Probing the Chiral Magnetic Wave with charge-dependent flow measurements in Pb-Pb collisions at the LHC

The Chiral Magnetic Wave (CMW) phenomenon is essential to provide insights into the strong interaction in QCD, the properties of the quark-gluon plasma, and the topological characteristics of the early universe, offering a deeper understanding of fundamental physics in high-energy collisions. Measurements of the charge-dependent anisotropic flow coefficients are studied in Pb-Pb collisions at center-of-mass energy per nucleon-nucleon collision $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV to probe the CMW. In particular, the slope of the normalized difference in elliptic ($v_{2}$) and triangular ($v_{3}$) flow coefficients of positively and negatively charged particles as a function of their event-wise normalized number difference, is reported for inclusive and identified particles. The slope $r_{3}^{\rm Norm}$ is found to be larger than zero and to have a magnitude similar to $r_{2}^{\rm Norm}$, thus pointing to a large background contribution for these measurements. Furthermore, $r_{2}^{\rm Norm}$ can be described by a blast wave model calculation that incorporates local charge conservation. In addition, using the event shape engineering technique yields a fraction of CMW ($f_{\rm CMW}$) contribution to this measurement which is compatible with zero. This measurement provides the very first upper limit for $f_{\rm CMW}$, and in the 10-60% centrality interval it is found to be 26% (38%) at 95% (99.7%) confidence level.


