Search for the chiral magnetic effect in heavy ion collisions

Search for the chiral magnetic effect in heavy ion collisions 1 2 corresp first-author Corresponding author, fqwang@zjhu.edu.cn Corresponding author, fqwang@zjhu.edu.cn fqwang@zjhu.edu.cn 2 School of Science, Huzhou University, Huzhou 313000, China School of Science, Huzhou University, Huzhou 313000, China Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA Quark interactions with topological gluon fields in quantum chromodynamics can yield local 𝒫 and 𝒞𝒫 violations that could explain the matter–antimatter asymmetry in our universe. Effects of 𝒫 and 𝒞𝒫 violations can lead to charge separation under a strong magnetic field, a phenomenon called the chiral magnetic effect (CME). Early measurements of the CME-induced charge separation in heavy ion collisions are dominated by physics backgrounds. This report discusses the recent innovative efforts in eliminating those backgrounds, namely, by event-shape engineering, invariant-mass dependence, and reaction and participant plane comparison. The background-free CME measurements using these novel methods are presented. Heavy ion collisions Chiral magnetic effect Azimuthal correlator Flow background Invariant mass Reaction plane Participant plane 1 Introduction and physics motivation 1 Our universe started from the Big Bang singularity with equal matter and antimatter [ 1 1 ]; however, it is dominated by matter today. This matter–antimatter asymmetry is caused by the charge conjugation parity ( 𝒞𝒫 ) violation, and a slight difference in the physical laws governing matter and antimatter [ 2 2 , 3 3 ]. 𝒞𝒫 is violated in the weak interaction; however, the magnitude of the violation is too small to explain the present matter–antimatter asymmetry [ 4 4 ]. 𝒞𝒫 violation in the strong interaction of the early universe is required to explain this. 𝒞𝒫 violation is not prohibited in the strong interaction, but it has not been observed experimentally. This is called the strong 𝒞𝒫 problem [ 5 5 ], one of the remaining problems in physics. The problem can be solved if the 𝒞𝒫 symmetry is violated in local metastable domains of topological gluon fields with nonzero topological charges (winding numbers) because of vacuum fluctuations in quantum chromodynamics (QCD) [ 6 6 - 9 9 6-9 ]. The topological charge, Q W , is proportional to the integral of the scalar product of the gluon (color) electric and magnetic fields over the local domain. Interactions with those topological gluon fields change the helicities of the quarks, thereby causing an imbalance between the left- and right-handed quarks, Q W = N L - N R ≠0, or a local parity ( 𝒫 ) violation [ 9 9 - 11 11 9-11 ]. Such an imbalance can exhibit experimental consequences if submerged in a sufficiently strong magnetic field ( <math id="M1"><mover accent="true"><mi>B</mi><mo>→</mo></mover></math> ). The quark spins will be locked, either parallel or anti-parallel to the magnetic field direction, depending on the quark charge. This would result in an experimentally observable charge separation in the final-state hadrons that are products of quark hadronization. This charge separation phenomenon is called the chiral magnetic effect (CME) [ 12 12 ]; see the illustration in Fig. 1 Fig. 1 . Relativistic heavy ion collisions provide an ideal environment for the realization of the CME, as illustrated in Fig. 1 Fig. 1 . The magnetic field produced by the fast moving spectator protons in the early times of Au + Au collisions at BNL’s Relativistic Heavy Ion Collider (RHIC) is of the order of B ~10 15 Tesla; <math id="M2"><mrow><mi>e</mi><mi>B</mi><mtext> </mtext><mo>~</mo><mtext> </mtext><mn>0.3</mn><msubsup><mi>m</mi><mi>π</mi><mn>2</mn></msubsup></mrow></math> , where m π is the pion mass [ 10 10 - 13 13 10-13 ]. The Laudau energy eB / m q ∼1 GeV is much larger than the typical transverse momenta of the quarks (or the system temperature); therefore, they are locked in the lowest Laudau level. Here, m q ∼ of a few MeV are the light quark masses under the approximate chiral symmetry, which is broken spontaneously under normal conditions but is likely restored in relativistic heavy ion collisions where the relevant degrees of freedom are current quarks and gluons [ 14 14 - 18 18 14-18 ]. The time variation of the magnetic field is less well understood; it can quickly die off with time when the relativistic nuclei pass by quickly, or it could sustain for a relatively long time in a conducting quark–gluon plasma produced in those collisions [ 19 19 , 20 20 ]. Therefore, even if the physics of the CME is correct, its observation is not guaranteed. Meanwhile, an observation of the CME-induced charge separation would confirm several fundamental properties of QCD and solve the long-standing strong 𝒞𝒫 problem. It is therefore of paramount importance. 2 Early measurements and the background issue 1 Intensive efforts have been invested to search for the CME in heavy ion collisions at BNL’s Relativistic Heavy Ion Collider (RHIC) and CERN’s Large Hadron Collider (LHC) [ 21 21 - 23 23 21-23 ]. Among various observables [ 24 24 - 28 28 24-28 ], a typically used observable to measure the CME-induced charge separation in heavy ion collisions is the three-point correlator [ 29 29 ], <math display="block" id="M3"><mrow><mi>γ</mi><mo>≡</mo><mo>〈</mo><mi>cos</mi><mo stretchy="false">(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>−</mo><mn>2</mn><mi>ψ</mi><mo stretchy="false">)</mo><mo>〉</mo><mn>,</mn></mrow></math> where α and β are the azimuthal angles of two particles, and ψ is the angle of the reaction plane (RP, span by the beam and impact parameter directions of the colliding nuclei, see Fig. 2 Fig. 2 for an illustration). Charge separation along the magnetic field, which is perpendicular to ψ on average, would yield different values of γ for particle pairs of the same-sign (SS) and opposite-sign (OS) charges: γ SS =-1 and γ OS =+1, respectively; the values have opposite signs but equal magnitude. Indeed, signals that are qualitatively consistent with the CME expectations have been observed [ 25 25 , 30 30 - 34 34 ]. Figure 3 Figure 3 shows the example results [ 32 32 ] from STAR in 200 GeV Au + Au