Search for the Chiral Magnetic Effect with charge-dependent azimuthal correlations in Xe–Xe collisions at √sNN = 5.44 TeV

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Search for the Chiral Magnetic Effect with charge-dependent azimuthal correlations in Xe–Xe collisions at √sNN = 5.44 TeV © 2024 The Author(s). Published by Elsevier B.V. Funded by SCOAP³ Published version ALICE Collaboration ALICE Collaboration. (2024). Search for the Chiral Magnetic Effect with charge-dependent azimuthal correlations in Xe–Xe collisions at √sNN = 5.44 TeV. Physics Letters B, 856, Article 138862. https://doi.org/10.1016/j.physletb.2024.138862 2024 Phys. Lett. B 856 (2024) 138862 Available online 9 July 2024 0370-2693/© 2024 The Author(s). Published by Elsevier B.V. Funded by SCOAP³. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Physics Letters B journal homepage: www.elsevier.com/locate/physletb Letter Search for the Chiral Magnetic Effect with charge-dependent azimuthal correlations in Xe–Xe collisions at √𝑠NN =5.44 TeV .ALICE Collaboration⋆ A R T I C L E I N F O A B S T R A C T Editor: M. Doser Dataset link: https:// www .hepdata .net /record /ins2172062 Charge-dependent twoand three-particle correlations measured in Xe–Xe collisions at √𝑠NN =5.44 TeV are presented. Results are obtained for charged particles in the pseudorapidity range |𝜂| <0.8and transverse momentum interval 0.2 ≤𝑝T<5.0GeV/𝑐for different collision centralities. The three-particle correlator 𝛾𝛼𝛽 ≡ ⟨cos(𝜑𝛼+𝜑𝛽−2Ψ 2)⟩, calculated for different combinations of charge sign 𝛼and 𝛽, is expected to be sensitive to the presence of the Chiral Magnetic Effect (CME). Its magnitude is similar to the one observed in Pb–Pb collisions in contrast to a smaller CME signal in Xe–Xe collisions than in Pb–Pb collisions predicted by Monte Carlo (MC) calculations including a magnetic field induced by the spectator protons. These observations point to a large nonCME contribution to the correlator. Furthermore, the charge dependence of 𝛾𝛼𝛽 can be described by a blast wave model calculation that incorporates background effects and by the Anomalous Viscous Fluid Dynamics model with values of the CME signal consistent with zero. The Xe–Xe and Pb–Pb results are combined with the expected CME signal dependence on the system size from the MC calculations including a magnetic field to obtain the fraction of CME contribution in 𝛾𝛼𝛽, 𝑓CME. The CME fraction is compatible with zero for the 30% most central events in both systems and then becomes positive. This yields an upper limit of 2% (3%) and 25% (32%) at 95% (99.7%) confidence level for the CME signal contribution to 𝛾𝛼𝛽 in the 0–70% Xe–Xe and Pb–Pb collisions, respectively. 1. Introduction The theory of the strong interaction applied to many-body systems predicts that, at sufficiently high densities and temperatures, the protons and neutrons that compose ordinary matter melt into a plasma where quarks and gluons are no longer confined into hadrons. This hot and dense state of matter is called the quark–gluon plasma (QGP) [1]. The transition from normal hadronic matter to a QGP is supported by Quantum Chromodynamics (QCD) calculations on the lattice [2–5], where it is found to occur at a temperature of about 155 MeV, and at an energy density 𝜖of about 0.5 GeV/fm3[6–8]. Collisions between heavy ions accelerated to ultrarelativistic energies can produce the necessary conditions for such a transition to take place [9–11]. Heavy-ion collisions may also allow us to access novel QCD phenomena associated with parity violation in strong interactions [12–20]. Theoretical expectations indicate that the interaction of quarks with gluonic fields describing transitions between topologically different QCD vacuum states changes the quark chirality and leads to a local chiral imbalance. In the presence of the strong magnetic field produced by the colliding ions [21–23], this leads to a charge separation (electric current) relative to the reaction plane, the plane defined by the impact ⋆E-mail address: alice -publications @cern .ch. parameter and the beam axis. This phenomenon is known as the Chiral Magnetic Effect (CME) [20]. The effects from local parity violation are quantified via the coefficient 𝑎1,𝛼 in a Fourier decomposition of the particle azimuthal distribution [24,25] d𝑁 dΔ𝜑𝛼 ∼1+2𝑣1,𝛼 cos(Δ𝜑𝛼)+2𝑎1,𝛼 sin(Δ𝜑𝛼)+2𝑣2,𝛼 cos(2Δ𝜑𝛼)+..., (1) where Δ𝜑𝛼=𝜑𝛼−Ψ RP, 𝜑𝛼is the azimuthal angle of the particle of charge 𝛼(+, −), and ΨRP is the reaction plane angle. The coefficients 𝑣n,𝛼 characterise the anisotropic flow, i.e., the azimuthal anisotropies in particle production relative to ΨRP due to initial spatial asymmetries of the collision. The degree of overlap between the two colliding nuclei is estimated by the centrality, with low percentage values corresponding to head-on collisions. The firstand second-order flow coefficients (𝑣1,𝛼 and 𝑣2,𝛼 ) are called directed and elliptic flow, respectively. Since 𝑎1,𝛼 changes sign from event to event and the average ⟨𝑎1,𝛼 ⟩over many events is equal to zero, one can only measure ⟨𝑎2 1,𝛼⟩or ⟨𝑎1,+𝑎1,−⟩ that can be accessed through azimuthal correlation techniques. Thus the CME is expected to have an experimentally accessible signal imprinted in the azimuthal correlations between two particles relative to https://doi.org/10.1016/j.physletb.2024.138862 Received 14 November 2022; Received in revised form 28 June 2024; Accepted 4 July 2024 Physics Letters B 856 (2024) 138862 2 ALICE Collaboration the reaction plane [25]of the form 𝛾𝛼𝛽 ≡⟨cos(𝜑𝛼+𝜑𝛽−2Ψ RP)⟩. The charge-dependent difference of 𝛾𝛼𝛽 is commonly used to search for the CME. In practice, the reaction plane angle is estimated by constructing the second harmonic symmetry plane angle Ψ2using azimuthal particle distributions [26], which is why 𝛾𝛼𝛽 is often referred to as a threeparticle correlator. The 𝛾𝛼𝛽 correlator measures the difference between the correlations projected onto the reaction plane and perpendicular to it. The contributions from correlations inand out-of-plane can also be evaluated by measuring the charge-dependent two-particle correlator 𝛿𝛼𝛽 ≡⟨cos(𝜑𝛼−𝜑𝛽)⟩. The first experimental results in Au–Au collisions at a centre-of-mass energy per nucleon–nucleon collision √𝑠NN = 200 GeV at the Relativistic Heavy-Ion Collider (RHIC) [27,28]were compatible with initial expectations for the existence of the CME. The subsequent first measurements at the Large Hadron Collider (LHC) in Pb–Pb collisions at √𝑠NN =2.76 TeV [29]showed a surprising agreement with the results at lower energies, despite the differences in magnitude of the magnetic field [21–23]. Considering that the charged-particle density, d𝑁ch∕d𝜂, at the LHC is about three times larger than at RHIC [30,31], any signal due to CME will be considerably diluted since it is expected to follow a 1∕(d𝑁ch∕d𝜂)scaling [19]. This effect will be referred to as dilution in the following. The similarity of the two measurements was indicative of the existence of background effects, coming mostly from “flowing clusters” – charge-dependent correlations modified by elliptic flow [25,32–34]. It was shown in Refs. [35,36]that the local charge conservation coupled to the anisotropic expansion of the medium could explain most if not all the measurements. To study background effects, the CMS Collaboration performed measurements of charge-dependent correlations in p–Pb collisions at √𝑠NN =5.02 TeV [37]and the STAR Collaboration in p–Au and d– Au collisions at √𝑠NN =0.2TeV [38]. The results suggest that these correlations are similar to those measured in peripheral Pb–Pb and Au– Au collisions. These results might further indicate the dominance of background effects in peripheral collisions where there is no strong correlation between the magnetic field direction and the orientation of the medium via ΨRP. These measurements highlighted the need to identify ways of isolating the CME signal from the background. A first attempt was presented by the ALICE Collaboration in Ref. [39]using the Event Shape Engineering method [40]. This method utilises 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. The study sets an upper limit of 26–33% at 95% confidence level for the CME signal contribution to the charge dependence of 𝛾𝛼𝛽 in the 10–50% centrality interval. A similar study was performed by the CMS Collaboration [41]and the results agree with the measurements in Ref. [39]. A recent study by the ALICE Collaboration [42]found that charge-dependent correlations relative to the higher harmonic symmetry planes can be used as a proxy for the background, assuming that the correlations relative to Ψ2and Ψ3can be