Pair invariant mass to isolate background in the search for the chiral magnetic effect in Au+Au collisions at s NN − − − √ = 200 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. CalderóndelaBarcaSánchez, 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, Y. Hu, et al. (265 additional authors not shown)
PPair invariant mass to isolate background in the search for the chiral magnetic effectin Au+Au collisions at √ s NN = 200 GeV J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev,
3, 35
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,
49, 6
A. V. Brandin, J. Butterworth, H. Caines, M. Calder´on de la Barca S´anchez, D. Cebra, I. Chakaberia,
29, 6
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, 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,
6, 52
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. 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, 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, 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,
49, 6
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, and M. Zyzak (STAR Collaboration) Abilene Christian University, Abilene, Texas 79699 a r X i v : . [ nu c l - e x ] J un 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 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 Yale University, New Haven, Connecticut 06520 (Dated: June 11, 2020)
Quark interactions with topological gluon configurations can induce local chirality imbalance andparity violation in quantum chromodynamics, which can lead to the chiral magnetic effect (CME)– an electric charge separation along the strong magnetic field in relativistic heavy-ion collisions.The CME-sensitive azimuthal correlator observable (∆ γ ) is contaminated by background arising,in part, from resonance decays coupled with elliptic anisotropy ( v ). We report here the firstdifferential measurements of the correlator as a function of the pair invariant mass ( m inv ) in 20-50%centrality Au+Au collisions at √ s NN = 200 GeV by the STAR experiment at RHIC. Strong resonancebackground contributions to ∆ γ are observed. At large m inv where this background is significantlyreduced, the ∆ γ value is found to be also significantly smaller. An event shape engineering techniqueis deployed to determine the v background shape as a function of m inv . A v -independent signal,possibly indicating a m inv -integrated CME contribution, is extracted to be ∆ γ signal = (0.03 ± ± × − , or (2 ± ± γ ( m inv > . c )= (1 . ± . ± . × − .This presents an upper limit of 0 . × − , or 15% of the inclusive result at 95% confidence level. PACS numbers: 25.75.-q, 25.75.Gz, 25.75.Ld
Quark interactions with a fluctuating topological gluonfield can induce chirality imbalance and local parity vi-olation in quantum chromodynamics (QCD) [1–3]. Thiscan lead to electric charge separation in the presence ofa strong magnetic field ( (cid:126)B ), a phenomenon known as thechiral magnetic effect (CME) [4, 5]. Such a strong (cid:126)B maybe present in non-central heavy-ion collisions, mainlygenerated by the spectator protons at early times [6, 7].Extensive theoretical and experimental efforts have beendevoted to the search for the CME-induced charge sepa-ration along (cid:126)B in heavy-ion collisions [8–10].In non-central heavy-ion collisions, the second-orderharmonic plane of the spatial distribution of the partici-pant nucleons (participant plane) [11], although fluctuat-ing, is generally aligned with the reaction plane (definedby the impact parameter direction and the beam), thusgenerally perpendicular to (cid:126)B on average. The partici-pant plane can be assessed by the second-order harmonicplane ( ψ ) from final-state particle azimuthal distribu-tions. The commonly used observable to measure thecharge separation is the three-point correlator with re-spect to ψ [12]: γ ≡ cos( φ α + φ β − ψ ) , (1)where φ α and φ β are the azimuthal angles of parti-cles α and β , respectively. Because of the charge-independent correlation background (e.g. from globalmomentum conservation), often the correlator differenceis used [12], ∆ γ ≡ γ OS − γ SS , where γ OS stands for the γ of opposite-sign pairs ( α and β have the opposite-signelectric charges) and γ SS for that of same-sign pairs ( α and β have the same-sign electric charge).Significant ∆ γ is indeed observed in heavy-ion colli-sions on the order of 10 − in mid-central collisions [13–17]. A difficulty in its interpretation as originating fromthe CME-induced charge separation is the large charge-dependent background contributions to ∆ γ [10, 17–22],such as those from resonance decays [12, 23]. Thisis because the ∆ γ variable is