Introduction
The primary goal of relativistic heavy-ion collisions at the Large Hadron Collider (LHC) is to study the properties of the emerging strongly interacting medium called the quark-gluon plasma (QGP) [1][2][3][4][5][6].The transition from normal hadronic matter to the QGP is predicted by quantum chromodynamics (QCD) calculations on the lattice [7,8].Heavy-ion collisions are also characterized by extremely strong short-lived electromagnetic fields (B ∼ 10 18 Gauss), primarily induced by protons from the incoming nuclei that do not undergo any inelastic collision and are referred to as spectators [9].The direction of B is perpendicular to the reaction plane, the plane spanned by the impact parameter of the colliding nuclei and the beam direction.The presence of this intense magnetic field allows for the possibility to study novel QCD phenomena, such as parity violation in strong interactions [10][11][12].
The potential to observe parity violation in strong interactions using ultrarelativistic heavy-ion collisions was first discussed in Refs.[12][13][14] and further reviewed in Refs.[15][16][17][18].Theoretically, the interactions of quarks with gluonic fields describing transitions between topologically different QCD vacuum states change the quark chirality, leading to a local chiral imbalance.The strong magnetic field leads to a charge separation (electric current) relative to the reaction plane, which is known as the Chiral Magnetic Effect (CME) [12,[19][20][21][22][23][24].The experimental search for the CME using heavy-ion collisions has intensified over the past decade.Though early measurements pointed to some similarities between the results and the theoretical predictions [25][26][27], there is substantial evidence that background sources, i.e., collective phenomena and local charge conservation (LCC), play a significant role in the experimental measurements [28,29].The LCC here refers to the principle that within a local region of a physical system, the balance or conservation of quantum numbers for eg., electric charge is upheld.Experimental results indicate that the upper limit of the CME signal contribution ranges from 7% to 20% at 95% confidence level in semicentral heavy-ion collisions [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].
A dual phenomenon to the CME is the Chiral Separation Effect (CSE) [40,41], which is theorized to induce a chirality current along B in the presence of a finite electric chemical potential (µ e ).The CME and the CSE interact with one another forming a long wavelength collective excitation, called the Chiral Magnetic Wave (CMW) [42][43][44][45][46]. Similar to the CME-induced electric dipole moment, the CMW would manifest itself in a finite electric quadrupole moment in the final state [42].This effect, if present, can be measured by charge-dependent anisotropic flow measurements [42].The anisotropic flow is quantified in terms of the Fourier coefficients v n of the azimuthal distribution of the produced particles with respect to the n th -order event plane angle Ψ n [47][48][49] where ϕ is the azimuthal angle of a particle.The first three coefficients v 1 , v 2 , and v 3 are known as the directed, elliptic, and triangular flow, respectively.The CMW-induced electric quadrupole moment evolves with the medium expansion, leading to an increase (decrease) of v 2 for negatively (positively) charged hadrons [42].The difference between negatively and positively charged hadron v 2 (∆v 2 ) is expected to be proportional to the event-by-event charge asymmetry (A ch ) [42,43], In the above equation, r 2 denotes the slope parameter between ∆v 2 and event-by-event charge asymmetry, and A ch is defined as where N + (N − ) are positively (negatively) charged hadrons measured in a given event.
The first experimental search for the CMW was performed by the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC) with charged pions in Au-Au collisions at center-of-mass energy per nucleon-nucleon collision √ s NN = 200 GeV [50], in which a positive linear dependence on A ch was observed for the v 2 difference between π − and π + .The extracted positive slopes as well as their centrality dependence agree well with theoretical calculations [42][43][44].A similar positive correlation was measured by the ALICE Collaboration at the Large Hadron Collider (LHC) with charged hadrons in semicentral Pb-Pb collisions at √ s NN = 2.76 TeV [51].Comparable slopes to those from Au-Au collisions in semicentral collisions were reported.However, the lifetime of the magnetic field in vacuum is expected to drop much faster at LHC energies compared to that at RHIC energies [52].Thus, it is highly unlikely that an identical slope value would be observed by different experiments with orders of magnitude difference in collision energies.Furthermore, a similar linear dependence was observed by the precision measurements of the CMS collaboration in p-Pb and Pb-Pb collisions at √ s NN = 5.02 TeV [53].This similarity questioned the CMW interpretation since the CMW signal is not expected to be present in p-Pb collisions due to the decoupling of the magnetic field from the reaction plane in such collisions [34,54].In addition, both STAR and CMS collaborations have observed a linear dependence between A ch and ∆v 3 , i.e. the difference between the v 3 coefficients of negatively and positively charged hadrons [53,55] However, this should not originate from the CMW-induced electric quadrupole configuration in the medium as the CMW is mainly driven by the magnetic field which is uncorrelated with the third order event plane.As a result of these observations, it appears likely that the slope observed in ∆v 2 as a function of A ch is not due to the CMW processes only.To ease the comparison between measurements performed by different experiments, one can define a normalized slope parameter as, where n = 2 or 3. Recently, it was proposed in Ref. [56], that one can also utilize the event shape engineering (ESE) technique [57] to estimate the CMW signal.This selection methodology was already employed to constrain the CME [33,36].The ESE approach utilizes the fluctuations in the shape of the initial state of the system and allows one to select events with the same centrality but different initial geometry, thus varying the background contributions.Instead of the A ch -v 2 slope, an alternative observable, the integral covariance [51] can be used.It is defined as where the angular bracket denotes the average over the events.This observable, by definition, calculates the covariance between A ch and v 2 and is equivalent to the slope parameter.The main advantage of such a covariance is the removal of the dependence on the detector acceptance and on the reconstruction efficiency of charged hadrons when expressed differentially [51].In addition, one no longer needs to divide each sub-sample of v 2 into several A ch intervals allowing for a reduction of the statistical fluctuations.
Understanding the background components and how they contribute to the experimental measurements is crucial to isolate the CMW signal.Among several background sources [58][59][60][61][62][63][64][65], the most dominant one is expected to be the LCC, convoluted with the collective motion of the QGP medium.The LCC mechanism depicts a scenario where pairs of particles with opposite charges are usually generated from resonance decays.Such particle production mechanism is studied with balance function measurements in heavyion collisions [66,67].In the CMW measurement, when one of the particles from the charge-conserving pair escapes from the limited detector acceptance, a non-zero A ch is consequently generated [58].It is demonstrated in Ref. [68] that the selection of specific A ch values automatically biases the η-p T phase space.This can trivially give rise to a A ch -∆v 2 correlation because of the v 2 dependence on η and p T leading to non-zero slopes, even in absence of CMW phenomena.Theoretical studies on A ch -∆v 2 correlations, without the CMW process, have been extensively investigated in Refs.[69][70][71][72][73].
The consensus is that the LCC interpretation can effectively explain both the observed A ch -∆v 3 and A ch -∆v 2 relations.A pure LCC mechanism is expected to lead to an identical [53,58] positive linear correlation between A ch -∆v Norm Although there are several measurements of CMW at LHC energies, there is lack of measurements with identified hadrons.Given that the predominant background influence on CMW arises from the interplay of LCC and elliptic flow (v 2 ), it would be useful to measure the CMW for identified particles, as it would provide us a better handle to control the background related to v 2 [42].The first theoretical study [42] predicted that only light quarks, i.e., u and d, are influenced by the chiral anomaly.However, recent theoretical calculations [74] suggest that the mass difference between the strange quark (s) and the u, d quarks can be neglected, indicating the possibility of exploring CMW effects with charged kaons.Nevertheless, the significant differences in the absorption cross section for (anti-)protons and kaons in the hadronic matter might obscure the signal.Additionally, a hydrodynamic study [62] suggests that the isospin chemical potential (µ I ) and the strangeness chemical potential (µ S ) can play essential roles.This study predicts a negative slope for kaons at RHIC energies [62].Therefore, it is difficult to disentangle the CMW signal and various background contributions, if the measurements are performed only with inclusive charged hadrons.This paper presents the first measurement of normalized slopes r Norm 2 and r Norm 3 for charged hadrons and identified π ± , K ± , and p+p in Pb-Pb collisions at √ s NN = 5.02 TeV.These measurements will provide experimental input to the ongoing theoretical developments for the flavor dependence of the chiral anomalies.Measurements from data are further compared with a recently developed blast wave model calculation, incorporating the LCC background (BW+LCC) [75].The measurement of integral covariance is also utilized to estimate an upper limit on the CMW contribution, for the first time, in Pb-Pb collisions at √ s NN = 5.02 TeV.
This article is organized as follows: Section 2 briefly describes the experimental setup, while Section 3 discusses the data sample, the selection criteria, and the analysis details. Section 4 describes the evaluation of the systematic uncertainties.The results are discussed and compared with model calculations in Section 5. A summary is outlined in Section 6.

