Measurement of the charge separation along the magnetic field with Signed Balance Function in 200 GeV Au + Au collisions at STAR
NNuclear Physics A 00 (2020) 1–4
NuclearPhysics A / locate / procedia XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2019)
Measurement of the charge separation along the magnetic fieldwith Signed Balance Function in 200 GeV Au + Au collisionsat STAR
Yufu Lin for the STAR Collaboration Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan430079, ChinaBrookhaven National Laboratory, Upton, New York 11973, USA
Abstract
Experimental searches for Chiral Magnetic E ff ect (CME) in heavy-ion collisions have been going on for a decade, andso far there is no conclusive evidence for its existence. Recently, the Signed Balance Function (SBF), based on the ideaof examining the momentum ordering of charged pairs along the in- and out-of-plane directions, has been proposed asa probe of CME. In this approach, a pair of observables is invoked: one is r rest , the out-of-plane to in-plane ratio of ∆ B measured in pair’s rest frame, where ∆ B is the di ff erence between signed balance functions; The other is a double ratio, R B = r rest / r lab , where r lab is a measurement similar to r rest but measured in the laboratory frame. These two observablesgive opposite responses to the CME-driven charge separation compared to the background correlations arising fromresonance flow and global spin alignment. Both r rest and R B being larger than unity can be regarded as a case in favor ofthe existence of CME. It is found experimentally that r rest , r lab and R B are larger than unity in Au + Au collisions at 200GeV, and larger than realistic model calculations with no CME implemented. These findings are di ffi cult to be explainedby a background-only scenario. Keywords:
Heavy-ion collisions, chiral magnetic e ff ect, signed balance function, reaction plane
1. Introduction
It has been pointed out that the hot and dense matter created in relativistic heavy-ion collisions may formmetastable domains where the parity and time-reversal symmetries are locally violated, creating fluctuating,finite topological charges [1]. In non-central collisions, when such domains are immersed in the ultra-strongmagnetic fields produced by spectator protons, they can induce electric charge separation parallel to thesystem’s orbital angular momentum — the chiral magnetic e ff ect (CME) [2]. To study the CME experi-mentally one has to look for the enhanced fluctuation of charge separation in the direction perpendicular [email protected] a r X i v : . [ nu c l - e x ] M a y / Nuclear Physics A 00 (2020) 1–4 to the reaction plane, relative to the fluctuation in the direction of reaction plane itself. This is the basis ofall CME searches in heavy-ion collisions. Recently, a new method, namely the Signed Balance Function(SBF) method, is proposed as an alternative way to study the charge separation induced by CME in rela-tivistic heavy-ion collisions [3]. The SBF method is based on the idea of examining the fluctuation of netmomentum ordering of charged pairs along the in- and out-of-plane directions. In this approach, a pair ofobservables were proposed, one is r rest , the out-of-plane to in-plane ratio of ∆ B measured in pair’s rest frame,where ∆ B is the di ff erence between signed balance functions; the other is a double ratio R B = r rest / r lab , where r lab is a measurement similar to r rest but performed in the laboratory frame. These two observables have pos-itive responses to signal, but opposite, limited responses to known backgrounds arising from resonance flowand global spin alignment. In this proceedings, we review tests made for the SBF with toy models, and givean update on tests made with realistic models. Latter ones include combinations of background and signalwith various strengths. After that we will show SBF results from Au + Au collisions at 200 GeV measuredby the STAR experiment at RHIC.
2. Results and discussion
The major challenge in CME searches is that backgrounds, in particular those related to resonanceelliptic flow and global spin alignment, can produce similar enhancement of fluctuations with the CMEsignal in the direction perpendicular to the reaction plane [3, 4]. The e ff ects of both signal and backgroundshave been implemented in toy model simulations [3], and for the configuration details of toy model pleasesee Ref [5]. With the toy model, the responses of SBF observables can be studied using various signal andbackground combinations, in a controlled and systematic way. a Primordial B R lab r rest r = B R r es t ( l a b ) r rest r lab r Fig. 1. The r rest , r lab and R B as a functionof a obtained for the toy model (signal only,no backgrounds) [3]. Resonance v B R ) /T exp(-p (cid:181) dpdN /T) T exp(-m (cid:181) dmdN/T) T exp(-m T m (cid:181) dmdN +T)] )/T] / [T(m -m T exp[-(m (cid:181) dmdN r es t r +T)] , )/T] / [T(m -m T exp[-(m (cid:181) dmdN : r -1 /T)-1] T [exp(m (cid:181) dmdN : p -1 /T)-1] T [exp(m (cid:181) dmdN /T) T exp(-p (cid:181) dpdN ) /T exp(-p (cid:181) dpdN = 0 a Primordial
Fig. 2. The r rest and R B as a function ofresonance v for various transverse momen-tum / mass spectra obtained for the toy model[3]. In Fig. 1 SBF observables are shown as a function of primordial a , which a refers to the signal ofCME, without any backgrounds. Here a represents the strength of CME signal [3]. The r rest , r lab and R B areconsistent with unity when a =