collisions. Experimentally, the angle ψ is often reconstructed from the azimuthal distribution of the final-state particle density by the fact that the particle density is the largest along the short axis of the collision overlap geometry (see Fig. 2 Fig. 2 )[ 35 35 ]. This is typically attributed to the hydrodynamic expansion of the high-density collision region, generating an elliptical flow ( v 2 ) [ 36 36 , 37 37 ]. In particular, it is the second harmonic (typically labeled as ψ 2 as in Fig. 3 Fig. 3 )of the particle density azimuthal distribution, corrected for finite multiplicity resolution [ 35 35 ]. Because of the fluctuations of the nucleon positions in the colliding nuclei, the reconstructed ψ 2 corresponds to the participant plane (PP). It unnecessarily coincides with the RP; however, it fluctuates about the RP event-by-event [ 38 38 ]. Meanwhile, the RP can be determined more accurately by the spectator neutrons measured by a zero-degree calorimeter (ZDC) [ 39 39 ] (typically labeled as ψ 1 , as in Fig. 3 Fig. 3 )because of a slight side kick they received from the collision [ 40 40 ]. More discussions are presented in Section 3.3. However, background correlations unrelated to the CME exist [ 41 41 - 48 48 41-48 ]. For example, transverse momentum conservation induces correlations among particles that are enhanced back to back pairs [ 42 42 - 46 46 42-46 ]. Because more pairs are emitted in the RP direction, the net effect of this background is negative, thus dragging the CME-induced γ SS and γ OS , originally symmetric about zero (as illustrated in Fig. 4a Fig. 4a ), both down in the negative direction ( Fig. 4b Fig. 4b ). This background is, fortunately, independent of particle charges, thus affecting the SS and OS pairs equally and cancels in the difference, <math display="block" id="M5"><mrow><mi>Δ</mi><mi>γ</mi><mo>≡</mo><msub><mi>γ</mi><mrow><mtext>OS</mtext></mrow></msub><mo>−</mo><msub><mi>γ</mi><mrow><mtext>SS</mtext></mrow></msub><mtext> </mtext><mn>.</mn></mrow></math> Experimental investigations have thus focused on the Δ γ observable [ 21 21 - 23 23 21-23 ]; the CME would yield Δ γ > 0. Unfortunately, mundane physics that differ between SS and OS pairs exist. One such physics is resonance/cluster decays [ 41 41 - 46 46 41-46 ], that affect OS pairs more significantly than SS pairs (as illustrated in Fig. 4c Fig. 4c ). This background is positive and arises from the coupling of elliptical anisotropy v 2 of resonances/clusters, and the angular correlations between their decay daughters (nonflow) [ 41 41 , 42 42 , 45 45 ]. Use ρ→πpπm as an example ( Fig. 5 Fig. 5 ). The effect on γ OS from the decay of a ρ in the RP direction is identical to a back-to-back pair from the CME in the <math id="M6"><mover accent="true"><mi>B</mi><mo>→</mo></mover></math> direction perpendicular to the RP [ 49 49 ]. Because more ρ resonances exist in the RP direction than the perpendicular direction because of the finite v 2 of the ρ , the overall effect on γ OS is positive. There are more sources of particle correlations except that from ρ decays, such as other resonances and jet correlations. We can generally refer to those as cluster correlations [ 41 41 ]. Mathematically, the background can be estimated by <math display="block" id="M7"><mrow><mi>Δ</mi><msub><mi>γ</mi><mrow><mtext>bkgd</mtext></mrow></msub><mo>≈</mo><mfrac><mrow><msub><mi>N</mi><mrow><mtext>clust</mtext><mtext>.</mtext></mrow></msub></mrow><mrow><msubsup><mi>N</mi><mi>π</mi><mn>2</mn></msubsup></mrow></mfrac><mo>〈</mo><mi>cos</mi><mo stretchy="false">(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>−</mo><mn>2</mn><msub><mi>ϕ</mi><mrow><mtext>clust</mtext><mtext>.</mtext></mrow></msub><mo stretchy="false">)</mo><mo>〉</mo><msub><mi>v</mi><mrow><mn>2,</mn><mtext>clust</mtext><mn>.</mn></mrow></msub><mn>,</mn></mrow></math> where N clust and N π are the numbers of clusters and single-charge pions ( N π ≈ N π + ≈ N π - ), respectively, and v 2,clust. ≡〈cos2( ϕ clust. - ψ )〉 is the v 2 of the clusters [ 22 22 , 23 23 , 29 29 , 49 49 ]. A simple estimate, again using the ρ resonance as an example, indicates that the background magnitude is <math id="M8"><mrow><mi>Δ</mi><msub><mi>γ</mi><mrow><mtext>bkgd</mtext></mrow></msub><mo>≈</mo><mfrac><mrow><mn>20</mn></mrow><mrow><msup><mrow><mn>100</mn></mrow><mn>2</mn></msup></mrow></mfrac><mo>×</mo><mn>0.65</mn><mo>×</mo><mn>0.1</mn><mo>≈</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math> for mid-central Au + Au collisions, comparable to the experimental data in Fig. 3 Fig. 3 . 3 Innovative methods and new results 1 Undoubtedly, the early Δ γ measurements [ 25 25 , 30 30 - 34 34 30-34 ] are dominated by backgrounds. Many proposals and attempts have been realized to reduce or eliminate these backgrounds [ 24 24 , 25 25 , 49 49 - 53 53 49-53 ]. Examining Eq. 3, it is easy to identify methods to remove backgrounds. One is to measure the Δ γ observable, where the elliptical anisotropy is zero. This has already been exploited in various data analyses [ 24 24 , 52 52 , 53 53 ] and is not a new method. The other is to measure where resonance contributions are small, or can be identified and removed [ 54 54 , 55 55 ]. This has not been explored until recently [ 56 56 - 58 58 56-58 ]. The following subsections (Sect. 3.1 and Sect. 3.2) will discuss these two methods with the emphasis on the second one. The third innovative method [ 59 59 - 61 61 59-61 ], which will be discussed in Sect. 3.3, is not as obvious, but may present the best and most robust method to search for the CME [ 58 58 ]. 