Experimental apparatus and data sample
The ALICE detector and its performance are described in detail in Refs.[76,77].The apparatus consists of a central barrel at midrapidity (|η| < 0.9), embedded in a cylindrical solenoid which provides a magnetic field of 0.5 T parallel to the beam direction, and a set of forward detectors.
Charged particles produced in the collisions at midrapidity are tracked by the Inner Tracking System (ITS) [76] and the Time Projection Chamber (TPC) [78].The ITS, composed of the Silicon Pixel Detector (SPD), Silicon Drift Detector (SDD), and Silicon Strip Detector (SSD), consists of six cylindrical silicon layers surrounding the beam vacuum pipe.The TPC, surrounding the ITS, provides up to 159 points for track reconstruction along with specific energy loss (dE/dx) measurements, which are utilized for charged-particle identification (PID).The PID is complemented by a Time-Of-Flight (TOF) detector [79], which measures the flight time of charged particles.The TOF detector provides pion-kaon separation at 3σ level up to p T ≃ 2.5 GeV/c and pion-proton separation up to p T ≃ 4 GeV/c.
On either sides of the interaction point, the V0 scintillator arrays [80], are used for triggering and event classification.The V0 detector consists of two arrays of 32 scintillator tiles covering the pseudorapidity ranges 2.8 < η < 5.1 (V0A) and −3.7 < η < −1.7 (V0C).Both V0 detectors are segmented in four rings in the radial direction with each ring divided into eight sectors in the azimuthal direction.The V0C is also used for ESE and event selection.Two tungsten-quartz neutron Zero Degree Calorimeters (ZDCs) [76], positioned 112.5 meters from the interaction point on each side, are used to reduce the contamination from beam-induced background.Using the time information from V0 and ZDC, offline event selection is performed to reject background from beam-gas collisions, from parasitic beam-beam interactions, and pileup events [77,81].
The analysis is performed using the data sample collected with the ALICE apparatus in the 2018 LHC Pb-Pb run at √ s NN = 5.02 TeV.The centrality intervals were defined in terms of percentiles of the hadronic Pb-Pb cross section, determined from selections on the sum of the V0 signal amplitudes [82].Central and semicentral Pb-Pb collisions were selected online by applying thresholds on the V0 signal amplitudes resulting in two separate trigger classes (central and semicentral triggers).
Only events with a reconstructed primary vertex located between ± 10 cm with respect to the nominal interaction point along the beam direction (z axis of the ALICE reference frame) are considered.The analysis is performed in different centrality intervals spanning from 0-5% which corresponds to the most central collisions to 50-60% corresponding to peripheral collisions.The total number of analyzed events after the event selection is approximately 240 million.

