Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions
STAR Collaboration, L. Adamczyk, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, A. Aparin, D. Arkhipkin, E. C. Aschenauer, G. S. Averichev, Bairathi, A. Banerjee, R. Bellwied, A. Bhasin, A. K. Bhati, P. Bhattarai, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, J. Bouchet, A. V. Brandin, I. Bunzarov, T. P. Burton, J. Butterworth, H. Caines, M. Calderón de la Barca Sánchez, J. M. Campbell, D. Cebra, M. C. Cervantes, I. Chakaberia, P. Chaloupka, Z. Chang, S. Chattopadhyay, J. H. Chen, X. Chen, J. Cheng, M. Cherney, W. Christie, G. Contin, H. J. Crawford, S. Das, L. C. De Silva, R. R. Debbe, T. G. Dedovich, J. Deng, A. A. Derevschikov, B. di Ruzza, L. Didenko, C. Dilks, X. Dong, J. L. Drachenberg, J. E. Draper, C. M. Du, L. E. Dunkelberger, J. C. Dunlop, L. G. Efimov, J. Engelage, G. Eppley, R. Esha, O. Evdokimov, O. Eyser, R. Fatemi, S. Fazio, P. Federic, J. Fedorisin, Z. Feng, P. Filip, Y. Fisyak, C. E. Flores, L. Fulek, C. A. Gagliardi, D. Garand, F. Geurts, A. Gibson, M. Girard, L. Greiner, D. Grosnick, D. S. Gunarathne, Y. Guo, A. Gupta, S. Gupta, W. Guryn, A. Hamad, A. Hamed, R. Haque, J. W. Harris, L. He, S. Heppelmann, S. Heppelmann, A. Hirsch, G. W. Hoffmann, D. J. Hofman, S. Horvat, B. Huang, X. Huang, H. Z. Huang, P. Huck, et al. (235 additional authors not shown)
OObservation of charge asymmetry dependence of pion elliptic flow and the possiblechiral magnetic wave in heavy-ion collisions
L. Adamczyk, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, A. Aparin, D. Arkhipkin, E. C. Aschenauer, G. S. Averichev, A. Banerjee, R. Bellwied, A. Bhasin, A. K. Bhati, P. Bhattarai, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, J. Bouchet, A. V. Brandin, I. Bunzarov, T. P. Burton, J. Butterworth, H. Caines, M. Calder´on de la Barca S´anchez, J. M. Campbell, D. Cebra, M. C. Cervantes, I. Chakaberia, P. Chaloupka, Z. Chang, S. Chattopadhyay, J. H. Chen, X. Chen, J. Cheng, M. Cherney, W. Christie, G. Contin, H. J. Crawford, S. Das, L. C. De Silva, R. R. Debbe, T. G. Dedovich, J. Deng, A. A. Derevschikov, B. di Ruzza, L. Didenko, C. Dilks, X. Dong, J. L. Drachenberg, J. E. Draper, C. M. Du, L. E. Dunkelberger, J. C. Dunlop, L. G. Efimov, J. Engelage, G. Eppley, R. Esha, O. Evdokimov, O. Eyser, R. Fatemi, S. Fazio, P. Federic, J. Fedorisin, Z. Feng, P. Filip, Y. Fisyak, C. E. Flores, L. Fulek, C. A. Gagliardi, D. Garand, F. Geurts, A. Gibson, M. Girard, L. Greiner, D. Grosnick, D. S. Gunarathne, Y. Guo, S. Gupta, A. Gupta, W. Guryn, A. Hamad, A. Hamed, R. Haque, J. W. Harris, L. He, S. Heppelmann, S. Heppelmann, A. Hirsch, G. W. Hoffmann, D. J. Hofman, S. Horvat, H. Z. Huang, B. Huang, X. Huang, P. Huck, T. J. Humanic, G. Igo, W. W. Jacobs, H. Jang, K. Jiang, E. G. Judd, S. Kabana, D. Kalinkin, K. Kang, K. Kauder, H. W. Ke, D. Keane, A. Kechechyan, Z. H. Khan, D. P. Kikola, I. Kisel, A. Kisiel, D. D. Koetke, T. Kollegger, L. K. Kosarzewski, L. Kotchenda, A. F. Kraishan, P. Kravtsov, K. Krueger, I. Kulakov, L. Kumar, R. A. Kycia, M. A. C. Lamont, J. M. Landgraf, K. D. Landry, J. Lauret, A. Lebedev, R. Lednicky, J. H. Lee, W. Li, Y. Li, C. Li, Z. M. Li, X. Li, X. Li, M. A. Lisa, F. Liu, T. Ljubicic, W. J. Llope, M. Lomnitz, R. S. Longacre, X. Luo, L. Ma, R. Ma, Y. G. Ma, G. L. Ma, N. Magdy, R. Majka, A. Manion, S. Margetis, C. Markert, H. Masui, H. S. Matis, D. McDonald, K. Meehan, N. G. Minaev, S. Mioduszewski, B. Mohanty, M. M. Mondal, D. A. Morozov, M. K. Mustafa, B. K. Nandi, Md. Nasim, T. K. Nayak, G. Nigmatkulov, L. V. Nogach, S. Y. Noh, J. Novak, S. B. Nurushev, G. Odyniec, A. Ogawa, K. Oh, V. Okorokov, D. L. Olvitt