ambiguous between aCME-induced back-to-back OS pair perpendicular to ψ (charge separation) and an OS pair from a resonance de- cay along ψ (charge conservation). There are more par-ticles/resonances produced along the ψ than perpendic-ular, the relative difference of which is quantified by theelliptic flow anisotropy parameter v , res . The backgroundarises from the coupling of this flow anisotropy, and theintrinsic decay correlation (nonflow) can be expressed as:∆ γ bkgd ∝ (cid:104) cos( φ α + φ β − φ res ) (cid:105) v , res , (2)where φ res is the azimuthal angle of the resonance, and α and β are the resonance decay daughters [10, 12, 20,23, 24]. Early model studies [13, 14] indicated thatthe background contributions were unable to fully ac-count for the measured ∆ γ . It was pointed out recentlythat one of the reasons was an insufficient description ofthe v anisotropy by the models [25]. Such backgroundsources are amply demonstrated by small-system colli-sions, where the participant plane is determined purelyby geometry fluctuations, essentially uncorrelated withthe impact parameter or the (cid:126)B direction [17]. Thereforeany CME signal is expected to be negligible in small sys-tems. However, a large ∆ γ signal was observed in p +Pbcollisions at the LHC, similar to that in Pb+Pb collisions.This challenged the CME interpretation of the heavy-iondata [17]. A large ∆ γ signal is also observed in p ( d )+Aucollisions at RHIC [26].In order to isolate the resonance background contribu-tions, we report new measurements of the ∆ γ variable,differential in pair invariant mass ( m inv ). The integral∆ γ with a minimum m inv limit is presented. To fullyexploit the data, an event shape engineering (ESE) [27]technique is deployed where events with different v butsame CME signal are selected so to determine the v background shape as a function of m inv . The ∆ γ ( m inv )data are then fitted to the v background shape plus a m inv -independent constant term. The extracted constantterm represents a v -independent component in the data,possibly a m inv -integrated CME signal.The data reported here were taken by the STAR ex-periment at the center-of-mass energy per nucleon pairof √ s NN = 200 GeV in the year 2011, 2014 and 2016. Atotal of 2.5 billions minimum-bias (MB) triggered eventswere used in the analysis. The STAR apparatus is de-scribed in Ref. [28].The main detectors used in this analysis are the timeprojection chamber (TPC) [29, 30] and the time-of-flight(TOF) detector [31]. Track trajectories are reconstructedfrom hits detected in the TPC; at least 10 points out ofa possible maximum of 45 points are required for a validtrack. The primary interaction vertex is reconstructedfrom charged particle tracks. The event centrality isdetermined from charged particle multiplicity for trackswhich are within pseudorapidity | η | < .
5, and have dis-tance of closest approach (DCA) to the primary vertexof less than 3 cm. Events with primary vertices within30 cm (year 2011) or 6 cm (years 2014, 2016) longitudi-nally and within 2 cm in the transverse plane from thegeometrical center of the TPC are used.Tracks used for the analysis are required to have atleast 20 points, and to have DCA less than 1 cm. Thefraction of points used to reconstruct a track out of themaximum number of points allowed for the track by theTPC geometry is required to be greater than 0.52 to avoidtrack splitting. Particle momenta are determined by thetrack trajectories in the STAR magnetic field. A mini-mum transverse momentum ( p T > . c ) is requiredto ensure that each charged track traveling through theTPC can reach the TOF detector inside the STAR mag-net. The charged particles can be identified by measuringtheir ionization energy loss (dE/dx) in the TPC gas andtheir time of flight using the TOF detector. Pions areidentified up to p T = 0.8 GeV/ c with TPC dE/dx infor-mation, and extended to p T = 1.8 GeV/ c with the TOF.This analysis uses the three-particle correlator methodto define γ : γ = (cid:104) cos( φ α + φ β − φ c ) (cid:105) /v ,c , (3)where α and β represent the pion index, and the average (cid:104) ... (cid:105) runs over all triplets and over all events. The az-imuthal angle of the third particle, φ c , serves as a mea-sure of ψ . The imprecision in determining the ψ bya single particle is corrected by dividing by the resolu-tion factor, equal to the particle’s elliptic flow anisotropy v ,c . Charged TPC tracks with p T from 0.2 to 2 GeV/ c are used for particle c . Two methods are used: 1) sub-event method, the main method used in this analysis,where the α , β particles are from one half of the TPC( − < η < − .