Analysis procedure
Charged particles reconstructed using the TPC and the ITS information within |η| < 0.8 and 0.2 < p T < 10 GeV/c are considered to determine A ch .For the measurement of flow coefficients, charged particles are restricted to 0.2 < p T < 2.0 GeV/c.Tracks are selected requiring |η| < 0.8, at least 70 (out of a maximum of 159) TPC space points, and χ 2 per TPC cluster < 2.5 for the momentum fit in the TPC.In order to reduce the contamination from secondary particles (i.e., particles originating from weak decays, conversions, and secondary hadronic interactions in the detector material) only tracks with a maximum distance of closest approach (DCA) to the reconstructed primary vertex in the transverse (|DCA xy | < 2.4 cm) and the longitudinal directions (|DCA z | < 3.2 cm) are accepted.Furthermore, tracks are required to have at least one hit in the two SPD layers.Charged pions, kaons, and (anti)protons are identified from the difference between the measured and expected values of dE/dx in TPC and time of flight to the TOF detector, expressed in units of resolution(|nσ | TPC , |nσ | TOF ), and applying a selection on the number of accepted nσ (see Table 1).Additionally, tracks without TOF information with p T larger than 0.5 GeV/c for pions, 0.45 GeV/c for kaons, and 0.6 GeV/c for protons are rejected.All particle species are required to lie within the rapidity range |y| < 0.5.By applying these selection criteria, the efficiency of identifying charged hadrons is approximately 70% around p T = 0.5 GeV/c and increases to about 80% for p T values above 1 GeV/c.Moreover, these selection criteria guarantee a purity exceeding 90% for all particle species across the entire range of p T values considered in the analysis.
An example of the measured raw A ch distribution is shown in the left panel of Fig. 1 for the 40-50% centrality interval.The raw A ch distribution is divided into ten A ch intervals, each roughly containing equal number of events.The edges of the ten A ch classes are displayed by the dashed lines in the left panel of Fig. 1.The raw A ch is corrected to account for the limited detector acceptance and the reconstruction and identification efficiency of charged hadrons.Using simulations based on the HIJING event generator [83] combined with the GEANT3 model [84] for particle transport in the detector material, a correlation is built between the raw and the true values of A ch [55].A linear fit to this correlation is performed and the fit function is used to map the raw A ch to the true A ch as shown in the right panel of Fig. 1.
Within each A ch interval, the flow coefficients v 2 and v 3 are measured separately for positively and negatively (identified and inclusive) charged hadrons.The measurements are performed using the two-particle cumulant method [85] with a pseudorapidity gap of |∆η| > 0.4 to suppress non-flow, i.e. correlations not related to the reaction plane [86].The normalized slope parameters, r Norm The ESE technique is further employed to estimate possible CMW signal contribution to the ∆IC as proposed in Ref. [56].In particular, the residual magnitude of this observable when v 2 goes to zero can be used to disentangle the potential CMW signal from the background contributions [33].The secondorder reduced flow vector q 2 is used for event shape selection as in Ref. [33].It is defined as where Q 2 is the magnitude of the flow vector and M is the multiplicity.The Q 2 is calculated from the azimuthal distribution of the energy deposited in the V0C detector.In order to account for a non-uniform detector response, the V0 detector is calibrated using two procedures: gain equalization and recentering.The former flattens the mean multiplicity distribution of the eight azimuthal sectors in each ring, while the latter corrects for systematic shifts of the mean values of the Q 2 vector components [48].For each centrality interval, ten q 2 ranges are explored, ranging from the most elliptic to the most isotropic event classes.
To separate the LCC background contributions from the potential CMW signal, the dependence of the ∆IC on v 2 (defined in Section 1) is fitted with a linear function.The CMW fraction to the ∆IC is then obtained by the ratio between the observable at zero v 2 and at finite v 2 where a and b are the slope and the intercept of the linear function, respectively, and ⟨v 2 ⟩ is the average value over the measured v 2 range.