Jr., B. S. Page, R. Pak, Y. X. Pan, Y. Pandit, Y. Panebratsev, B. Pawlik, H. Pei, C. Perkins, A. Peterson, P. Pile, M. Planinic, J. Pluta, N. Poljak, K. Poniatowska, J. Porter, M. Posik, A. M. Poskanzer, N. K. Pruthi, J. Putschke, H. Qiu, A. Quintero, S. Ramachandran, S. Raniwala, R. Raniwala, R. L. Ray, H. G. Ritter, J. B. Roberts, O. V. Rogachevskiy, J. L. Romero, A. Roy, L. Ruan, J. Rusnak, O. Rusnakova, N. R. Sahoo, P. K. Sahu, I. Sakrejda, S. Salur, J. Sandweiss, A. Sarkar, J. Schambach, R. P. Scharenberg, A. M. Schmah, W. B. Schmidke, N. Schmitz, J. Seger, P. Seyboth, N. Shah, E. Shahaliev, P. V. Shanmuganathan, M. Shao, B. Sharma, M. K. Sharma, W. Q. Shen, S. S. Shi, Q. Y. Shou, E. P. Sichtermann, R. Sikora, M. Simko, M. J. Skoby, D. Smirnov, N. Smirnov, L. Song, P. Sorensen, H. M. Spinka, B. Srivastava, T. D. S. Stanislaus, M. Stepanov, R. Stock, M. Strikhanov, B. Stringfellow, M. Sumbera, B. J. Summa, X. Sun, X. M. Sun, Z. Sun, Y. Sun, B. Surrow, D. N. Svirida, M. A. Szelezniak, Z. Tang, A. H. Tang, T. Tarnowsky, A. N. Tawfik, J. H. Thomas, A. R. Timmins, D. Tlusty, M. Tokarev, S. Trentalange, R. E. Tribble, P. Tribedy, S. K. Tripathy, B. A. Trzeciak, O. D. Tsai, T. Ullrich, D. G. Underwood, I. Upsal, G. Van Buren, G. van Nieuwenhuizen, M. Vandenbroucke, R. Varma, A. N. Vasiliev, R. Vertesi, F. Videbaek, Y. P. Viyogi, S. Vokal, S. A. Voloshin, A. Vossen, F. Wang, Y. Wang, H. Wang, J. S. Wang, Y. Wang, G. Wang, G. Webb, J. C. Webb, L. Wen, G. D. Westfall, H. Wieman, S. W. Wissink, R. Witt, Y. F. Wu, Z. Xiao, W. Xie, K. Xin, Y. F. Xu, N. Xu, Z. Xu, Q. H. Xu, H. Xu, Y. Yang, Y. Yang, C. Yang, S. Yang, Q. Yang, Z. Ye, P. Yepes, L. Yi, K. Yip, I. -K. Yoo, N. Yu, H. Zbroszczyk, W. Zha, X. P. Zhang, J. B. Zhang, J. Zhang, Z. Zhang, S. Zhang, Y. Zhang, J. L. Zhang, F. Zhao, J. Zhao, C. Zhong, L. Zhou, X. Zhu, Y. Zoulkarneeva, and M. Zyzak (STAR Collaboration) AGH University of Science and Technology, Cracow 30-059, Poland Argonne National Laboratory, Argonne, Illinois 60439, USA Brookhaven National Laboratory, Upton, New York 11973, USA University of California, Berkeley, California 94720, USA University of California, Davis, California 95616, USA a r X i v : . [ nu c l - e x ] M a y University of California, Los Angeles, California 90095, USA Central China Normal University (HZNU), Wuhan 430079, China University of Illinois at Chicago, Chicago, Illinois 60607, USA Creighton University, Omaha, Nebraska 68178, USA Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic Nuclear Physics Institute AS CR, 250 68 ˇReˇz/Prague, Czech Republic Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany Institute of Physics, Bhubaneswar 751005, India Indian Institute of Technology, Mumbai 400076, India Indiana University, Bloomington, Indiana 47408, USA Alikhanov Institute for Theoretical and Experimental Physics, Moscow 117218, Russia University of Jammu, Jammu 180001, India Joint Institute for Nuclear Research, Dubna, 141 980, Russia Kent State University, Kent, Ohio 44242, USA University of Kentucky, Lexington, Kentucky, 40506-0055, USA Korea Institute of Science and Technology Information, Daejeon 305-701, Korea Institute of Modern Physics, Lanzhou 730000, China Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Max-Planck-Institut fur Physik, Munich 80805, Germany Michigan State