3.1 Make the anisotropy vanish 2 This method comprises two variations. The central idea of the first variation is that "round" events with zero elliptical anisotropy ( <math id="M9"><mrow><msubsup><mi>v</mi><mn>2</mn><mrow><mtext>o</mtext><mi>b</mi><mi>s</mi></mrow></msubsup></mrow></math> ) exists owing to event-by-event statistical and dynamical fluctuations. This was exploited by STAR [ 24 24 ], where a charge asymmetry observable (similar to Δ γ ) was analyzed as a function of the observed event-by-event <math id="M10"><mrow><msubsup><mi>v</mi><mn>2</mn><mrow><mtext>o</mtext><mi>b</mi><mi>s</mi></mrow></msubsup></mrow></math> ; both the Δ γ and <math id="M11"><mrow><msubsup><mi>v</mi><mn>2</mn><mrow><mtext>o</mtext><mi>b</mi><mi>s</mi></mrow></msubsup></mrow></math> are calculated from the same group of particles (particles of interest, or POI). This is shown in Fig. 6 Fig. 6 . A clear linear dependence was observed, as expected from the background. The background-suppressed CME signal can be extracted from the intercept at <math id="M12"><mrow><msubsup><mi>v</mi><mn>2</mn><mrow><mtext>o</mtext><mi>b</mi><mi>s</mi></mrow></msubsup><mo>=</mo><mn>0</mn></mrow></math> . With the limited statistics from Run-4 data (taken in the year 2004 by STAR), the extracted intercept is consistent with the zero in the 200 GeV Au + Au collisions [ 24 24 ]. Analysis of higher statistics data from later runs indicates that the intercept is finite [ 62 62 ]. However, the intercept at <math id="M13"><mrow><msubsup><mi>v</mi><mn>2</mn><mrow><mtext>o</mtext><mi>b</mi><mi>s</mi></mrow></msubsup><mo>=</mo><mn>0</mn></mrow></math> may still contain residual backgrounds because the backgrounds are owing to the non-vanishing v 2,clust of the correlation sources (resonances/clusters) (see Eq. 3), and not the <math id="M14"><mrow><msubsup><mi>v</mi><mn>2</mn><mrow><mtext>o</mtext><mi>b</mi><mi>s</mi></mrow></msubsup></mrow></math> measured by the final-state charged hadrons. It was shown by a toy-model resonance simulation [ 49 49 ] that the resonance v 2 is not zero when the event-by-event <math id="M15"><mrow><msubsup><mi>v</mi><mn>2</mn><mrow><mtext>o</mtext><mi>b</mi><mi>s</mi></mrow></msubsup></mrow></math> of the final-state hadrons is required to be zero. Even if one could ensure that the event-by-event v 2 of one resonance type is zero, it is nearly impossible to ensure the event-by-event v 2 ’s of all the background sources to be zero. Furthermore, the background in Eq. 3 is proportional to v 2,clust only when cos( α + β -2 ϕ clust. ) and cos2( ϕ clust. - ψ ) are factorized. This may not be the case because both depend on the transverse momentum ( p T ) of the cluster [ 49 49 ]. The second variation of the method is to analyze the Δ γ observable of the POI as a function of the flow vector magnitude ( q 2 ) [ 63 63 ] that is calculated not using the POI but the particles from different phase spaces [ 52 52 , 53 53 ]. The q 2 is closely related to v 2 , and this method is known as "event-shape engineering (ESE)" [ 63 63 ]. ALICE [ 52 52 ] divided their data in each collision centrality according to q 2 and found the Δ γ to be approximately proportional to the v 2 of the POI; this is consistent with the background contributions. This is shown in Fig. 7 Fig. 7 . One could fit the data with the linear function in v 2 and extract the possible CME signal by the fit intercept. However, within each relatively wide centrality bin, the magnetic field most probably varies. Thus, ALICE modeled B ( v 2 ) to extract the CME signal. The extracted signal is found to be smaller than 20% of the early, inclusive Δ γ measurement at the 95% conference level [ 52 52 ]. The attractive aspect of this second variation of the method is that it can maintain the magnetic field, and vary the event-by-event v 2 [ 24 24 , 64 64 , 65 65 ]. CMS attempts to achieve this using narrow centrality bins [ 53 53 ] such that the extracted CME signal is less model dependent. The CMS results indicate that the CME signal is less than 7% of the inclusive Δ γ at the 95% confidence level [ 53 53 ]. Because the ESE control knob q 2 and the POI are from different phase spaces, a given q 2 cut-bin samples a v 2 distribution of the POI. The extrapolated zero average v 2 of the POI likely corresponds to the zero average v 2 of all particle species, including the CME background sources of resonances and clusters. This is clearly advantageous over the first variation of the method using the event-by-event <math id="M18"><mrow><msubsup><mi>v</mi><mn>2</mn><mrow><mtext>o</mtext><mi>b</mi><mi>s</mi></mrow></msubsup></mrow></math> . The disadvantage is that an extrapolation to v 2 =0 is required as the ESE q 2 sampling does not cover the most important v 2 =0 region. A dependence of the backgrounds on v 2 that is not strictly linear would introduce imprecision in the extracted CME signal. 3.2 Identify backgrounds by invariant mass 2 The particle pair invariant mass ( m inv ) is a typical method to identify resonances. Until recently [ 54 54 ], m inv had not been utilized to investigate the CME Δ γ signal. The upper panel in Fig. 8 Fig. 8 shows the relative OS excess over the SS pion pairs in Run-11 Au + Au collisions from STAR [ 56 56 - 58 58 ]. The pions are identified by the TPC and time-of-flight (TOF) detector within pseudorapidity and p T ranges of | ≤ | < 1 and 0.2 < p T < 1.8 GeV/ c , respectively. The resonance peaks of K S and ρ are clearly shown. The large increase toward the low- m inv kinematic limit is owing to the acceptance edge effect, where the OS and SS pair acceptance differences of the detector are amplified [ 58 58 , 66 66 ]. The lower panel shows the Δ γ measurement as a function of m inv . A clear peak at the K S mass is observed; a peak at the ρ mass is observable. Most π + π - pair resonances are below m inv < 1.5 GeV/ c 2 ; at higher m inv , the resonance contribution can be neglected. The easiest method to remove resonance contributions from Δ γ is, therefore, to restrict the measurements to the large- m inv region. Figure 9 Figure 9 shows the measured Δ γ at m inv > 1.5 GeV/ c 2 , compared to the inclusive Δ γ . The large-mass Δ γ is significantly lower by a factor of 20, compared to the inclusive Δ γ , and is consistent with zero within a 2 σ standard deviation. The CME is a low- p T phenomenon and may not be appreciable at high m inv , although theoretical calculations suggest that the CME survives at m inv > 1.5 GeV/ c [ 67 67 ]. To extract the CME signal in the low- m inv region, one needs the m inv dependence of the background contribution. STAR used the ESE technique [ 58 58 ], dividing events from each narrow centrality bin into two classes according to the event-by-event q 2 [ 63 63 ]. Because the magnetic fields are approximately equal while the backgrounds differ, the Δ γ ( m inv ) difference between the two