Systematic uncertainties
To estimate the systematic uncertainties on the normalized slopes and f CMW , the event and track selection criteria are varied from their nominal values.Table 1 provides a list of variables used in the selections along with their default and varied values.These include modifying the range of z coordinate of the primary vertex (V z ) from |V z | ≤10 cm to |V z | ≤8 cm to examine the detector acceptance dependence.
The impact of the track-quality selections is evaluated by changing the minimum number of TPC space points from 70 to 80 and varying the χ 2 TPC per TPC space point from 2.5 to 2.0.To test the influence of the contamination from secondary particles on the measurement, tighter selection criteria than the nominal ones are applied to both DCA xy and DCA z .To estimate the effects of non-flow contributions, the pseudorapidity gap (∆η) is varied from |∆η| ≥ 0.4 to |∆η| ≥ 0.6 for charged hadrons and pions, and to |∆η| ≥ 0.5 for kaons and protons.Particle identification criteria, namely |nσ | TPC and |nσ | TOF , are also subject to variations to account for potential systematic effects in the particle identification process and their impact on the final analysis results.The reconstruction efficiency for charged hadrons is calculated using only pions, kaons, and protons and the differences observed in the results are incorporated as systematic uncertainties.For each systematic variation, the corrections for the non-uniform acceptance and for the reconstruction efficiency of inclusive and identified charged hadrons are estimated using collision data and MC simulations.To identify the statistically significant systematic sources, the ratio B = Y/σ B is calculated, where Y represents the difference between the results with the default and the modified selections, and σ B is the error of the difference estimated as |σ 2 default ± σ 2 varied |, where "+" is used for the uncorrelated and "-" for the correlated sources.The statistical uncertainties σ default and σ varied are estimated separately for the results using the default and varied event/particle selection criteria, following a subsampling method, with 20 equally sized independent samples.Each variation that exhibits a significant difference from the nominal result by more than 1σ B , according to the recommendations from Ref. [87], is considered a source of systematic uncertainty.The total systematic uncertainties are then obtained by summing the different contributions in quadrature.