University, East Lansing, Michigan 48824, USA Moscow Engineering Physics Institute, Moscow 115409, Russia National Institute of Science Education and Research, Bhubaneswar 751005, India Ohio State University, Columbus, Ohio 43210, USA Institute of Nuclear Physics PAN, Cracow 31-342, Poland Panjab University, Chandigarh 160014, India Pennsylvania State University, University Park, Pennsylvania 16802, USA Institute of High Energy Physics, Protvino 142281, Russia Purdue University, West Lafayette, Indiana 47907, USA Pusan National University, Pusan 609735, Republic of Korea University of Rajasthan, Jaipur 302004, India Rice University, Houston, Texas 77251, USA University of Science and Technology of China, Hefei 230026, China Shandong University, Jinan, Shandong 250100, China Shanghai Institute of Applied Physics, Shanghai 201800, China Temple University, Philadelphia, Pennsylvania 19122, USA Texas A&M University, College Station, Texas 77843, USA University of Texas, Austin, Texas 78712, USA University of Houston, Houston, Texas 77204, USA Tsinghua University, Beijing 100084, China United States Naval Academy, Annapolis, Maryland, 21402, USA Valparaiso University, Valparaiso, Indiana 46383, USA Variable Energy Cyclotron Centre, Kolkata 700064, India Warsaw University of Technology, Warsaw 00-661, Poland Wayne State University, Detroit, Michigan 48201, USA World Laboratory for Cosmology and Particle Physics (WLCAPP), Cairo 11571, Egypt Yale University, New Haven, Connecticut 06520, USA University of Zagreb, Zagreb, HR-10002, Croatia
We present measurements of π − and π + elliptic flow, v , at midrapidity in Au+Au collisions at √ s NN = 200, 62.4, 39, 27, 19.6, 11.5 and 7.7 GeV, as a function of event-by-event charge asymmetry, A ch , based on data from the STAR experiment at RHIC. We find that π − ( π + ) elliptic flow linearlyincreases (decreases) with charge asymmetry for most centrality bins at √ s NN = 27 GeV and higher.At √ s NN = 200 GeV, the slope of the difference of v between π − and π + as a function of A ch exhibits a centrality dependence, which is qualitatively similar to calculations that incorporate achiral magnetic wave effect. Similar centrality dependence is also observed at lower energies. PACS numbers: 25.75.Ld
In heavy-ion collisions at the Relativistic Heavy IonCollider (RHIC) and the Large Hadron Collider (LHC),energetic spectator protons produce a strong magneticfield reaching eB y ≈ m π [1], or ∼ × T. The in- terplay between the magnetic field and the quark-gluonmatter created in these collisions might result in two phe-nomena: the chiral magnetic effect (CME) and the chiralseparation effect (CSE). The CME is the phenomenonof electric charge separation along the axis of the mag-netic field in the presence of a finite axial chemical po-tential [1–5]. The STAR [6–9] and PHENIX [10, 11] Col-laborations at the RHIC and the ALICE Collaborationat the LHC [12] have reported experimental observationsof charge separation fluctuations, possibly providing ev-idence for the CME. This interpretation is still underdiscussion (see e.g. [13–15] and references therein). TheCSE refers to the separation of chiral charge, which char-acterizes left/right handedness, along the axis of the mag-netic field in the presence of the finite density of electriccharge [16, 17]. In this Letter, we report the results froma search for these effects using a new approach.In a chirally symmetric phase, the CME and CSEcan form a collective excitation, the