalResearch, Development and Innovation Office, New NationalExcellency Programme of the Hungarian Ministry of HumanCapacities, Department of Atomic Energy and Departmentof Science and Technology of the Government of India, theNational Science Centre of Poland, the Ministry of Science,Education and Sports of the Republic of Croatia, RosAtomof Russia and German Bundesministerium fur Bildung, Wis-senschaft, Forschung and Technologie (BMBF), HelmholtzAssociation, Ministry of Education, Culture, Sports, Science,and Technology (MEXT) and Japan Society for the Promotionof Science (JSPS). [1] A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C , 1671(1998).[2] D. Teaney and L. Yan, Phys. Rev. C , 064904 (2011).[3] M. Luzum and J. Y. Ollitrault, Phys. Rev. Lett. , 102301(2011).[4] P. Bo ˙z ek and I. Wyskiel, Phys. Rev. C , 054902 (2010).[5] M. Aggarwal et al. (STAR Collaboration), arXiv:1007.2613(2010). [6] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. Lett. ,162301 (2014).[7] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. Lett. ,062301 (2018).[8] H. St ¨o cker, Nucl. Phys. A , 121 (2005).[9] J. I. Kapusta, Phys. Rev. C , 1301 (1980).[10] A. Z. Mekjian, Phys. Rev. C , 1051 (1978).[11] L. P. Csernai and J. I. Kapusta, Phys. Rep. , 223(1986). [12] R. Mattiello, H. Sorge, H. St ¨o cker, and W. Greiner, Phys. Rev.C , 1443 (1997).[13] K. J. Sun, L. W. Chen, C. M. Ko, and Z. Xu, Phys. Lett. B ,103 (2017).[14] P. Braun-Munzinger and J. Stachel, J. Phys. G , L17 (1995).[15] S. Chatterjee and B. Mohanty, Phys. Rev. C , 034908 (2014).[16] A. Andronic, P. Braun-Munzinger, J. Stachel, and H. St ¨o cker,Phys. Lett. B , 203 (2011).[17] J. Cleymans, S. Kabana, I. Kraus, H. Oeschler, K. Redlich, andN. Sharma, Phys. Rev. C , 054916 (2011); J. H. Chen, D.Keane, Y. G. Ma, A. H. Tang, and Z. B. Xu, Phys. Rep. , 1(2018).[18] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C ,044904 (2017).[19] S. T. Butler and C. A. Pearson, Phys. Rev. , 836 (1963).[20] H. H. Gutbrod et al. , Phys. Rev. Lett. , 667 (1976).[21] H. Sato and K. Yazaki, Phys. Lett. B , 153 (1981).[22] S. Zhang, J. H. Chen, H. Crawford, D. Keane, Y. G. Ma, and Z.B. Xu, Phys. Lett. B , 224 (2010).[23] J. Steinheimer, K. Gudima, A. Botvina, I. Mishustin, M. Ble-icher, and H. St ¨o cker, Phys. Lett. B , 85 (2012).[24] M. D. Partlan et al. (EOS Collaboration), Phys. Rev. Lett. ,2100 (1995).[25] S. Wang et al. (EOS Collaboration), Phys. Rev. Lett. , 2646(1995). [26] W. Reisdorf et al. (FOPI Collaboration), Nucl. Phys. A , 1(2012).[27] Z. W. Lin, C. M. Ko, B. A. Li, B. Zhang, and S. Pal, Phys. Rev.C , 064901 (2005).[28] K. H. Ackermann et al. , Nucl. Instrum. Methods A , 624(2003).[29] M. Anderson et al. , Nucl. Instrum. Methods A , 659 (2003).[30] W. J. Llope, Nucl. Instrum. Methods A , S110 (2012).[31] J. Cleymans, H. Oeschler, K. Redlich, and S. Wheaton, Phys.Rev. C , 034905 (2006).[32] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C ,054908 (2012).[33] H. Bichsel, Nucl. Instrum. Methods A , 154 (2006).[34] J. Adam et al. (STAR Collaboration), Phys. Rev. C , 064905(2019).[35] C. A. Whitten Jr., (STAR Collaboration) AIP Conf. Proc.
390 (2008).[36] B. A. Li and C. M. Ko, Phys. Rev. C , 2037 (1995).[37] D. Moln ´a r and S. A. Voloshin, Phys. Rev. Lett. , 092301(2003).[38] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C ,034908 (2016).[39] J. Barrette et al. (E877 Collaboration), Phys. Rev. C59