(7) Efficiency calculation All unidentified charged hadrons Identified charged hadrons (π+K+p)
Table 2 summarizes the maximum magnitude of the systematic uncertainties on the normalized slopes over all the centrality intervals from each individual source which passes the criteria described above.The systematic sources for the f CMW observable are only a few, namely Primary V z , χ 2 TPC /cluster, and DCA selections.The associated uncertainties are 0.024, 0.047, and 0.068, respectively.The top left and top right panels of Fig. 2 show, respectively, the v 2 and v 3 of positively and negatively charged hadrons as a function of A ch for Pb-Pb collisions at √ s NN = 5.02 TeV in the 40-50% centrality interval.A significant decreasing (increasing) trend of v 2 for positively (negatively) charged hadrons as a function of A ch is observed.Such trends are also present for the v 3 coefficient though the fluctuations are larger.In Fig. 2 the correlated uncertainties between the hadrons and among A ch intervals are represented with shaded bands.The normalized difference between the v 2 and v 3 of positive and negative charged particles, as defined in Eq. 5, is shown as a function of A ch in the bottom left and right panels of Fig. 2, respectively.They are fitted with linear functions to obtain the slopes, r Norm  .In addition to a positive slope for ∆v 2 /⟨v 2 ⟩, a non-zero slope is also found for ∆v 3 /⟨v 3 ⟩ (i.e., r Norm 3 > 0), which mainly contains the background correlations.This non-zero r Norm 3 indicates that similar background is also present in r Norm 2 which need to be subtracted to make a quantitative measurement of CMW.Note that the difference in non-flow contributions to same-sign and opposite-sign pairs can induce a trivial correlation between v n and A ch [55,88].However, it is estimated that this trivial correlation is negligible at this collision energy.Figure 3  , for most of the centrality range.The CMW is expected to develop in the direction of the magnetic field B, i.e., approximately perpendicular to the second order event plane rather than the third order.The third order plane has very little correlation with the second order event plane [89][90][91].Hence, the non-zero r Norm 3 value cannot originate from the CMWinduced electric quadrupole moment, but it should rather be attributed to the LCC mechanism.Thus, the similarity between the magnitudes of r Norm 2 and r Norm 3 could indicate that both of them are mainly dominated by the LCC background.The results are also in good agreement with the CMS measurements for the same collision system and energy [53].While the precision of the CMS measurements is notable, the findings presented in this study expand the scope of measurements to encompass the most central collision scenarios.The r Norm 2 is further compared with a blast wave model calculation (green band) which takes into account the LCC effect [75].This model uses blast wave parameters obtained from the simultaneous fit of p T -differential yields and v 2 of identified particles from Pb−Pb collisions at √ s NN = 5.02 TeV [81].Then, the model distributes source points within an ellipsoid (defined by the blast wave parameter) from where it produces oppositely charged particles (i.e.balancing charges).The number of sources is tuned in such a way that the A ch distribution from the output of the model matches with the experimental data.Then, the normalized slope values are calculated from the model, following the , the slope for kaons behaves similarly as the slope for pions, while the slope for protons slightly differs with a weak A ch -∆v 2 dependence on centrality.In the 20% most central collisions, a hint of mass ordering is observed, i.e., the slopes of pions are slightly larger than those of kaons, and the slopes of kaons are slightly larger than those of protons.However, the uncertainties are too large for a definitive conclusion to be made.The LCC process, the dominant background for this measurement, can reproduce the measurement of r Norm 2 in data.Therefore, it is expected that the mass ordering of v 2 of identified particles might be the reason behind the apparent particle type dependence of r Norm 2 seen in Fig. 4.This finding contradicts the predictions of the hydrodynamic study, which anticipated negative slopes for kaons and protons [62].A similar behavior is found in the STAR CMW measurement at a lower collision energy, in which the isospin and strangeness chemical potentials and the different absorption cross section are expected to play a role [55,62,92].However, at LHC energies, the values of the chemical potentials are close to zero, suggesting that their influence should be negligible.For r Norm 3 , the slopes of all the measured hadron species are compatible with each other within the uncertainties.Since no predictions for the CMW for different particle species are available at LHC energies, the results shown here provide, for the first time, an experimental input

Constraining the fraction of the CMW with the ESE
Figure 5 shows the difference of the integrated covariance ∆IC as a function of v 2 for q 2 -selected events in six centrality intervals.Solid lines, representing linear fits, and colored bands, denoting three standard deviation uncertainties of the linear fits are also shown.The ∆IC values exhibit a decrease as v 2 approaches zero, as discussed in Ref. [56].The small magnitude of the intercepts in all centrality intervals indicates that the measurement is dominated by the LCC background.
After obtaining the slope and intercept from the fit of ∆IC as a function of v 2 , the fraction of the CMW signal, denoted as f CMW , can be determined using Eq. 8.The centrality dependence of f CMW is presented in Fig. 6 where the error bars display the statistical uncertainties extracted from the fits of Fig. 5. Meaningful measurements are not possible in the most central and peripheral collisions, due to the small v 2 values and the large statistical fluctuations.Therefore, the f CMW results are reported only in the 10-60% centrality range.The systematic uncertainties are estimated for the different possible sources, as discussed in Sec. 4. The systematic sources, which are found to be significant among centrality intervals, are combined in quadrature and shown as a dark shaded band in Fig. 6, at centrality around 60%.It is found that the f CMW is consistent with zero within the reported statistical and systematic uncertainties.
The f CMW data points in Fig. 6 are fitted with a constant, yielding a value of f CMW = 0.081 ± 0.055(the dashed blue line), which should be combined with the systematic uncertainty of 0.087(the gray box on the edge) to establish an upper limit on f CMW of 26% (38%) at 95% (99.7%) confidence level shown by the dotted magenta line.This result provides the first quantitative assessment of the upper limit of the fraction of the Chiral Magnetic Wave (CMW) at the top LHC energy.