chiral magnetic wave(CMW). It is a propagation of chiral charge density ina long wavelength hydrodynamic mode [18–20]. TheCMW, which requires chiral symmetry restoration, man-ifests itself in a finite electric quadrupole moment ofthe collision system, where the “poles” (“equator”) ofthe collision system acquire additional positive (negative)charge [18]. This effect, if present, will increase(decrease)the elliptic flow of negative (positive) particles. Ellipticflow refers to an azimuthally anisotropic collective motionof soft (low momentum) particles. It is characterized bya second-order harmonic in a particle’s azimuthal distri-bution, φ , with respect to the reaction plane azimuthalangle, Ψ RP , which is determined by the impact parameterand the beam direction, v = (cid:104) cos[2( φ − Ψ RP )] (cid:105) . (1)The CMW is theoretically expected to modify the ellipticflow of charged particles, e.g. pions, on top of the baseline v base2 ( π ± ) [18] v ( π ± ) = v base2 ( π ± ) ∓ r A ch , (2)where r is the quadrupole moment normalized by thenet charge density and A ch = ( N + − N − ) / ( N + + N − )is the charge asymmetry of the collision system. As thecolliding nuclei are positively charged, the average chargeasymmetry, (cid:104) A ch (cid:105) , is always positive. Thus, the A ch -integrated v of π − ( π + ) should be above (below) thebaseline because of the CMW. However, the v base2 maybe different between π + and π − because of several otherpossible physical mechanisms [21–24]. It is preferable tostudy CMW via the A ch dependence of the pion v otherthan A ch -integrated v .This Letter reports the A ch -differential measurementsof the pion v , based on Au+Au samples of 2 × eventsat 200 GeV from RHIC year 2010, 6 × at 62.4 GeV(2010), 10 at 39 GeV (2010), 4 . × at 27 GeV (2011),2 × at 19.6 GeV (2011), 1 × for 11.5 (2010) and4 × for 7.7 GeV (2010). All events were obtainedwith a minimum-bias trigger which selects all particle-producing collisions, regardless of the extent of overlap ch Observed A - C oun t s · Au+Au 200 GeV: 30-40% (a) ch Observed A - c h A - HIJING (b)
FIG. 1. (Color online) (a) the distribution of observed chargeasymmetry from STAR data and, (b) the relationship betweenthe observed charge asymmetry and the charge asymmetryfrom HIJING generated events, for 30-40% central Au+Aucollisions at 200 GeV. In this centrality, the mean chargeasymmetry (cid:104) A ch (cid:105) of HIJING events is about 0.004. The errorsare statistical only. of the incident nuclei [25]. Charged particle tracks withpseudorapidity | η | < | η | < . . . < A ch was determined from the measuredcharged particles with transverse momentum p T > . c and | η | <
1; protons and anti-protons with p T < . c were excluded to reject background pro-tons from the nuclear interactions of pions with innerdetector materials. Fig. 1(a) shows an example of theobserved A ch distribution, which was divided into fivesamples roughly containing equal numbers of events, asindicated by the dashed lines. Fig. 1(b) shows the rela-tionship between the observed A ch and the A ch from theHIJING event generator [28], where the same cuts as usedin data were applied to calculate A ch . The relationshipis linear. To select pions with high purity, we eliminatecharged particles more than 2 σ away from the expectedenergy loss of pions in the TPC. For energies less thanor equal to 62 . v { η sub } approach [29], where twosubevent planes register charged particles with η > . η < − .
