Nuclear Science and Techniques

Special Section on International Workshop on Nuclear Dynamics in Heavy-Ion Reactions (IWND2018)

Search for the chiral magnetic effect in heavy ion collisions

Fu-Qiang Wang，

Jie Zhao

Vol.29, No.12

Article number 179

Published in print 01 Dec 2018

Available online 23 Nov 2018

DOI：10.1007/s41365-018-0520-z

7001

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 collisionsChiral magnetic effectAzimuthal correlatorFlow backgroundInvariant massReaction planeParticipant plane

1 Introduction and physics motivation

Our universe started from the Big Bang singularity with equal matter and antimatter [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, 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]. 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], 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) [6-9]. The topological charge, QW, 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, QW=N_L-N_R≠0, or a local parity (𝒫) violation [9-11]. Such an imbalance can exhibit experimental consequences if submerged in a sufficiently strong magnetic field ( $\vec{B}$ ). 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]; see the illustration in Fig. 1.

Figure 1:

(Color online) Illustration of the CME. The red arrows denote the direction of momentum, the blue arrows the spin of the quarks. (1) Initially, there were as many left-handed as right-handed quarks. Owing to the strong magnetic field, the up and down quarks are in the lowest Landau level and can only move along the magnetic field. (2) The quarks interact with a topological gluon field with nonzero Qw, converting left-handed quarks into right-handed ones (in this case Qw < 0) by reversing the momentum direction. (3) The right-handed up quarks will move upward, and the right-handed down quarks will move downward, resulting in a charge separation. From Ref. [11].

Relativistic heavy ion collisions provide an ideal environment for the realization of the CME, as illustrated in 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 ~10¹⁵ Tesla; $e B ~ 0.3 m_{π}^{2}$ , where mπ is the pion mass [10-13]. The Laudau energy eB/mq∼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, mq∼ 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 [14-18]. 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, 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

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) [21-23]. Among various observables [24-28], a typically used observable to measure the CME-induced charge separation in heavy ion collisions is the three-point correlator [29],

γ \equiv 〈 \cos (α + β - 2 ψ) 〉,

(1)

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 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.

Figure 2:

(Color online) Illustration of a noncentral heavy ion collision, where the overlap participant region is an ellipse (on the transverse plane) with anisotropic expansion (indicated by radial arrows), and a strong magnetic field pointing upward generated by the spectator protons. The reaction plane is defined by the impact parameter direction and the beam direction.

Indeed, signals that are qualitatively consistent with the CME expectations have been observed [25, 30 -34]. Figure 3 shows the example results [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 )[35]. This is typically attributed to the hydrodynamic expansion of the high-density collision region, generating an elliptical flow (v₂) [36, 37]. In particular, it is the second harmonic (typically labeled as ψ₂ as in Fig. 3 )of the particle density azimuthal distribution, corrected for finite multiplicity resolution [35]. Because of the fluctuations of the nucleon positions in the colliding nuclei, the reconstructed ψ₂ corresponds to the participant plane (PP). It unnecessarily coincides with the RP; however, it fluctuates about the RP event-by-event [38]. Meanwhile, the RP can be determined more accurately by the spectator neutrons measured by a zero-degree calorimeter (ZDC) [39] (typically labeled as ψ₁, as in Fig. 3 )because of a slight side kick they received from the collision [40]. More discussions are presented in Section 3.3.

Figure 3:

(Color online) The azimuthal correlator γ measured with the first-order event plane ψ₁ from the ZDCs and the second-order event plane from the time projection chamber (TPC) as functions of centrality in Au + Au collisions at

\sqrt{s_{_{N N}}} = 200

GeV from STAR. The Y4 and Y7 represent the results from the 2004 and 2007 RHIC runs, respectively. Shaded areas for the results measured with ψ₂ represent the systematic uncertainty of the event plane determination. Systematic uncertainties for the results with respect to ψ₁ are negligible compared to the statistical ones shown. From Ref. [32].