05 or 0 . < η <
1) and the particle c is from the other half of the TPC (0 . < η < − < η < − .
05) [32]; 2) full-event method, where the α , β and c particle are all taken from the pseudo-rapidityrange | η | < γ correlator is studied as a func-tion of m inv of the α and β particle pairs. The analysisloops over α and β particles, and the c particle is handledby the cumulant method [33].The systematic uncertainties are estimated for eachrun by varying the required minimum number of points from 20 to 15, and the DCA of the track from 1.0 cm to2.0 and 0.8 cm. In the full-event method, the η gap usedto determine v ,c via two-particle correlations is variedfrom 1 to 0.5 and 1.4 [26, 32]. In the sub-event method,the η gap between the east and west sub-events is var-ied from 0.1 to 0.3 [34]. In the systematic uncertaintyestimation of each source, the statistical fluctuation ef-fect arising from the change in the data sample due toeach variation is subtracted. For each source when mul-tiple variations are assessed, the systematic uncertaintyis taken as the root mean square. The systematic uncer-tainties from the above sources are added in quadraturefor each dataset of the three runs. The three datasetsare then combined assuming their systematic uncertain-ties are fully correlated. The final value is quoted as ± m inv . For the extracted possible CME signalfrom the ESE fit method, a fit result is obtained for eachof the above variations, and the systematic uncertaintyis estimated in the same way as described above. The m inv range used to extract the possible signal is variedfrom above 0.4 GeV/ c to above 0.35 and 0.45 GeV/ c ,which yields negligible change in the results. Table I liststhe total systematic uncertainty and the individual con-tributions on the extracted possible CME signal relativeto the inclusive ∆ γ from the ESE fit method. total dca nHits sub-event η gap ± ± ± ± γ in 20-50% centrality Au+Au colli-sions at 200 GeV from the ESE fit method. Figure 1 (a) shows the relative OS and SS π - π pairabundance difference, r = ( N OS − N SS ) /N OS , as a func-tion of m inv for 20-50% centrality Au+Au collisions at √ s NN = 200 GeV. Figure 1 (b) shows the measured ∆ γ as a function of m inv in a similar way. The sub-eventmethod is used. The m inv < . c region is ex-cluded because the acceptance difference between OS andSS pairs, mostly close in azimuthal angle, starts to be-come severe. A clear peak from K s → π + + π − decayis observed in ∆ γ , and possible ρ and f peaks are alsovisible [35]. These peaks correspond to the resonanceproduction peaks in r shown in panel (a) of Fig. 1. Theresults indicate strong contributions from resonances tothe ∆ γ observable.As indicated by Fig. 1 (a), most of the excess of OSover SS pion pair contributions are from the small m inv region. Applying a minimum m inv requirement wouldreduce those contributions. It may, however, also re-duce the possible CME signal, likely decreasing withthe pion p T [6, 13] ( (cid:104) p T (cid:105) ∼ m inv / p T independent signal above0.2 GeV/ c . Nevertheless, it is interesting to examinethe ∆ γ ( m inv > m lowinv ) above a certain m lowinv value, whichwould be more sensitive to the CME signal if the signalis a more slowly decreasing function of m inv than reso-nance contributions. This is shown in Fig. 2 where thefull-event method is used. The ∆ γ ( m inv > m lowinv ) de-creases with increasing m lowinv and approaches zero when m lowinv becomes large. Note that residual resonance andother correlation backgrounds may still remain at highmass, and detailed model and theoretical studies are re-quired to draw further conclusions. O S ) / N SS - N O S r = ( N (a) s0 K r f = 200 GeV NN s20-50% Au+Au : 0.2-0.8 GeV/c T p – p ) (GeV/c inv m SS g - O S g = gD (b) Sub-event method <1 h <-0.05 or 0.05< h (pions): -1< b , a <-0.05 h <1 or -1< h c (charged): 0.05< FIG. 1. Pion pair invariant mass ( m inv ) dependences of (a)the relative excess of opposite-sign (OS) over same-sign (SS)pion pairs, r = ( N OS − N SS ) /N OS , and (b) the three-pointcorrelator difference, ∆ γ = γ OS − γ SS in 20-50% centralityAu+Au collisions at 200 GeV. The pions are identified byTPC dE/dx up to p T = 0.8 GeV/ c . The α , β particles (pi-ons) are from one half of the TPC and the particle c (uniden-tified charged particle) is from the other half. Error bars arestatistical errors. The shaded areas (b) are systematic uncer-tainties. In order to fully exploit the data to extract a possibleCME signal over the entire m inv range, resonance con-tributions need to be removed. This may be achievedby taking advantage of the presumably different m inv dependences of the background and the possible CMEsignal. Assuming the ∆ γ data contain two-componentsof a possible v -independent signal and the v -dependentbackground, the inclusive ∆ γ can be expressed as [37]∆ γ ( m inv ) = r ( m inv ) (cid:104) cos( φ α + φ β − φ res . ) (cid:105) v , res . +∆ γ signal . (4)The v -independent component may represent the possi-ble CME signal, ∆ γ signal . The m inv shape of the back- ) (GeV/c lowinv m ) l o w i n v > m i n v ( m gD - - · = 200 GeV NN s20-50% Au+Au limit lowinv with m gD Full-event method |<1 h (pions), c (charged): | b , a :0.2-1.8 GeV/c T p – p FIG. 2. The identified π pair ∆ γ at m inv > m lowinv as afunction of m lowinv . The pions are identified by TPC dE/dx and TOF up to p T = 1.8 GeV/ c . All three particles ( α, β, c )are from the full TPC acceptance ( | η | < ground, the first term of Eq. 4 on the right hand side, canbe assessed by the ESE method, selecting events from anarrow centrality bin with different v values by using thereduced flow vector q quantity; q = | (cid:80) Nj =1 e i φ j | / √ N summing over the α, β particles in each event. The dif-ference of the ∆ γ ( m inv ) from the different q classes canbe regarded as the background ∆ γ ( m inv ) shape [9], be-cause the CME for events within a narrow centrality binare the same even for different q classes (the spectatorprotons and the participant particle anisotropy are un-correlated [38]). We have verified that the r ( m inv ) distri-butions are the same between the two event classes, andthe decay angular correlations are presumably also thesame. Since the α , β particles are used for q calcula-tion, this ESE method is selecting mainly on the statisti-cal fluctuations of the α / β particle’s elliptic anisotropy.The events shown in Fig. 1 are divided into two equal-size groups according to the q value: event sample Awith the 50% largest q and event sample B with the50% smallest q . Figure 3 (a) shows the m inv dependenceof the ∆ γ A and ∆ γ B from ESE-selected event samples Aand B, respectively, integrated over the 20-50% centralityrange. Figure 3 (b) shows the inclusive (no q restriction,i.e. the same data as shown in Fig. 1 (b)) ∆ γ comparedwith ∆ γ A − ∆ γ B . The systematic uncertainty of the latteris larger than twice that of the former, which is approxi-mately (∆ γ A + ∆ γ B ) /
2. This is due to an anticorrelationbetween the two event classes as they are selected largelyon statistical fluctuations as aforementioned.The inclusive ∆ γ contains both the background andthe possible CME. With the background shape given by∆ γ A − ∆ γ B , the possible CME signal can be extractedfrom a two component fit: ∆ γ = b (∆ γ A − ∆ γ B )+∆ γ signal ,assuming ∆ γ signal is independent of m inv . However, since gD (a) = 200 GeV NN s20-50% Au+Au A: large q B: small q