3, respectively. Pions at positive (negative) η are then correlated with the subevent plane at nega-tive (positive) η to calculate v . The η gap of 0.3 unitsuppresses several short-range correlations such as the ch Observed A - ( % ) v p + p Au+Au 200 GeV: 30-40% < 0.5 GeV/c T (a) ch A - - ) ( % ) + p ( ) - v - p ( v - (b) 0.2903 – r = 3.1985 FIG. 2. (Color online) (a) pion v { } as a function of ob-served charge asymmetry and, (b) v difference between π − and π + as a function of charge asymmetry with the trackingefficiency correction, for 30-40% central Au+Au collisions at200 GeV. The errors are statistical only. Bose-Einstein interference and the Coulomb final-stateinteractions [30]. There are correlations that are unre-lated to the reaction plane that are not suppressed bythe η gap, e.g. those due to back-to-back jets. Theseare largely canceled in the v difference between π − and π + . For 200 GeV, the two-particle cumulant method v { } [30, 31] was employed, which was consistent with v { η sub } , and allowed the comparison with the v { } method discussed later in this letter. The same η gapwas also used in the v { } analysis. To focus on the softphysics regime, only pions with 0 . < p T < . c were used to calculate the p T -integrated v , and this p T range covers 65-70% of all the produced pions. The cal-culation of the p T -integrated v was corrected with the p T -dependent tracking efficiency for pions.Taking Au+Au 200 GeV collisions in the 30-40% cen-trality range as an example, the pion v is shown as afunction of the observed A ch in Fig. 2(a). The π − v increases with increasing observed A ch while the π + v decreases with a similar magnitude of the slope. Afterapplying the tracking efficiency to A ch , the v differencebetween π − and π + has been fitted with a straight line asshown in Fig. 2(b). The slope parameter, r , from Eq. 2,is positive and qualitatively consistent with the expecta-tions of the CMW picture. The fit function is non-zeroat the average charge asymmetry (cid:104) A ch (cid:105) , which is a smallpositive number in case of Au + Au collisions. This indi-cates the A ch − integrated v for π − and π + are different,which was observed in Ref. [32]. We follow the same pro-cedure as above to extract the slope parameter, r , forall centrality bins at 200 GeV. The results are shownin Fig. 3, together with simulations using the UrQMDevent generator [33] and with the theoretical calculationswith CMW [34] with different duration times of the mag-netic field. For most data points, the slopes are positiveand reach a maximum in mid-central/mid-peripheral col-lisions, a feature also seen in the theoretical calculationsof the CMW. The gray bands in Fig. 3 include threetypes of systematic errors: the DCA cut for pion tracks % Most Central S l ope pa r a m e t e r r ( % ) - - STAR dataUrQMD = 5 fm/c) t CMW ( = 4 fm/c) t CMW (
Au+Au 200 GeV
FIG. 3. (Color online) The slope parameter, r , as a function ofcentrality for Au+Au collisions at 200 GeV. Also shown is theUrQMD [33] simulation, and the calculations with CMW [34]with different duration times. The grey bands include thesystematic errors due to the DCA cut, the tracking efficiencyand the p T range of particles involved in the event plane deter-mination. The cross-hatched band indicates the STAR mea-surement with the v { } method and the height of this bandshows only the statistical error. was tightened to 0.5 cm, to study the contribution fromweak decays, which dominates the systematic errors; thetracking efficiency for charged particles was varied by rel-ative 5%, to determine the uncertainty of A ch ; and the p T range of particles involved in the event plane determi-nation was shrunk from [0 . ,