However, background correlations unrelated to the CME exist [41-48]. For example, transverse momentum conservation induces correlations among particles that are enhanced back to back pairs [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), both down in the negative direction (Fig. 4b). This background is, fortunately, independent of particle charges, thus affecting the SS and OS pairs equally and cancels in the difference,

Figure 4:

(Color online) Left: expected CME signals (Eq. 1) for opposite-sign (OS) and same-sign (SS) particle pairs; they have opposite signs but equal magnitude. Center: effect of momentum conservation is negative and equal for OS and SS. Right: effect of local charge conservation (e.g., neutral resonance decays) is positive and only applies to OS.

Δ γ \equiv γ_{OS} - γ_{SS} .

(2)

Experimental investigations have thus focused on the Δ_γ observable [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 [41-46], that affect OS pairs more significantly than SS pairs (as illustrated in Fig. 4c). This background is positive and arises from the coupling of elliptical anisotropy v₂ of resonances/clusters, and the angular correlations between their decay daughters (nonflow) [41, 42, 45]. Use ρ→πpπm as an example (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 $\vec{B}$ direction perpendicular to the RP [49]. Because more ρ resonances exist in the RP direction than the perpendicular direction because of the finite v₂ of the ρ, the overall effect on γ_OS is positive.

Figure 5:

(Color online) Illustration of the decay π⁺π^- pair from a ρ moving in the RP direction exhibiting the same effect on the γ observable (Eq. 1) as a CME π⁺π^- pair perpendicular to the RP.

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]. Mathematically, the background can be estimated by

Δ γ_{bkgd} \approx \frac{N_{clust .}}{N_{π}^{2}} 〈 \cos (α + β - 2 ϕ_{clust .}) 〉 v_{2, clust .},

(3)

where N_clust and Nπ are the numbers of clusters and single-charge pions (Nπ ≈ N_π⁺ ≈ N_π^-), respectively, and v_2,clust.≡〈cos2(ϕ_clust.-ψ)〉 is the v₂ of the clusters [22, 23, 29, 49]. A simple estimate, again using the ρ resonance as an example, indicates that the background magnitude is $Δ γ_{bkgd} \approx \frac{20}{100^{2}} \times 0.65 \times 0.1 \approx 10^{- 4}$ for mid-central Au + Au collisions, comparable to the experimental data in Fig. 3.

3 Innovative methods and new results

Undoubtedly, the early Δ_γ measurements [25, 30-34] are dominated by backgrounds. Many proposals and attempts have been realized to reduce or eliminate these backgrounds [24, 25, 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, 52, 53] and is not a new method. The other is to measure where resonance contributions are small, or can be identified and removed [54, 55]. This has not been explored until recently [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 [59-61], 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].

3.1 Make the anisotropy vanish

This method comprises two variations. The central idea of the first variation is that "round" events with zero elliptical anisotropy ( $v_{2}^{o b s}$ ) exists owing to event-by-event statistical and dynamical fluctuations. This was exploited by STAR [24], where a charge asymmetry observable (similar to Δ_γ) was analyzed as a function of the observed event-by-event $v_{2}^{o b s}$ ; both the Δ_γ and $v_{2}^{o b s}$ are calculated from the same group of particles (particles of interest, or POI). This is shown in 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 $v_{2}^{o b s} = 0$ . 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]. Analysis of higher statistics data from later runs indicates that the intercept is finite [62]. However, the intercept at $v_{2}^{o b s} = 0$ 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 $v_{2}^{o b s}$ measured by the final-state charged hadrons. It was shown by a toy-model resonance simulation [49] that the resonance v₂ is not zero when the event-by-event $v_{2}^{o b s}$ of the final-state hadrons is required to be zero. Even if one could ensure that the event-by-event v₂ of one resonance type is zero, it is nearly impossible to ensure the event-by-event v₂’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-2ϕ_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].

