Probing Chiral Magnetic Wave phenomena in Pb–Pb collisions with ALICE at the LHC

The interplay of the chiral anomaly and the strong magnetic field ( ∼1015 T) created in non central heavy-ion collisions could give rise to a collective excitation in the quark-gluon plasma called the Chiral Magnetic Wave (CMW), which can be experimentally sought through the charge asymmetry (A ch) dependence of the elliptic flow v 2 of positively and negatively charged hadrons. However, non-CMW mechanisms such as local charge conservation (LCC) interwined with collective flow can also lead to a similar dependence of v 2 on A ch. The measurement of triangular flow (v 3) thus serves as a reference as it is not expected to be affected by the CMW. In this study the slope parameters of Δv 2 vs A ch and Δv 3 vs A ch are estimated and compared with each other and with theoretical models to probe the CMW background.


Introduction
In non-central heavy-ion collisions, a strong magnetic field is expected to be created by the moving spectator protons [1].This magnetic field, together with the presence of non-zero electric and axial charge densities, give rise to vector and axial currents called the Chiral Magnetic Effect (CME) [2] and Chiral Separation Effect (CSE) [3], respectively.The coupling of CME and CSE leads to a wave in the quark-gluon plasma called the Chiral Magnetic Wave (CMW) [4].The CMW signifies the formation of parity-odd domains in the QCD vacuum, resulting in parity violation in the strong interaction [5].
Theoretical calculations [4] suggest that CMW can separate the elliptic flow of positive and negative charges as a function of net charge asymmetry (A ch ) defined as: where N + and N − are the number of positive and negative particles in an event, respectively.The elliptic flow thus becomes charge dependent.The observable sensitive to the CMW effect is the slope (r Norm ∆v 2 ) of ∆v 2 / v 2 when calculated as a function of A ch [6], where ∆v 2 is the difference in the elliptic flow of negative and positive charged particles and v 2 is their average elliptic flow.A finite positive value of the slope hints at the presence of CMW phenomena.However, hydrodynamic calculations suggest a positive value of the slope even without invoking the CMW, via Local Charge Conservation (LCC) phenomena [7].A similar measurement with v 3 can probe this type of background, as v 3 of positive and negative charged particles are not expected to be affected by CMW phenomena.

Data set and analysis method
Analysis is done using 240 million events in Pb−Pb collsions at √ s NN = 5.02 TeV using minimum bias events with enhanced collection of central (0-10%) and semi-central (30-50%) events using dedicated triggers.The ALICE V0 detectors [8] are used for triggering and centrality determination.Measurements of anisotropic flow coefficients (v 2 and v 3 ) are performed for unidentified charged particles in the pseudorapidity (η) and transverse momentum (p T ) ranges |η| < 0.8 and 0.2 < p T < 2.0 GeV/c, respectively.The A ch is estimated with charged particles within |η| < 0.8 and 0.2 < p T < 10.0 GeV/c.The flow coefficients are calculated in 10 quantile A ch bins for all the centralities.The v 2 and v 3 are calculated using the Q-cumulant method [9], as described in the following.In this analysis, two subevents (A and B) have been used with a pseudorapidity gap > 0.4 to reduce non-flow effects.The two-particle correlation for a single event is given by where p A n is the differential flow vector from subevent A formed with the particles of interest and Q B n is the reference flow vector obtained with all charged particles from subevent B. The multiplicities of these two subevents are m A and M B .The two-particle correlation averaged over all events within the same centrality and A ch bin is given by where i is the event index, N is the total number of events and w 2 is the event weight.Finally v n can be calculated using Eq. 4, where d n {2} = 2 A is the differential cumulant and c n {2} is the reference cumulant obtained as

Results
The left panel of Fig. 1  The data points are fitted with a first-order polynomial to obtain the corresponding normalized slope r Norm ∆v 2 .A similar technique is followed to estimate the normalized slope r Norm ∆v 3 to probe the background from LCC.
The left panel of Fig. 2 compares the normalized slopes r Norm ∆v 2 and r Norm ∆v 3 for unidentified charged hadrons as a function of centrality in Pb−Pb collisions at √ s NN = 5.02 TeV.Both normalized slopes are found to be positive and consistent with each other within uncertainties.This result indicates that the postive value of r Norm ∆v 2 may come from background mechanisms unrelated to CMW phenomena.Results are further compared with AMPT and BW-LCC model predictions.AMPT is a transport-based model [10] which doesn't incorporate local charge conservation or CMW phenomena.As expected, the model gives a zero slope within uncertainties.BW-LCC is a hydrodynamic-based model which simultaneously describes the v 2 (p T ), v 4 (p T ) and p T spectra in Pb−Pb collisions at 5.02 TeV [11].In the LCC model, an elliptic system is assumed with eccentricty obtained from a Blast Wave fit to v 2 (p T ), v 4 (p T ) and p T spectra [12].Charged-particles are uniformly distributed in the ellipse and they are further tuned to match the observed charge asymmetry in data.After matching the charge asymmetry with data, the normalized v 2 slope is calculated and shown in the right panel of Fig. 2 with the blue band.The BW-LCC model qualitatively describes the trend in data in mid-central collisions which signifies that the positive value of the normalized slope may come solely from the LCC background.

Conclusion
The normalized slopes r Norm similar magnitude across the centrality classes signifying the presence of background unrelated to the CMW.Comparison of results with BW-LCC model predictions suggest that the positive value of r Norm ∆v 2 can arise from the LCC background itself.In the future a more realistic decription of the background is necessary to state a firm conclusion regarding the presence of CMW phenomena at LHC energies.
shows the v 2 of positively and negatively charged hadrons as a function of charge asymmetry for the 40−50% centrality class in Pb−Pb collisions at √ s NN = 5.02 TeV.The v 2 of positive (negative) particles shows a decreasing (increasing) trend with charge asymmetry.The difference in their normalized elliptic flow coefficients is shown in the right panel of Fig. 1.

Figure 1 . 3 vFigure 2 .
Figure 1.(Left panel): v 2 of positive (red marker) and negative (blue marker) hadrons as a function of corrected charge asymmetry.(Right panel): Normalized ∆v 2 as a function of corrected charge asymmetry.Red line is the linear fit to the data points.

∆v 2 and r Norm ∆v 3
of charged hadrons are calculated as a function of centrality in Pb−Pb collisions at √ s NN = 5.02 TeV.The normalized slopes are found to be of 28th International Nuclear Physics Conference (INPC 2022) Journal of Physics: Conference Series 2586 (2023) 012025