classes is a good estimate of the background shape. Figure 10 Figure 10 shows the Δ γA and Δ γB from such two q 2 classes in the upper panel, and the difference Δ γA -Δ γB together with the inclusive Δ γ of all events in the lower panel [ 58 58 ]. With the background shape given by Δ γA -Δ γB , the CME can be extracted from a two-component fit to the following form: Δ γ = κ Δ γA -Δ γB +Δ γ CME . The left panel in Fig. 11 Fig. 11 shows Δ γ as a function of Δ γA -Δ γB , where each data point corresponds to one m inv bin in the lower panel of Fig 10 Fig 10 [ 58 58 ]. Only the m inv > 0.4 GeV/ c 2 data points are included in Fig. 11 Fig. 11 because the Δ γ from the lower m inv region is affected by the edge effects of the STAR TPC acceptance [ 58 58 , 66 66 ]. As shown, a positive linear correlation exists between Δ γ and Δ γA -Δ γB . However, because the same data were used in the measurements of Δ γ and Δ γA -Δ γB , their statistical errors are correlated. To accommodate the statistical errors, one can simply fit the independent measurements of Δ γA against Δ γB , namely by <math display="block" id="M23"><mrow><mi>Δ</mi><msub><mi>γ</mi><mi>A</mi></msub><mo>=</mo><mi>b</mi><mi>Δ</mi><msub><mi>γ</mi><mi>B</mi></msub><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>b</mi><mo stretchy="false">)</mo><mi>Δ</mi><msub><mi>γ</mi><mrow><mtext>C</mtext><mi>M</mi><mi>E</mi></mrow></msub><mn>,</mn></mrow></math> where b and Δ γ CME are the fitting parameters. The right panel of Fig. 11 Fig. 11 shows Δ γA against Δ γB , and the fit by Eq. 4 superimposed as the straight line [ 58 58 ]. The straight line superimposed on the left panel of Fig. 11 Fig. 11 is the same fit to Eq. 4, converted properly. The parameter b reflects the relative background contribution in the large- q 2 (large- v 2 ) event class to that in the small- q 2 (small- v 2 ) event class; further, because the background increases with v 2 , the value of b is larger than unity. The CME signal Δ γ CME obtained from the fit is consistent with zero. In this fit model, unlike the simple ESE method described in Sect. 3.1, the background is not required to be strictly proportional to v 2 . Provided that the backgrounds are different for different q 2 event classes, one can extract the background shape as a function of m inv . The slope fit parameter in Eq. 4 indicates how good the linearity of the background is against v 2 The fit model, however, assumes that the CME signal is independent of m inv . The good fit quality shown in Fig. 10 Fig. 10 indicates that this is a good assumption within the current statistical precision of the data. 3.3 Compare participant plane and reaction plane 2 The magnetic field is primarily produced by spectator protons; therefore, its direction is determined by the spectator plane. It is found that the spectator plane nearly coincides with the RP in heavy ion collisions except for highly central collisions [ 60 60 ]. The elliptic flow v 2 is generated by the participants, and is therefore determined by the PP [ 38 38 ]. The PP and RP are correlated, but, owing to fluctuations [ 38 38 ], they are not identical. See the illustration in the left panel of Fig. 12 Fig. 12 . The CME-induced charge separation, driven by the magnetic field [ 11 11 ], will be the strongest along the direction perpendicular to the spectator plane, and will be weaker along the direction perpendicular to the PP. The reduction factor is determined by the opening angle between the two planes and equals to <math display="block" id="M24"><mrow><mi>a</mi><mo>=</mo><mo>〈</mo><mi>cos</mi><mn>2</mn><mo stretchy="false">(</mo><msub><mi>ψ</mi><mrow><mtext>PP</mtext></mrow></msub><mo>−</mo><msub><mi>ψ</mi><mrow><mtext>RP</mtext></mrow></msub><mo stretchy="false">)</mo><mo>〉</mo><mn>.</mn></mrow></math> The v 2 -induced background, meanwhile, will be the largest in the Δ γ measurement with respect to the PP, and will be reduced by the same factor a in the Δ γ measurement with respect to the RP. In other words, the Δ γ measurements with respect to the PP and RP contain different amounts of v 2 backgrounds and CME signals. Thus, the two Δ γ measurements can disentangle the background and the CME signal. This is illustrated in the right panel of Fig. 12 Fig. 12 ; the PP and RP serve as two different filters for the v 2 background and CME signal. In the experiment, the spectator plane (or closely the RP) can be measured by the ZDCs because of the slight side kick to the spectators in the collision [ 40 40 ]. The PP is, as usual, measured by final-state particles, for example, by the TPC in the STAR experiment [ 68 68 ]. The Δ γ measurements with respect to the RP and PP can readily present the CME signal fraction in the inclusive Δ γ measurement [ 60 60 ]. It is noteworthy that the ZDCs measure only the spectator neutrons [ 69 69 ]; therefore, the measured first-order harmonic plane fluctuates about the RP. Similarly, the final-state particle measurement of the second-harmonic plane is affected by effects other than the elliptic flow [ 70 70 ] and fluctuates about the PP. However, our method does not require a precise determination of the RP and PP [ 60 60 ]. Provided that two experimentally assessable planes exist, onto which the projections of the magnetic field and the elliptic flow are the opposite, our method is robust and is not affected by the uncertainties in assessing the true RP and PP. The plane projection relationship is given by Eq. (5), where the ψ PP and ψ RP , in an experimental data analysis context should be regarded as the experimentally measured harmonic planes. Figure 13 Figure 13 shows the CME signal in terms of its fraction in the inclusive Δ γ measurement as a function of centrality in 200 GeV Au + Au collisions [ 58 58 ]. The two sets of data points correspond to two different acceptance cuts in the analysis. The results are primarily consistent with zero. 4 Discussions and Summary 1 At the LHC, the CMS and ALICE experiments used the ESE method to measure the CME signal without flow background contamination. The CME signal was found to be less than 7% (CMS) [ 53 53 ] and 20% (ALICE) [ 52 52 ] of the inclusive Δ γ measurement at the 95% confidence level. At the RHIC, two