2] GeV/ c to [0 . ,
2] GeV/ c ,to further suppress short-range correlations. The A ch bincenter may not accurately reflect the true center of each A ch bin in Fig. 2, as the v measurements are effectivelyweighted by the number of particles of interest. Such anuncertainty on r has been estimated to be negligible formost centrality bins, except for the most peripheral col-lisions, where this systematic error is still much smallerthan the statistical error.To further study the charge-dependent contributionfrom jets and/or resonance decays, we separated positiveand negative particles in each subevent to form positively(negatively) charged subevents. Then each π + ( π − ) isonly correlated with the positive (negative) subevent inthe opposite hemisphere. The slope parameters thus ob-tained are statistically consistent with the previous re-sults though with larger uncertainties.The event plane reconstructed with particles recordedin the TPC approximates the participant plane, the mea-sured v are not the mean values, but closer to the root-mean-square values [35]. Another method, v { } [36] issupposed to better represent the measurement with re-spect to the reaction plane. For 20 −
50% Au+Au col-lisions at 200 GeV, the slope parameter obtained with v { } is illustrated with the cross-hatched band in Fig. 3,which is systematically lower than the v { } results, but -505 Au+Au 200 GeV (a) -505
Au+Au 62.4 GeV (b) -505
Au+Au 27 GeV (d) -505 Au+Au 11.5 GeV (f) -505
CMW = 6 fm/c t = 5 fm/c t = 4 fm/c t = 3 fm/c t -505 Au+Au 39 GeV (c) -505
Au+Au 19.6 GeV (e) -505 Au+Au 7.7 GeV (g) % Most Central S l ope pa r a m e t e r r ( % ) FIG. 4. (Color online) The slope parameter r as a functionof centrality for all the collision energies under study. Forcomparison, we also show the calculations with CMW [34]with different duration times. The grey bands carry the samemeaning as those in Fig. 3. still has a finite positive value with a larger statisticalerror.Since the prediction of the consequence of CMW on v [18, 19], this subject has recently drawn increasingattention from theorists [34, 37–42]. It was pointed outin Ref. [42] that local charge conservation at freeze-out,when convoluted with the characteristic shape of v ( p T )and v ( η ), may provide a qualitative explanation for thefinite v slope we observe. Such an effect depends on thestrength of the A ch dependence on the mean p T and the η -dependence of v . However, our measurements werecarried out in a narrow p T range ([0.15,0.5] GeV/c) andwith a (cid:104) p T (cid:105) ( A ch ) variation of 0.1% at most. Furthermore,the measured η -dependence of v is only half as strongas that used in Ref. [42]. We estimate the contributionof this mechanism to be smaller than the measurementby an order of magnitude.To check if the observed slope parameters come fromconventional physics, such as Coulomb interactions, orfrom a bias due to the analysis approach, we carried outthe same analysis in Monte Carlo events from UrQMD.As shown in Fig. 3, the slopes extracted from UrQMDevents of 200 GeV Au+Au collisions are consistent with zero for 10-60% centrality collisions, where the signal isprominent in the data. Similarly, the AMPT event gener-ator [43, 44] also produces events with slopes r consistentwith zero. With the AMPT model, we also studied theweak decay contribution to the slope, which was negli-gible. On the other hand, the CMW calculations [18]demonstrate a similar centrality dependence of the slopeparameter. Recently, a more realistic implementation ofthe CMW [40] suggested that the CMW contribution to r is sizable, and the centrality dependence of r is sim-ilar to the data. In these theoretical calculations suchcentrality dependence mainly results from the central-ity dependence of the magnetic field and the system vol-ume. Quantitative comparisons between data and theoryrequire further work on both sides to match the kine-matic regions used in the analyses. For example, themeasured A ch only represents the charge asymmetry ofa slice ( | η | <