Figure 6:

(Color online) Charge multiplicity asymmetry correlation (Δ) as a function of the event-by-event anisotropy

v_{2}^{o b s}

in 20–40% Au + Au collisions at

\sqrt{s_{_{N N}}} = 200

GeV from Run-4 by STAR. Errors are statistical. From Ref. [24].

The second variation of the method is to analyze the Δ_γ observable of the POI as a function of the flow vector magnitude (q₂) [63] that is calculated not using the POI but the particles from different phase spaces [52, 53]. The q₂ is closely related to v₂, and this method is known as "event-shape engineering (ESE)" [63]. ALICE [52] divided their data in each collision centrality according to q₂ and found the Δ_γ to be approximately proportional to the v₂ of the POI; this is consistent with the background contributions. This is shown in Fig. 7. One could fit the data with the linear function in v₂ 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(v₂) 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].

Figure 7:

(Color online) The charged-particle density-scaled azimuthal correlator, Δ_γ·dN_ch/dη, as a function of v₂ for q₂ shape-selected events for various centrality classes in Pb + Pb collisions by ALICE. Error bars (shaded boxes) represent the statistical (systematic) uncertainties. [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 v₂ [24, 64, 65]. CMS attempts to achieve this using narrow centrality bins [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].

Because the ESE control knob q₂ and the POI are from different phase spaces, a given q₂ cut-bin samples a v₂ distribution of the POI. The extrapolated zero average v₂ of the POI likely corresponds to the zero average v₂ 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 $v_{2}^{o b s}$ . The disadvantage is that an extrapolation to v₂=0 is required as the ESE q₂ sampling does not cover the most important v₂=0 region. A dependence of the backgrounds on v₂ that is not strictly linear would introduce imprecision in the extracted CME signal.

3.2 Identify backgrounds by invariant mass

The particle pair invariant mass (m_inv) is a typical method to identify resonances. Until recently [54], m_inv had not been utilized to investigate the CME Δ_γ signal.

The upper panel in Fig. 8 shows the relative OS excess over the SS pion pairs in Run-11 Au + Au collisions from STAR [56 -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 KS 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, 66]. The lower panel shows the Δ_γ measurement as a function of m_inv. A clear peak at the KS mass is observed; a peak at the ρ mass is observable. Most π⁺π^- pair resonances are below m_inv < 1.5 GeV/c²; 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 shows the measured Δ_γ at m_inv > 1.5 GeV/c², 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 2σ standard deviation.

Figure 8:

(Color online) m_inv dependences of the relative OS excess over SS pairs (upper) and Δ_γ (lower) in 20–50% central Au + Au collisions at

\sqrt{s_{_{N N}}} = 200

GeV from Run-11 by STAR. Errors are statistical. [58].

Figure 9:

(Color online) Average Δ_γ at large pair mass m_inv > 1.5 GeV/c², compared to the inclusive Δ_γ, as a function of centrality in 20–50% central Au + Au collisions at

\sqrt{s_{_{N N}}} = 200

GeV from Run-11 by STAR. Errors are statistical. [58].

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]. 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], dividing events from each narrow centrality bin into two classes according to the event-by-event q₂ [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 shows the Δ_γA and Δ_γB from such two q₂ 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].

Figure 10:

(Color online) m_inv dependences of the Δ_γ in large and small q₂ events (upper), and the Δ_γ difference between large and small q₂ events together with the inclusive Δ_γ (lower) in 20–50% central Au + Au collisions at

\sqrt{s_{_{N N}}} = 200

GeV from Run-16 by STAR. Errors are statistical. From Ref. [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=κΔ_γA-Δ_γB+Δ_γCME. The left panel in 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 [58]. Only the m_inv > 0.4 GeV/c² data points are included in Fig. 11 because the Δ_γ from the lower m_inv region is affected by the edge effects of the STAR TPC acceptance [58, 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

Figure 11:

(Color online) Δ_γ versus Δ_γA-Δ_γB (left), and Δ_γA versus Δ_γB (right) in 20–50% central Au + Au collisions at

\sqrt{s_{_{N N}}} = 200

GeV from Run-16 by STAR. Each data point in the left (right) panel corresponds to one m_inv bin in the lower (upper) panel of Fig. 10; only the m_inv > 0.4 GeV/c² data points are included. Errors are statistical. [58].