novel methods—invariant mass dependence and comparative PP-RP measurements—have been developed recently. Figure 14 Figure 14 summarizes the current status of the CME signal from STAR in 20–50% central Au + Au collisions at <math id="M25"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><msub><mrow/><mrow><mtext>N</mtext><mi>N</mi></mrow></msub></mrow></msub></mrow></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV [ 58 58 ] using these two methods. The data indicate that the CME signal is small, of the order of a few percent of the inclusive Δ γ measurement, with relatively large errors [ 58 58 ]. In summary, the CME resulted from local 𝒫 and 𝒞𝒫 violations caused by topological charge fluctuations in QCD. Relativistic heavy ion collisions provided an ideal environment to search for the CME with the strong color gluon field and electromagnetic field. An observation of the CME would confirm several fundamental properties of QCD and solve the strong 𝒞𝒫 problem responsible for the matter–antimatter asymmetry in today’s universe. Charge-dependent azimuthal correlations with respect to the RP (and PP) were sensitive to the CME, but were contaminated by major physics backgrounds arising from the coupling of resonance/cluster decays and their elliptic flows ( v 2 ). Intensive theoretical and experimental efforts have been devoted to eliminating those backgrounds and significant progresses have been made in this regard. We herein discussed three novel methods that could potentially measure the background-free CME: ESE, invariant-mass ( m inv ) dependence, and comparative measurements with respect to the PP and RP. The current estimates on the strength of the possible CME signal are of the order of a few percent of the inclusive Δ γ values, and 1–2 σ standard deviation from zero. It is clear that the experimental challenges in the CME search are daunting, but the important physics warrants continued efforts. References R. A. Alpher , H. Bethe , G. Gamow , The origin of chemical elements . Phys. Rev . 73 , 803 ( 1948 ). doi: 10.1103/PhysRev.73.803 http://doi.org/10.1103/PhysRev.73.803 The origin of chemical elements A. D. Sakharov , Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe . Pisma Zh. Eksp. Teor. Fiz . 5 , 32 ( 1967 ) Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe A. D. Sakharov , Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe . [ JETP Lett. 5 , 24 ( 1967 )] Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe A. D. Sakharov , Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe . [ Sov. Phys. Usp. 34 , no. 5 , 392 ( 1991 )] Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe A. D. Sakharov , Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe . [ Usp. Fiz. Nauk 161 , no. 5 , 61 ( 1991 )]. doi: 10.1070/PU1991v034n05ABEH002497 http://doi.org/10.1070/PU1991v034n05ABEH002497 Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe M. Dine , A. Kusenko , The origin of the matter - antimatter asymmetry . Rev. Mod. Phys . 76 , 1 ( 2003 ) doi: 10.1103/RevModPhys.76.1 http://doi.org/10.1103/RevModPhys.76.1 The origin of the matter - antimatter asymmetry T. Mannel , Theory and phenomenology of CP violation . Nucl. Phys. Proc. Suppl . 167 , 115 ( 2007 ). doi: 10.1016/j.nuclphysbps.2006.12.083 http://doi.org/10.1016/j.nuclphysbps.2006.12.083 Theory and phenomenology of CP violation R. D. Peccei , H. R. Quinn , CP conservation in the presence of instantons . Phys. Rev. Lett . 38 , 1440 ( 1977 ). doi: 10.1103/PhysRevLett.38.1440 http://doi.org/10.1103/PhysRevLett.38.1440 CP conservation in the presence of instantons T. D. Lee , A theory of spontaneous T violation . Phys. Rev. D 8 , 1226 ( 1973 ). doi: 10.1103/PhysRevD.8.1226 http://doi.org/10.1103/PhysRevD.8.1226 A theory of spontaneous T violation T. D. Lee , G. C. Wick , Vacuum stability and vacuum excitation in a spin 0 field theory . Phys. Rev. D 9 , 2291 ( 1974 ). doi: 10.1103/PhysRevD.9.2291 http://doi.org/10.1103/PhysRevD.9.2291 Vacuum stability and vacuum excitation in a spin 0 field theory P. D. Morley , I. A. Schmidt , Strong P, CP, T violations in heavy ion collisions . Z. Phys. C 26 , 627 ( 1985 ). doi: 10.1007/BF01551807 http://doi.org/10.1007/BF01551807 Strong P, CP, T violations in heavy ion collisions D. Kharzeev , R. Pisarski , M. H. Tytgat , Possibility of spontaneous parity violation in hot QCD . Phys.Rev.Lett . 81 , 512 ( 1998 ). doi: 10.1103/PhysRevLett.81.512 http://doi.org/10.1103/PhysRevLett.81.512 Possibility of spontaneous parity violation in hot QCD D. Kharzeev , Parity violation in hot QCD: Why it can happen, and how to look for it . Phys. Lett. B 633 , 260 ( 2006 ). doi: 10.1016/j.physletb.2005.11.075 http://doi.org/10.1016/j.physletb.2005.11.075 Parity violation in hot QCD: Why it can happen, and how to look for it D. E. Kharzeev , L. D. McLerran , H. J. Warringa , The effects of topological charge change in heavy ion collisions: ’Event by event P and CP violation’ . Nucl. Phys. A 803 , 227 ( 2008 ). doi: 10.1016/j.nuclphysa.2008.02.298 http://doi.org/10.1016/j.nuclphysa.2008.02.298 The effects of topological charge change in heavy ion collisions: ’Event by event P and CP violation’ K. Fukushima , D. E. Kharzeev , H. J. Warringa , The Chiral Magnetic Effect . Phys. Rev. D 78 , 074033 ( 2008 ). doi: 10.1103/PhysRevD.78.074033 http://doi.org/10.1103/PhysRevD.78.074033 The Chiral Magnetic Effect B. Muller , A. Schafer , Charge Fluctuations from the Chiral Magnetic Effect in Nuclear Collisions . Phys. Rev. C 82 , 057902 ( 2010 ). doi: 10.1103/PhysRevC.82.057902 http://doi.org/10.1103/PhysRevC.82.057902 Charge Fluctuations from the Chiral Magnetic Effect in Nuclear Collisions J. Adams et al . [STAR Collaboration] , Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration’s critical assessment of the evidence from RHIC collisions . Nucl. Phys. A 757 , 102 ( 2005 ). doi: 10.1016/j.nuclphysa.2005.03.085 http://doi.org/10.1016/j.nuclphysa.2005.03.085 Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration’s critical assessment of the evidence from RHIC collisions K. Adcox et al . [PHENIX Collaboration] , Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration . Nucl. Phys. A 757 , 184 ( 2005 ). doi: 10.1016/j.nuclphysa.2005.03.086 http://doi.org/10.1016/j.nuclphysa.2005.03.086 Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration I. Arsene et al . [BRAHMS Collaboration] , Quark gluon plasma and color glass condensate at RHIC? The Perspective from the BRAHMS experiment . Nucl. Phys. A 757 , 1 ( 2005 ). doi: 10.1016/j.nuclphysa.2005.02.130 http://doi.org/10.1016/j.nuclphysa.2005.02.130 Quark gluon plasma and color glass condensate at RHIC? The Perspective from the BRAHMS experiment B. B. Back et al ., The PHOBOS perspective on discoveries at RHIC . Nucl. Phys. A 757 , 28 ( 2005 ). doi: 10.1016/j.nuclphysa.2005.03.084 http://doi.org/10.1016/j.nuclphysa.2005.03.084 The PHOBOS perspective on discoveries at RHIC B. Muller , J. Schukraft , B. Wyslouch , First Results from Pb+Pb collisions at the LHC . Ann. Rev. Nucl. Part. Sci . 