Summary
The difference between the v 2 and v 3 coefficients of positively and negatively charged particles are measured as a function of the charge asymmetry A ch for inclusive and identified hadrons in Pb-Pb collisions at √ s NN = 5.02 TeV.The slopes r Norm 2 and r Norm 3 are found to be consistent with each other within the reported uncertainties, suggesting that the dominant contribution to r Norm 2 is not due to CMW.A blast wave parameterization that incorporates local charge conservation, tuned to reproduce the A ch distribution, is able to fully describe the magnitude of r Norm 2 which is expected to be sensitive to CMW.Additionally, a hint for mass ordering of the r Norm 2 slopes of pions, kaons, and protons is discernible in the most central collisions, though it is accompanied by large uncertainties.Furthermore, using the Event Shape Engineering (ESE) technique, both the fraction and the upper limit of the CMW signal are extracted.Averaging over the 10-60% centrality interval, the CMW fraction is consistent with zero within uncertainties and an upper limit of 26% (38%) is estimated at 95% (99.7%) confidence level.

2 and A ch -∆v Norm 3 .
Consequently, this implies that any difference between the normalized slopes r Norm 2 and r Norm 3 may indicate the existence of the CMW signal.

2 and r Norm 3 ,Figure 1 :
Figure 1: (Left panel): Raw A ch distribution in Pb-Pb collisions at √ s NN = 5.02 TeV for the 40-50% centrality interval.Red dotted lines depict the edges of the ten A ch classes.(Right panel): Correlation between true and raw A ch obtained from HIJING simulations combined with a GEANT3 detector model for Pb-Pb collisions at √ s NN = 5.02 TeV in the 40-50% centrality interval.

shows r Norm 2 ( 3 (
red markers) and r Norm green markers) as a function of centrality for inclusive charged hadrons in Pb-Pb collisions at √ s NN = 5.02 TeV.Despite the large uncertainties, r Norm 3 seems to be of similar magnitude to r Norm 2

Figure 2 :
Figure 2: The top left panel shows the v 2 of positively (red markers) and negatively (blue markers) charged hadrons as a function of the corrected A ch , while the top right panel shows the same for v 3 .Statistical uncertainties are shown by bars and uncorrelated (correlated) systematic uncertainties by open boxes (shaded bands).The bottom left panel shows ∆v 2 /⟨v 2 ⟩ as a function of the corrected A ch and bottom right panel shows the same for ∆v 3 /⟨v 3 ⟩, all for the 40-50% centrality interval in Pb−Pb collisions at √ s NN = 5.02 TeV.The dotted blue line shows the linear fit to the data points to obtain the values of normalized slopes (r Norm 2

Figure 5 :
Figure 5: Dependence of ∆IC on v 2 of shape-selected events from the 0-10% (top left panel) to the 50-60% (bottom right panel) centrality intervals of Pb-Pb collisions at √ s NN = 5.02 TeV.The solid lines are straight line fit to the data points.Only statistical uncertainties are shown.The bands represent the three standard deviation uncertainties from the linear fit.

Figure 6 :
Figure 6: Centrality dependence of the extracted CMW fraction.The 95% confidence level of the upper limit is also shown by the dotted magenta line.Statistical uncertainties are depicted by bars, while the correlated systematic uncertainty is represented by a shaded band on the right edge.The blue line is the constant fit line of the data points.

Table 1 :
Nominal event and track selection criteria and the corresponding variations used for the estimation of the systematic uncertainties.

Table 2 :
Maximum systematic uncertainty (absolute value) on normalized slope per particle species over all centrality intervals from individual sources (see Table1for an explanation of each source).
5.1 A ch dependence of v n and centrality dependence of the slope r Norm n