Sub-event method ) (GeV/c inv m gD (b) cut No qA - B:0.2-0.8 GeV/c T p – p FIG. 3. Pion pair invariant mass ( m inv ) dependences of (a)the ∆ γ from ESE-selected event samples A (50% largest q )and B (50% smallest q ), respectively, and (b) the inclusive(no q restriction) ∆ γ compared with ∆ γ A − ∆ γ B in 20-50%centrality Au+Au collisions at 200 GeV. The pions are iden-tified by TPC dE/dx up to p T = 0.8 GeV/ c . The α , β par-ticles (pions) are from one half of the TPC and the particle c (unidentified charged particle) is from the other half. Errorbars are statistical errors. The shaded areas are systematicuncertainties. the same data are used in ∆ γ and ∆ γ A − ∆ γ B , theirstatistical errors are not independent. To properly handlestatistical errors, an alternative function is used to fitthe two independent measurements of ∆ γ A versus ∆ γ B ,namely: ∆ γ B = k ∆ γ A + (1 − k )∆ γ signal , (5)where k and ∆ γ signal are the fit parameters. If ∆ γ =(∆ γ A + ∆ γ B ) /
2, then b = (1 + k ) / (1 − k ) /
2. In thisfit model, the background is not required to be strictlyproportional to v [37, 39]. Figure 4 shows ∆ γ A ver-sus ∆ γ B in 20-50% centrality Au+Au collisions at 200GeV. Each data point corresponds to one m inv bin inFig. 3 (a). The line is the fits by Eq. 5. The good χ / ndf indicates that the fit model assumption of a m inv -independent ∆ γ signal is reasonable. The potential CMEis likely dependent of m inv , the feature of which couldin principle, given enough statistics, be revealed exper-imentally by more sophisticated ESE analysis. The fit-ted ∆ γ signal is (0.03 ± ± × − and is foundto be (2 ± ±
5) % of the inclusive ∆ γ ( m inv > . c ) = (1 . ± . ± . × − . These valuesrepresent over an order of magnitude reduction from theinclusive ∆ γ measurement. Our results indicate that thepossible CME signal is small in the inclusive ∆ γ , consis-tent with zero with current precision. This presents an A gD - · B gD - · = 200 GeV NN s20-50% Au+Au :0.2-0.8 GeV/c T p – p Sub-event method > 1.0 GeV/c / ndf c – signal gD - · – (2.7 FIG. 4. ∆ γ A versus ∆ γ B in 20-50% centrality Au+Au colli-sions at 200 GeV, superimposed on the linear function fit ofEq. 5. Error bars are statistical errors. Horizontal and ver-tical caps are the systematic uncertainties on ∆ γ A and ∆ γ B ,respectively. Different colors indicate the data from differ-ent m inv regions (black points: 0.4-0.6 GeV/ c , red points:0.6-1.0 GeV/ c , blue points: > . c ). upper limit of 0 . × − , or 15% of the inclusive resultat 95% confidence level [40].In summary, we report differential measurements of thereaction-plane-dependent azimuthal correlation of pionpairs (∆ γ ), sensitive to the topological-charge-inducedchiral magnetic effect (CME) in QCD, as a function of thepair invariant mass ( m inv ). Resonance structures are ob-served in ∆ γ ( m inv ), indicating major background contri-butions. At large m inv , where this background is signif-icantly reduced, the ∆ γ is also significantly smaller. Toisolate the possible CME signal from background, eventshape engineering by the sub-event method is used to de-termine the background shape in m inv . The backgroundshape is used in a two-component fit to the ∆ γ ( m inv )data, assuming it contains a v -independent signal inadditional to the v -dependent background. Such a fityields a v -independent signal of ∆ γ signal = (0.03 ± ± × − in 20-50% centrality Au+Au collisions at200 GeV, (2 ± ± γ ( m inv > . c )=(1.58 ± ± × − ,within pion p T = 0 . − . c and averaged be-tween pseudorapidity ranges of − < η < − .