62 , 361 ( 2012 ). doi: 10.1146/annurev-nucl-102711-094910 http://doi.org/10.1146/annurev-nucl-102711-094910 First Results from Pb+Pb collisions at the LHC K. Tuchin , Synchrotron radiation by fast fermions in heavy-ion collisions . Phys. Rev. C 82 , 034904 ( 2010 ). doi: 10.1103/PhysRevC.82.034904 http://doi.org/10.1103/PhysRevC.82.034904 Synchrotron radiation by fast fermions in heavy-ion collisions Erratum: Synchrotron radiation by fast fermions in heavy-ion collisions [ Phys. Rev. C 82 , 034904 ( 2010 )]. Synchrotron radiation by fast fermions in heavy-ion collisions Erratum: Synchrotron radiation by fast fermions in heavy-ion collisions Phys. Rev. C 83 , 039903 ( 2011 ) doi: 10.1103/PhysRevC.83.039903 http://doi.org/10.1103/PhysRevC.83.039903 Synchrotron radiation by fast fermions in heavy-ion collisions D. She , S. Q. Feng , Y. Zhong , et al ., Chiral magnetic currents with QGP medium response in heavy ion collisions at RHIC and LHC energies . Eur. Phys. J. A 54 , 48 ( 2018 ). doi: 10.1140/epja/i2018-12481-x http://doi.org/10.1140/epja/i2018-12481-x Chiral magnetic currents with QGP medium response in heavy ion collisions at RHIC and LHC energies D. E. Kharzeev , J. Liao , S. A. Voloshin , et al ., Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report . Prog. Part. Nucl. Phys . 88 , 1 ( 2016 ). doi: 10.1016/j.ppnp.2016.01.001 http://doi.org/10.1016/j.ppnp.2016.01.001 Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report J. Zhao , Search for the chiral magnetic effect in relativistic heavy-ion collisions . Int. J. Mod. Phys. A 33 , 1830010 ( 2018 ). doi: 10.1142/S0217751X18300107 http://doi.org/10.1142/S0217751X18300107 Search for the chiral magnetic effect in relativistic heavy-ion collisions J. Zhao , Z. Tu , F. Wang , Status of the Chiral Magnetic Effect Search in Relativistic Heavy-Ion Collisions . arXiv:1807.05083 [nucl-ex] . Status of the Chiral Magnetic Effect Search in Relativistic Heavy-Ion Collisions L. Adamczyk et al . [STAR Collaboration] , Measurement of charge multiplicity asymmetry correlations in high-energy nucleus-nucleus collisions at <math id="M27"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo></mrow></math> 200 GeV . Phys. Rev. C 89 , 044908 ( 2014 ). doi: 10.1103/PhysRevC.89.044908 http://doi.org/10.1103/PhysRevC.89.044908 Measurement of charge multiplicity asymmetry correlations in high-energy nucleus-nucleus collisions at sNN=200 GeV N. N. Ajitanand , R. A. Lacey , A. Taranenko , et al ., A New method for the experimental study of topological effects in the quark-gluon plasma . Phys. Rev. C 83 , 011901 ( 2011 ). A New method for the experimental study of topological effects in the quark-gluon plasma N. Magdy , S. Shi , J. Liao , et al ., New correlator to detect and characterize the chiral magnetic effect . Phys. Rev. C 97 , 061901 ( 2018 ). doi: 10.1103/PhysRevC.97.061901 http://doi.org/10.1103/PhysRevC.97.061901 New correlator to detect and characterize the chiral magnetic effect P. Bozek , Azimuthal angle dependence of the charge imbalance from charge conservation effects . Phys. Rev. C 97 , 034907 ( 2018 ). doi: 10.1103/PhysRevC.97.034907 http://doi.org/10.1103/PhysRevC.97.034907 Azimuthal angle dependence of the charge imbalance from charge conservation effects Y. Feng , J. Zhao , F. Wang , Responses of the chiral-magnetic-effect-sensitive sine observable to resonance backgrounds in heavy-ion collisions . Phys. Rev. C 98 , 034904 ( 2018 ). doi: 10.1103/PhysRevC.98.034904 http://doi.org/10.1103/PhysRevC.98.034904 Responses of the chiral-magnetic-effect-sensitive sine observable to resonance backgrounds in heavy-ion collisions S. A. Voloshin , Parity violation in hot QCD: How to detect it . Phys. Rev. C 70 , 057901 ( 2004 ). doi: 10.1103/PhysRevC.70.057901 http://doi.org/10.1103/PhysRevC.70.057901 Parity violation in hot QCD: How to detect it B. I. Abelev et al . [STAR Collaboration] , Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy ion collisions . Phys. Rev. C 81 , 054908 ( 2010 ). doi: 10.1103/PhysRevC.81.054908 http://doi.org/10.1103/PhysRevC.81.054908 Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy ion collisions B. I. Abelev et al . [STAR Collaboration] , Azimuthal charged-particle correlations and possible local strong parity violation . Phys. Rev. Lett . 103 , 251601 ( 2009 ). doi: 10.1103/PhysRevLett.103.251601 http://doi.org/10.1103/PhysRevLett.103.251601 Azimuthal charged-particle correlations and possible local strong parity violation L. Adamczyk et al . [STAR Collaboration] , Fluctuations of charge separation perpendicular to the event plane and local parity violation in <math id="M28"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>N</mtext><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider . Phys. Rev. C 88 , no. 6 , 064911 ( 2013 ). doi: 10.1103/PhysRevC.88.064911 http://doi.org/10.1103/PhysRevC.88.064911 Fluctuations of charge separation perpendicular to the event plane and local parity violation in sNN=200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider L. Adamczyk et al . [STAR Collaboration] , Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC . Phys. Rev. Lett . 113 , 052302 ( 2014 ). doi: 10.1103/PhysRevLett.113.052302 http://doi.org/10.1103/PhysRevLett.113.052302 Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC B. Abelev et al . [ALICE Collaboration] , Charge separation relative to the reaction plane in Pb-Pb collisions at <math id="M29"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>N</mtext><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.76</mn></mrow></math> TeV . Phys. Rev. Lett . 