1) of an event, instead of that of the wholecollision system. We expect these two values of A ch tobe proportional to each other, but the determination ofthe ratio will be model dependent. In addition to theUrQMD and AMPT simulation studies which reveal notrivial correlation between A ch and pion v , tests wereperformed using the experimental data. For example, A ch and the pion v were calculated in two kinematicallyseparated regions, i.e., different rapidity bins. In suchcases, the slope parameters decrease but remain signifi-cant and positive. This may reflect the local nature ofthe A ch dependence of v , but additional theoretical de-velopment is necessary.Figure 4 shows a similar trend in the centrality de-pendence of the slope parameter for all the beam energiesexcept 11.5 and 7 . A ch -integrated v difference between particles and anti-particles can beexplained by the effect of quark transport from the pro-jectile nucleons to mid-rapidity, assuming that the v of transported quarks is larger than that of producedones. The same model, however, when used to study v ( π − ) − v ( π + ) as a function of A ch , suggested a nega-tive slope [45], which is contradicted by the data.The mean field potentials from the hadronicphase [22] and the partonic phase [24] also qualitativelyexplain the A ch -integrated v difference between parti-cles and anti-particles, especially at lower beam energies.In general, the mean field potential is expected to bepositively correlated with A ch and thus may explain thetrends in those data, but no conclusive statement can bemade here due to the lack of specific predictions. Thiseffect may be tested in the future by studying the K ± v slopes, whose v ordering is opposite to that of π ± .In summary, pion v exhibits a linear dependence on A ch , with positive (negative) slopes for π − ( π + ). The v ( π − ) − v ( π + ) increases as a function of A ch , qual-itatively reproducing the expectation from the CMWmodel. The slope r of v ( A ch ) difference between π − and π + has been studied as a function of centrality,and we observe a dependence also similar to the calcu-lation based on the CMW model. The slope parameter r remains significantly positive for 10 −
60% centralityAu+Au collisions at √ s NN = 27 −
200 GeV, and displaysno obvious trend of the beam energy dependence withthe current statistics. None of the conventional modelsdiscussed, as currently implemented, can explain our ob-servations.We thank the RHIC Operations Group and RCF atBNL, the NERSC Center at LBNL, the KISTI Center inKorea, and the Open Science Grid consortium for pro-viding resources and support. This work was supportedin part by the Office of Nuclear Physics within the U.S.DOE Office of Science, the U.S. NSF, the Ministry of Ed-ucation and Science of the Russian Federation, NNSFC,the MoST of China (973 Program No. 2014CB845400),CAS, MoST and MoE of China, the Korean ResearchFoundation, GA and MSMT of the Czech Republic, FIASof Germany, DAE, DST, and UGC of India, the NationalScience Centre of Poland, National Research Foundation,the Ministry of Science, Education and Sports of the Re-public of Croatia, and RosAtom of Russia. [1] D. E. Kharzeev, L. D. McLerran and H. J. Warringa,Nucl. Phys. A , 227 (2008).