Δ γ_{A} = b Δ γ_{B} + (1 - b) Δ γ_{C M E},

(4)

where b and Δ_γCME are the fitting parameters. The right panel of Fig. 11 shows Δ_γA against Δ_γB, and the fit by Eq. 4 superimposed as the straight line [58]. The straight line superimposed on the left panel of Fig. 11 is the same fit to Eq. 4, converted properly. The parameter b reflects the relative background contribution in the large-q₂ (large-v₂) event class to that in the small-q₂ (small-v₂) event class; further, because the background increases with v₂, the value of b is larger than unity. The CME signal Δ_γCME 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 v₂. Provided that the backgrounds are different for different q₂ 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 v₂ The fit model, however, assumes that the CME signal is independent of m_inv. The good fit quality shown in 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

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]. The elliptic flow v₂ is generated by the participants, and is therefore determined by the PP [38]. The PP and RP are correlated, but, owing to fluctuations [38], they are not identical. See the illustration in the left panel of Fig. 12. The CME-induced charge separation, driven by the magnetic field [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

Figure 12:

(Color online) Left: sketch of a heavy ion collision projected onto the transverse plane (perpendicular to the beam direction). ψ_RP is the RP (impact parameter, b) direction, ψ_PP the PP direction (of interacting nucleons, denoted by the solid circles), and ψB the magnetic field direction (primarily from spectator protons, denoted by the open circles together with spectator neutrons). Right: illustration of the "CME-background filter." In a single collision, a CME signal "along" the RP and a background "along" the PP are present. The RP and PP are not the same but differ by an opening angle factor, a =〈cos2(ψ_PP-ψ_RP)〉. With the "filter" RP, the background is reduced by a factor of a and the CME remains the same, whereas with the "filter" PP, the background remains the same and the CME is reduced by the same factor a.

a = 〈 \cos 2 (ψ_{PP} - ψ_{RP}) 〉 .

(5)

The v₂-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 v₂ 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; the PP and RP serve as two different filters for the v₂ 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]. The PP is, as usual, measured by final-state particles, for example, by the TPC in the STAR experiment [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]. It is noteworthy that the ZDCs measure only the spectator neutrons [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] and fluctuates about the PP. However, our method does not require a precise determination of the RP and PP [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 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]. The two sets of data points correspond to two different acceptance cuts in the analysis. The results are primarily consistent with zero.

Figure 13:

(Color online) Extracted fraction of potential CME signal as a function of collision centrality in 200 GeV Au + Au collisions by STAR, combining data from Run-11, Run-14, and Run-16. Error bars (horizontal caps) represent statistical (systematic) uncertainties. [58].

4 Discussions and Summary

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] and 20% (ALICE) [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 summarizes the current status of the CME signal from STAR in 20–50% central Au + Au collisions at $\sqrt{s_{_{N N}}} = 200$ GeV [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].

Figure 14:

(Color online) The possible CME signal, relative to the inclusive Δ_γ measurement, extracted from the PP–RP comparative measurements and the invariant mass method, in 20–50% central Au + Au collisions at

\sqrt{s_{_{N N}}} = 200

GeV by STAR, with a total of 2.5 billion minimum-bias events combining Run-11, Run-14, and Run-16 data. Error bars (vertical caps) represent statistical (systematic) uncertainties. From [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 (v₂). 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 1–2σ standard deviation from zero. It is clear that the experimental challenges in the CME search are daunting, but the important physics warrants continued efforts.

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