110 , 012301 ( 2013 ). doi: 10.1103/PhysRevLett.110.012301 http://doi.org/10.1103/PhysRevLett.110.012301 Charge separation relative to the reaction plane in Pb-Pb collisions at sNN=2.76 TeV A. M. Poskanzer , S. A. Voloshin , Methods for analyzing anisotropic flow in relativistic nuclear collisions . Phys. Rev. C 58 , 1671 ( 1998 ). doi: 10.1103/PhysRevC.58.1671 http://doi.org/10.1103/PhysRevC.58.1671 Methods for analyzing anisotropic flow in relativistic nuclear collisions J. Y. Ollitrault , Anisotropy as a signature of transverse collective flow . Phys. Rev. D 46 , 229 ( 1992 ). doi: 10.1103/PhysRevD.46.229 http://doi.org/10.1103/PhysRevD.46.229 Anisotropy as a signature of transverse collective flow U. Heinz and R. Snellings , Collective flow and viscosity in relativistic heavy-ion collisions . Ann. Rev. Nucl. Part. Sci . 63 , 123 ( 2013 ). doi: 10.1146/annurev-nucl-102212-170540 http://doi.org/10.1146/annurev-nucl-102212-170540 Collective flow and viscosity in relativistic heavy-ion collisions B. Alver et al . [PHOBOS Collaboration] , System size, energy, pseudorapidity, and centrality dependence of elliptic flow . Phys. Rev. Lett . 98 , 242302 ( 2007 ). doi: 10.1103/PhysRevLett.98.242302 http://doi.org/10.1103/PhysRevLett.98.242302 System size, energy, pseudorapidity, and centrality dependence of elliptic flow C. Adler , A. Denisov , E. Garcia , et al ., The RHIC zero-degree calorimeters . Nucl. Instrum. Meth. A 499 , 433 ( 2003 ). doi: 10.1016/j.nima.2003.08.112 http://doi.org/10.1016/j.nima.2003.08.112 The RHIC zero-degree calorimeters W. Reisdorf , H. G. Ritter , Collective flow in heavy-ion collisions . Ann. Rev. Nucl. Part. Sci . 47 , 663 ( 1997 ). doi: 10.1146/annurev.nucl.47.1.663 http://doi.org/10.1146/annurev.nucl.47.1.663 Collective flow in heavy-ion collisions F. Wang , Effects of cluster particle correlations on local parity violation observables . Phys. Rev. C 81 , 064902 ( 2010 ). doi: 10.1103/PhysRevC.81.064902 http://doi.org/10.1103/PhysRevC.81.064902 Effects of cluster particle correlations on local parity violation observables A. Bzdak , V. Koch , J. Liao , Remarks on possible local parity violation in heavy ion collisions . Phys. Rev. C 81 , 031901 ( 2010 ). doi: 10.1103/PhysRevC.81.031901 http://doi.org/10.1103/PhysRevC.81.031901 Remarks on possible local parity violation in heavy ion collisions J. Liao , V. Koch , A. Bzdak , On the charge separation effect in relativistic heavy ion collisions . Phys. Rev. C 82 , 054902 ( 2010 ). doi: 10.1103/PhysRevC.82.054902 http://doi.org/10.1103/PhysRevC.82.054902 On the charge separation effect in relativistic heavy ion collisions A. Bzdak , V. Koch , J. Liao , Azimuthal correlations from transverse momentum conservation and possible local parity violation . Phys. Rev. C 83 , 014905 ( 2011 ). doi: 10.1103/PhysRevC.83.014905 http://doi.org/10.1103/PhysRevC.83.014905 Azimuthal correlations from transverse momentum conservation and possible local parity violation S. Schlichting , S. Pratt , Charge conservation at energies available at the BNL Relativistic Heavy Ion Collider and contributions to local parity violation observables . Phys. Rev. C 83 , 014913 ( 2011 ). doi: 10.1103/PhysRevC.83.014913 http://doi.org/10.1103/PhysRevC.83.014913 Charge conservation at energies available at the BNL Relativistic Heavy Ion Collider and contributions to local parity violation observables S. Pratt , S. Schlichting , S. Gavin , Effects of momentum conservation and flow on angular correlations at RHIC . Phys. Rev. C 84 , 024909 ( 2011 ). doi: 10.1103/PhysRevC.84.024909 http://doi.org/10.1103/PhysRevC.84.024909 Effects of momentum conservation and flow on angular correlations at RHIC H. Petersen , T. Renk , S. A. Bass , Medium-modified jets and initial state fluctuations as sources of charge correlations measured at RHIC . Phys. Rev. C 83 , 014916 ( 2011 ). doi: 10.1103/PhysRevC.83.014916 http://doi.org/10.1103/PhysRevC.83.014916 Medium-modified jets and initial state fluctuations as sources of charge correlations measured at RHIC V. D. Toneev , V. P. Konchakovski , V. Voronyuk , et al ., Event-by-event background in estimates of the chiral magnetic effect . Phys. Rev. C 86 , 064907 ( 2012 ). doi: 10.1103/PhysRevC.86.064907 http://doi.org/10.1103/PhysRevC.86.064907 Event-by-event background in estimates of the chiral magnetic effect F. Wang , J. Zhao , Challenges in flow background removal in search for the chiral magnetic effect . Phys. Rev. C 95 , no. 5 , 051901 ( 2017 ). doi: 10.1103/PhysRevC.95.051901 http://doi.org/10.1103/PhysRevC.95.051901 Challenges in flow background removal in search for the chiral magnetic effect A. Bzdak , Suppression of elliptic flow induced correlations in an observable of possible local parity violation . Phys. Rev. C 85 , 044919 ( 2012 ). doi: 10.1103/PhysRevC.85.044919 http://doi.org/10.1103/PhysRevC.85.044919 Suppression of elliptic flow induced correlations in an observable of possible local parity violation F. Wen , J. Bryon , L. Wen , et al ., Event-shape-engineering study of charge separation in heavy-ion collisions . Chin. Phys. C 42 , no. 1 , 014001 ( 2018 ). doi: 10.1088/1674-1137/42/1/014001 http://doi.org/10.1088/1674-1137/42/1/014001 Event-shape-engineering study of charge separation in heavy-ion collisions S. Acharya et al . [ALICE Collaboration] , Constraining the magnitude of the Chiral Magnetic Effect with Event Shape Engineering in Pb-Pb collisions at <math id="M30"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt></mrow></math> = 2.76 TeV . Phys. Lett. B 777 , 151 ( 2018 ). doi: 10.1016/j.physletb.2017.12.021 http://doi.org/10.1016/j.physletb.2017.12.021 Constraining the magnitude of the Chiral Magnetic Effect with Event Shape Engineering in Pb-Pb collisions at sNN = 2.76 TeV A. M. Sirunyan et al . [CMS Collaboration] , Constraints on the chiral magnetic effect using charge-dependent azimuthal correlations in pPb and PbPb collisions at the CERN Large Hadron Collider . Phys. Rev. C 97 , 044912 ( 2018 ). doi: 10.1103/PhysRevC.97.044912 http://doi.org/10.1103/PhysRevC.97.044912 Constraints on the chiral magnetic effect using charge-dependent azimuthal correlations in pPb and PbPb collisions at the CERN Large Hadron Collider J. Zhao , H. Li , F. Wang , Isolating the chiral magnetic effect from backgrounds by pair invariant mass . arXiv:1705.05410 [nucl-ex] . Isolating the chiral magnetic effect from backgrounds by pair invariant mass H. Li , J. Zhao , F. Wang , A novel invariant mass method to isolate resonance backgrounds from the chiral magnetic effect . arXiv:1808.03210 [nucl-ex] . A novel invariant mass method to isolate resonance backgrounds from the chiral magnetic effect J. Zhao [STAR Collaboration] , Chiral magnetic effect search in p+Au, d+Au and Au+Au collisions at RHIC . EPJ Web Conf . 