[2] D. Kharzeev, Phys. Lett. B , 260 (2006).[3] D. Kharzeev and A. Zhitnitsky, Nucl. Phys. A , 67(2007).[4] K. Fukushima, D. E. Kharzeev and H. J.Warringa, Phys.Rev. D , 074033 (2008).[5] D. E. Kharzeev, Annals Phys. , 205 (2010).[6] B. I. Abelev et al. (STAR Collaboration), Phys. Rev.Lett. , 251601 (2009).[7] B. I. Abelev et al. (STAR Collaboration), Phys. Rev.C , 054908 (2010).[8] L. Adamczyk et al. (STAR Collaboration), Phys. Rev.C , 064911 (2013).[9] L. Adamczyk et al. (STAR Collaboration), Phys. Rev.Lett. , 052302 (2014).[10] N. N. Ajitanand, S. Esumi, R. A. Lacey, Proc. of theRBRC Workshops, vol. , 2010: ”P- and CP-odd effectsin hot and dense matter”.[11] N. N. Ajitanand, R. A. Lacey, A. Taranenko and J. M.Alexander, Phys. Rev. C , 011901 (2011).[12] B. I. Abelev et al. (ALICE Collaboration), Phys. Rev.Lett. , 012301 (2013).[13] A. Bzdak, V. Koch, and J. Liao, Phys. Rev. C , 031901(2010); J. Liao, V. Koch, and A. Bzdak, Phys. Rev. C , 054902 (2010).[14] D. E. Kharzeev, D. T. Son, Phys. Rev. Lett. , 062301(2011). [15] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. C , 044908 (2014).[16] D. T. Son and A. R. Zhitnitsky, Phys. Rev. D , 074018(2004).[17] M. A. Metlitski and A. R. Zhitnitsky, Phys. Rev. D ,045011 (2005).[18] Y. Burnier, D. E. Kharzeev, J. Liao and H.-U. Yee, Phys.Rev. Lett. , 052303 (2011).[19] G. M. Newman, JHEP , 158 (2006).[20] E. V. Gorbar, V. A. Miransky, and I. A. Shovkovy, Phys.Rev. D , 085003 (2011).[21] J. C. Dunlop, M. A. Lisa, and P. Sorensen, Phys. Rev. C , 044914 (2011).[22] J. Xu, L.-W. Chen, C. M. Ko, and Z.-W. Lin, Phys. Rev.C , 041901 (2012).[23] J. Steinheimer, V. Koch, M. Bleicher, Phys. Rev. C ,044903 (2012).[24] T. Song, S. Plumari, V. Greco, C.M. Ko and F. Li,arXiv:1211.5511 (2012).[25] F. Bieser et al. , Nucl. Instr. Meth. A , 766 (2003).[26] M. Anderson et al. , Nucl. Instr. Meth. A , 659 (2003).[27] L. Adamczyk et al. (STAR Collaboration), Phys. Rev.C , 054908 (2012).[28] M. Gyulassy and X.-N. Wang, Comput. Phys. Commun. , 307 (1994); X.N. Wang and M. Gyulassy, Phys. Rev.D , 3501 (1991).[29] A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C ,1671 (1998).[30] J. Adams et al. (STAR Collaboration), Phys. Rev. C ,014904 (2005).[31] S. Voloshin and Y. Zhang, Z. Phys. C , 665 (1996).[32] L. Adamczyk et al. (STAR Collaboration), Phys. Rev.Lett. , 142301 (2013).[33] S.A. Bass et al. , Prog. Part. Nucl. Phys. , 255 (1998);M. Bleicher et al. , J. Phys. G , 1859 (1999).[34] Y. Burnier, D.E. Kharzeev, J. Liao, H.-U. Yee, arXiv:1208.2537 (2012); Y. Burnier at the conference “P andCP-odd effects in hot and dense matter 2012”; privatecommunication.[35] J.-Y. Ollitrault, A.M. Poskanzer and S.A. Voloshin, Phys.Rev. C , 014904 (2009).[36] N. Borghini, P.M. Dinh and J.-Y. Ollitrault, Phys. Rev.C , 054906 (2001); A. Bilandzic, R. Snellings and S.A.Voloshin, Phys. Rev. C , 044913 (2011); S.A. Voloshin,A.M. Poskanzer, A. Tang and G. Wang, Phys. Lett. B , 537 (2008).[37] M. Stephanov and H.-U. Yee, Phys. Rev. C , 014908(2013).[38] M. Hongo, Y. Hirono, and T. Hirano, arXiv:1309.2823.[39] S. F. Taghavi and U. A. Wiedemann, Phys. Rev. C ,024902 (2015).[40] H.-U. Yee and Y. Yin, Phys. Rev. C , 044909 (2014).[41] J. Bloczynski, X.-G. Huang, X. Zhang, and J. Liao, Phys.Lett. B , 1529 (2013).[42] A. Bzdak and P. Bozek, Phys. Lett. B , 239 (2013).[43] Z.-W. Lin and C.M. Ko, Phys. Rev. C , 034904 (2002);L.-W. Chen, C.M. Ko, J. Phys. G , S49 (2005).[44] G.-L. Ma, Phys. Lett. B , 383 (2014).[45] J. M. Campbell and M. A. Lisa, Journal of Physics: Con-ference Series446