05 and0 . < η <
1. This may represent a possible CME signalintegrated over m inv , an upper limit of 0 . × − , or15% of the inclusive result at 95% confidence level.We thank the RHIC Operations Group and RCF atBNL, the NERSC Center at LBNL, and the Open Sci-ence Grid consortium for providing resources and sup-port. This work was supported in part by the Officeof Nuclear Physics within the U.S. DOE Office of Sci-ence, the U.S. National Science Foundation, the Min-istry of Education and Science of the Russian Federa-tion, National Natural Science Foundation of China, Chi-nese 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). [1] T. D. Lee and G. C. Wick. Vacuum Stability and Vac-uum Excitation in a Spin 0 Field Theory. Phys. Rev. D ,9:2291–2316, 1974.[2] Dmitri Kharzeev, R. D. Pisarski, and Michel H. G. Tyt-gat.
Phys. Rev. Lett. , 81:512–515, 1998.[3] Dmitri Kharzeev and Robert D. Pisarski. Pionic mea-sures of parity and CP violation in high-energy nuclearcollisions.
Phys. Rev. D , 61:111901, 2000.[4] Kenji Fukushima, Dmitri E. Kharzeev, and Harmen J.Warringa.
Phys. Rev. D , 78:074033, 2008.[5] Berndt Muller and Andreas Schafer. Charge Fluctuationsfrom the Chiral Magnetic Effect in Nuclear Collisions.
Phys. Rev. C , 82:057902, 2010.[6] Dmitri E. Kharzeev, Larry D. McLerran, and Harmen J.Warringa.
Nucl. Phys. A , 803:227–253, 2008.[7] Masayuki Asakawa, Abhijit Majumder, and BerndtMuller. Electric Charge Separation in Strong TransientMagnetic Fields.
Phys. Rev. C , 81:064912, 2010.[8] D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang.
Prog. Part. Nucl. Phys. , 88:1–28, 2016.[9] Jie Zhao.
Int. J. Mod. Phys. A , 33(13):1830010, 2018.[10] Jie Zhao and Fuqiang Wang. Experimental searches forthe chiral magnetic effect in heavy-ion collisions.
Prog.Part. Nucl. Phys. , 107:200–236, 2019.[11] B. Alver et al. System size, energy, pseudorapidity, andcentrality dependence of elliptic flow.
Phys. Rev. Lett. ,98:242302, 2007.[12] Sergei A. Voloshin.
Phys. Rev. C , 70:057901, 2004.[13] B. I. Abelev et al. Observation of charge-dependent az-imuthal correlations and possible local strong parity vi-olation in heavy ion collisions.
Phys. Rev. C , 81:054908,2010.[14] B. I. Abelev et al. Azimuthal Charged-Particle Correla-tions and Possible Local Strong Parity Violation.
Phys.Rev. Lett. , 103:251601, 2009.[15] L. Adamczyk et al. Beam-energy dependence of chargeseparation along the magnetic field in Au+Au collisionsat RHIC.
Phys. Rev. Lett. , 113:052302, 2014.[16] Betty Abelev et al. Charge separation relative to the reaction plane in Pb-Pb collisions at √ s NN = 2 .
76 TeV.
Phys. Rev. Lett. , 110(1):012301, 2013.[17] Vardan Khachatryan et al. Observation of charge-dependent azimuthal correlations in p -Pb collisions andits implication for the search for the chiral magnetic ef-fect. Phys. Rev. Lett. , 118(12):122301, 2017.[18] Fuqiang Wang.
Phys. Rev. C , 81:064902, 2010.[19] Adam Bzdak, Volker Koch, and Jinfeng Liao.