172 , 01005 ( 2018 ). doi: 10.1051/epjconf/201817201005 http://doi.org/10.1051/epjconf/201817201005 Chiral magnetic effect search in p+Au, d+Au and Au+Au collisions at RHIC J. Zhao [STAR Collaboration] , Chiral magnetic effect search in p(d)+Au, Au+Au collisions at RHIC . Int. J. Mod. Phys. Conf. Ser . 46 , 1860010 ( 2018 ). doi: 10.1142/S2010194518600108 http://doi.org/10.1142/S2010194518600108 Chiral magnetic effect search in p(d)+Au, Au+Au collisions at RHIC J. Zhao [STAR Collaboration] , Measurements of the chiral magnetic effect with background isolation in 200 GeV Au+Au collisions at STAR . arXiv:1807.09925 [nucl-ex] . Measurements of the chiral magnetic effect with background isolation in 200 GeV Au+Au collisions at STAR H. J. Xu , X. Wang , H. Li , et al ., Importance of isobar density distributions on the chiral magnetic effect search . Phys. Rev. Lett . 121 , 022301 ( 2018 ). doi: 10.1103/PhysRevLett.121.022301 http://doi.org/10.1103/PhysRevLett.121.022301 Importance of isobar density distributions on the chiral magnetic effect search H. j. Xu , J. Zhao , X. Wang , et al ., Varying the chiral magnetic effect relative to flow in a single nucleus-nucleus collision . Chin. Phys. C 42 , 084103 ( 2018 ). doi: 10.1088/1674-1137/42/8/084103 http://doi.org/10.1088/1674-1137/42/8/084103 Varying the chiral magnetic effect relative to flow in a single nucleus-nucleus collision H. j. Xu , J. Zhao , X. Wang , et al ., Re-examining the premise of isobaric collisions and a novel method to measure the chiral magnetic effect . arXiv:1808.00133 [nucl-th] . Re-examining the premise of isobaric collisions and a novel method to measure the chiral magnetic effect B. Tu , Charge Asymmetry Correlations to Search for the Chiral Magnetic Effect from Beam Energy Scan by STAR. Kobe, Japan, Sep. 27 - Oct. 3, 2015 https://drupal.star.bnl.gov/STAR/presentations/qm2015/biao-tu https://drupal.star.bnl.gov/STAR/presentations/qm2015/biao-tu NoStop Charge Asymmetry Correlations to Search for the Chiral Magnetic Effect from Beam Energy Scan by STAR. Kobe, Japan, Sep. 27 - Oct. 3, 2015 J. Schukraft , A. Timmins , S. A. Voloshin , Ultra-relativistic nuclear collisions: event shape engineering . Phys. Lett. B 719 , 394 ( 2013 ). doi: 10.1016/j.physletb.2013.01.045 http://doi.org/10.1016/j.physletb.2013.01.045 Ultra-relativistic nuclear collisions: event shape engineering S. A. Voloshin , Testing the chiral magnetic effect with central U+U collisions . Phys. Rev. Lett . 105 , 172301 ( 2010 ). doi: 10.1103/PhysRevLett.105.172301 http://doi.org/10.1103/PhysRevLett.105.172301 Testing the chiral magnetic effect with central U+U collisions S. Chatterjee and P. Tribedy , Separation of flow from the chiral magnetic effect in U + U collisions using spectator asymmetry . Phys. Rev. C 92 , no. 1 , 011902 ( 2015 ). doi: 10.1103/PhysRevC.92.011902 http://doi.org/10.1103/PhysRevC.92.011902 Separation of flow from the chiral magnetic effect in U + U collisions using spectator asymmetry L. Adamczyk et al . [STAR Collaboration] , Measurements of dielectron production in Au+Au collisions at <math id="M31"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>N</mtext><mi>N</mi></mrow></msub></mrow></msqrt></mrow></math> = 200 GeV from the STAR experiment . Phys. Rev. C 92 , no. 2 , 024912 ( 2015 ). doi: 10.1103/PhysRevC.92.024912 http://doi.org/10.1103/PhysRevC.92.024912 Measurements of dielectron production in Au+Au collisions at sNN = 200 GeV from the STAR experiment S. Shi , Y. Jiang , E. Lilleskov , et al ., Anomalous chiral transport in heavy ion collisions from anomalous-viscous fluid dynamics . Annals Phys . 394 , 50 ( 2018 ). doi: 10.1016/j.aop.2018.04.026 http://doi.org/10.1016/j.aop.2018.04.026 Anomalous chiral transport in heavy ion collisions from anomalous-viscous fluid dynamics M. Anderson , J. Berkovitz , W. Betts , et al ., The Star time projection chamber: A Unique tool for studying high multiplicity events at RHIC . Nucl. Instrum. Meth. A 499 , 659 ( 2003 ). doi: 10.1016/S0168-9002(02)01964-2 http://doi.org/10.1016/S0168-9002(02)01964-2 The Star time projection chamber: A Unique tool for studying high multiplicity events at RHIC C. Adler , A. Denisov , E. Garcia , et al ., The RHIC zero degree calorimeter . Nucl. Instrum. Meth. A 470 , 488 ( 2001 ). doi: 10.1016/S0168-9002(01)00627-1 http://doi.org/10.1016/S0168-9002(01)00627-1 The RHIC zero degree calorimeter N. M. Abdelwahab et al . [STAR Collaboration] , Isolation of flow and nonflow correlations by two- and four-particle cumulant measurements of azimuthal harmonics in <math id="M32"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><msub><mrow/><mrow><mtext>N</mtext><mi>N</mi></mrow></msub></mrow></msub></mrow></msqrt><mo>=</mo></mrow></math> 200 GeV Au+Au collisions . Phys. Lett. B 745 , 40 ( 2015 ). doi: 10.1016/j.physletb.2015.04.033 http://doi.org/10.1016/j.physletb.2015.04.033 Isolation of flow and nonflow correlations by two- and four-particle cumulant measurements of azimuthal harmonics in sNN= 200 GeV Au+Au collisions 10.1007/s41365-018-0520-z This work was supported in part by the National Natural Science Foundation of China (No. 11747312) and the U.S. Department of Energy (No. de-sc0012910). 2018-09-15 2018-11-02 2018-11-10 2018-11-23 2018-12-01 2021-12-20 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2018 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0520-z http://dx.doi.org/10.1007/s41365-018-0520-z . 2018 Nuclear Science and Techniques 12 29