0, and increase with increasing a . The r rest and r lab follow each other tothe first order but r rest responds to signal more than r lab does, which is the information shown in the bottompanel. The results indicate that SBF observables are sensitive to the CME signal. The influence of ellipticflow of resonances are shown in Fig. 2. The R B is found to decrease with the increasing of resonance v ,while the r rest increases with it. The two observables show opposite dependence on resonance v assumingvarious transverse momentum ( p T ) spectra shape. More cases with additional background configurationscan be found in Ref [3]. Figure 3 shows toy model results with CME signal and two major backgrounds Nuclear Physics A 00 (2020) 1–4 (resonance flow and global spin alignment) considered, which are closer to the realistic scenario. One cansee that similar to the case of resonance flow only, r rest and R B respond in opposite directions to the changeof global spin alignment ( ρ ). On top of that, both increase with increasing signal ( a ). It will be a casesupporting CME if both r rest and R B are larger than unity, barring additional background from Local ChargeConservation (LCC) and Transverse Momentum Conservation (TMC). Both LCC and TMC have to bestudied with realistic models, which will be presented below. r Resonance B R r es t r a Primordial = 1 % a Primordial = 0.5 % a Primordial = 0 % a Primordial
Fig. 3. The r rest and R B as a function ofresonance ρ for various a values obtainedfor the toymodel [3]). Centrality (%) B R r es t r AVFD LCC = 0 ~ 2 %) a = 0.2 ( /s n ~ 1 %) a = 0.1 ( /s n = 0 %) a = 0. ( /s n AVFD LCC = 33% ~ 2 %) a = 0.2 ( /s n ~ 1 %) a = 0.1 ( /s n = 0 %) a = 0. ( /s n = 0 % a AMPT | < 1.0 η | Fig. 4. The r rest and R B as a function of cen-trality, calculated for events from AMPT andAVFD. The two observables are also tested with two popular realistic models, namely the AMPT [6] andAVFD [7] models. Both models can reasonably describe data’s key features (spectra, elliptic flow, etc.).For the AMPT version that is used in the test, no CME signal is implemented and charge-conservation hasbeen assured. It can serve as a good baseline for apparent charge separation arising from pure backgrounds.In the AVFD model [7], the anomalous transport current from CME has been implemented by introducingfinite ratio of axial charge over entropy ( n / s ), allowing a quantitatively and systematically study on observ-able’s responses to signal embedded an environment of realistic backgrounds. Figure 4 shows the results of r rest and R B as a function of centrality for AMPT and AVFD events. To match the typical acceptance usedby the STAR Collaboration, only particles in | η | < . < p T < / c are considered in the analysis.For the two cases without CME (AMPT and AVFD with n / s = r rest and R B are consistent with unitywithin statistical uncertainties. Both r rest and R B increase with increasing n / s in AVFD results, results forthe two LCC cases (LCC =
33% and LCC = r rest and R B upwards, but only limited response is seen for the SBF observables when LCC changes from 0% to 33%.More detailed investigation on LCC is ongoing. + Au collisions at 200 GeV
Experimental data used in this analysis are 200 GeV Au + Au collisions taken by the STAR experimentin year 2016. About one billion minimum-bias events were used in the analysis. The transverse momentumrange for particles included in the analysis is 0 . < p T < / c. The second order event-plane (EP), ψ ,is reconstructed with Time Projection Chamber (TPC) withing 0 . < η < .
0. Pions are used to calculateSBF, and they are identified with the information from both the TPC and the Time-Of-Flight detector. Pionkinematic region is confined in | η | < .
5, a di ff erent region than that for ψ to avoid auto-correlation e ff ects.In Fig. 5, r rest , r lab and R B are shown as a function of centrality for both experimental data and AVFDmodel events. Results presented in Fig. 5 are not corrected for the EP resolution. Instead, we smearedreaction plane in AVFD events with measured event plane resolution in order to compare with data. Thefinite e ffi ciency e ff ect is also applied to AVFD events to assure a fair comparison. One can find that both r rest , r lab , and R B are larger than unity for all centralities for experimental data. As a consistency check, / Nuclear Physics A 00 (2020) 1–4 we also randomized each particle’s charge while keep the total number of charged particles (positive andnegative) in event unchanged. Such events and they are called shu ffl ed events, and they are analyzed in thesame way as what real events are analyzed. As shown in 5, SBF observables for shu ffl ed events are at unityas expected. In the centrality of 30-40%, r rest and R B from data are both larger than the AFVD calculationwithout CME (the case of a = ffi cult to be explained by background-only model. Centrality (%) r AuAu 200GeV rest
Real r lab
Real rAuAu 200GeV rest
Real r lab
Real r rest
Shuffled r lab
Shuffled r LCC = 33% rest /s=0, r n rest /s=0.1, r n rest /s=0.2, r nAVFD (30~40%)| < 0.5 h | preliminarySTARCentrality (%) Centrality (%) B R AuAu 200GeVRealAuAu 200GeVRealShuffled /s=0 n /s=0.1 n /s=0.2 n| < 0.5 h | STAR preliminary Fig. 5. (Color online) r rest , r lab and R B as a function of centrality from Au + Au 200 GeV at STAR.
3. Summary
We reviewed tests of SBF with toy models, and gave an update on studies made with two realisticmodels. Toy model simulation studies show that the two observables, r rest and R B , respond in oppositedirections to signal and backgrounds arising from resonance v and ρ . If both r rest and R B are larger thanunity, then it can be regarded as a case in favor of the existence of CME. In Au + Au collisions at 200 GeV, r rest , r lab and R B are found to be larger than unity, and larger than AVFD model calculation with no CMEimplemented. Our results are di ffi cult to be explained by a background-only scenario. Acknowledgments
We thank S. Shi and J. Liao for providing AVFD Beta1.0 source code. In particularwe thank the RHIC Operations Group and RCF at BNL. Y. Lin is supported by the China ScholarshipCouncil (CSC). This work is supported by the Fundamental Research Funds for the Central Universitiesunder Grant No. CCNU19ZN019 and the Ministry of Science and Technology (MoST) under Grant No.2016YFE0104800.
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