Phys. Rev.C , 81:031901, 2010.[20] Soren Schlichting and Scott Pratt.
Phys. Rev. C ,83:014913, 2011.[21] L. Adamczyk et al.
Phys. Rev. C , 89(4):044908, 2014.[22] Albert M Sirunyan et al. Constraints on the chiral mag-netic effect using charge-dependent azimuthal correla-tions in p Pb and PbPb collisions at the CERN LargeHadron Collider.
Phys. Rev. C , 97(4):044912, 2018.[23] Fuqiang Wang and Jie Zhao.
Phys. Rev. C , 95(5):051901(R), 2017.[24] Adam Bzdak, Volker Koch, and Jinfeng Liao. Azimuthalcorrelations from transverse momentum conservation andpossible local parity violation.
Phys. Rev. C , 83:014905,2011.[25] Jie Zhao, Yicheng Feng, Hanlin Li, and Fuqiang Wang.HIJING can describe the anisotropy-scaled charge-dependent correlations at the BNL Relativistic Heavy IonCollider.
Phys. Rev. C , 101:034912, 2020.[26] J. Adam et al. Charge-dependent pair correlations rela-tive to a third particle in p +Au and d +Au collisions atRHIC. Phys. Lett. B , 798:134975, 2019.[27] Jurgen Schukraft, Anthony Timmins, and Sergei A.Voloshin.
Phys. Lett. B , 719:394–398, 2013.[28] K. H. Ackermann et al. STAR detector overview.
Nucl.Instrum. Meth. A , 499:624–632, 2003.[29] M. Anderson et al. The Star time projection chamber:A Unique tool for studying high multiplicity events atRHIC.
Nucl. Instrum. Meth. A , 499:659–678, 2003.[30] K. H. Ackermann et al. The STAR time projection cham-ber.
Nucl. Phys. A , 661:681–685, 1999.[31] W. J. Llope. Multigap RPCs in the STAR experiment atRHIC.
Nucl. Instrum. Meth. A , 661:S110–S113, 2012.[32] L. Adamczyk et al. Inclusive charged hadron elliptic flowin Au + Au collisions at √ s NN = 7.7 - 39 GeV. Phys.Rev. C , 86:054908, 2012.[33] N. Borghini, P. M. Dinh, and J. Y. Ollitrault. Analysis ofdirected flow from elliptic flow.
Phys. Rev. C , 66:014905,2002.[34] L. Adamczyk et al. Elliptic flow of identified hadrons inAu+Au collisions at √ s NN = 7.7-62.4 GeV. Phys. Rev.C , 88:014902, 2013.[35] J. Adams et al. Rho0 production and possible modifi-cation in Au+Au and p+p collisions at S(NN)**1/2 =200-GeV.
Phys. Rev. Lett. , 92:092301, 2004.[36] Shuzhe Shi, Yin Jiang, Elias Lilleskov, and Jinfeng Liao.Anomalous Chiral Transport in Heavy Ion Collisionsfrom Anomalous-Viscous Fluid Dynamics.
Annals Phys. ,394:50–72, 2018.[37] Jie Zhao, Hanlin Li, and Fuqiang Wang. Isolating thechiral magnetic effect from backgrounds by pair invariantmass.
Eur. Phys. J. C , 79(2):168, 2019.[38] Hao-Jie Xu, Jie Zhao, Xiaobao Wang, Hanlin Li, Zi-WeiLin, Caiwan Shen, and Fuqiang Wang. Varying the chiralmagnetic effect relative to flow in a single nucleus-nucleuscollision.
Chin. Phys. C , 42(8):084103, 2018.[39] Hanlin Li, Jie Zhao, and Fuqiang Wang. A novel invariant mass method to isolate resonance backgrounds from thechiral magnetic effect.
Nucl. Phys. A , 982:563–566, 2019.[40] Gary J. Feldman and Robert D. Cousins. A Unified ap- proach to the classical statistical analysis of small signals.