factorised. An upper limit of 15–18% at 95% confidence level for the CME signal has been reported for the 0–40%centrality interval, consistent with previous measurements. Another approach to address the large backgrounds experimentally is to compare measurements performed in collision systems where the CME contribution is expected to vary significantly, while the background is similar. The STAR Collaboration has recently reported the results of the CME search in an analysis of the three-particle correlator 𝛾𝛼𝛽 measured in collisions of isobar 96 44Ru–96 44Ru and 96 40Zr–96 40Zr nuclei at √𝑠NN = 200 GeV [43]. No anticipated CME signature (i.e., a larger magnitude of 𝛾𝛼𝛽 in Ru–Ru than in Zr–Zr collisions due to a larger magnetic field in the former) was observed in that analysis. However, a quantitative analysis taking into account the small geometrical differences between the isobar nuclei is needed for the interpretation of the measurements. One can also try to separate the CME signal and background by comparing the results from Pb–Pb and Xe–Xe collisions at the LHC since the differences in 𝑣2are typically within 10% in the 5–70% centrality interval [44]but the magnetic field is expected to be significantly larger in Pb–Pb collisions [45], leading to an increase in the CME contribution. In this article, measurements of charge-dependent azimuthal correlations from Xe–Xe collisions at √𝑠NN = 5.44 TeV are presented. The results are compared with earlier measurements in Pb–Pb collisions at √𝑠NN =5.02 TeV [42]and calculations from a blast wave parameterisation that incorporate background effects and from the Anomalous Viscous Fluid Dynamics (AVFD) model [46–48]. Furthermore, Monte Carlo (MC) simulations of the magnetic field induced by spectator protons with different initial conditions are used to evaluate the expected change in the CME signal between the Xe–Xe and Pb–Pb collisions. This change is then employed to estimate the fraction of the CME signal in both collision systems. 2. Analysis details The data set used for these measurements was recorded with the ALICE detector during the 2017 Xe–Xe run at √𝑠NN =5.44 TeV. A detailed overview of the ALICE detector and its performance are available in Refs. [49,50]. The Inner Tracking System (ITS) [51], the Time Projection Chamber (TPC) [52], the V0 [53], and the Zero Degree Calorimeter (ZDC) [54], the main subsystems used in this analysis, are briefly described in the following. The ITS and TPC cover the full azimuth within the pseudorapidity range |𝜂| <0.9. The ITS consists of six layers of silicon detectors and is employed for tracking, vertex reconstruction, and event selection. The TPC is used to reconstruct charged-particle tracks and to identify particles via specific energy loss, d𝐸∕d𝑥. The V0 detector, two arrays of 32 scintillator tiles covering −3.7 <𝜂<−1.7(V0C) and 2.8 <𝜂<5.1(V0A), is used for triggering, event selection, and the determination of centrality [55]and symmetry plane Ψ2. Both V0 detectors are segmented in four rings in the radial direction with each ring divided into eight sectors in the azimuthal direction. Two tungstenquartz neutron ZDCs, installed 112.5 meters from the interaction point on each side, are also used for event selection. The trigger conditions and the event selection criteria can be found in Ref. [56]. Beam-induced background and pileup events are removed using an offline event selection, employing information from the V0, ZDC, and tracking detectors. The primary vertex position is determined from tracks reconstructed in the ITS and TPC as described in Ref. [50]. Approximately 106Xe–Xe events in the 0–70% centrality interval, with a primary vertex position within ±10 cm from the nominal interaction point along the beam direction, are used in the analysis. The centrality of the collision is estimated from the energy deposition measured in the V0 detector [55]. The charged-particle tracks reconstructed using the ITS and TPC within |𝜂| <0.8and 0.2 ≤𝑝T<5.0GeV/𝑐are used to measure the charge-dependent correlations. Each track is required to have a minimum number of 70 space points (out of a maximum of 159) with a 𝜒2per TPC space point lower than 4, to cross at least 70 TPC readout rows, and to have the ratio between the number of crossed rows and the number of findable space points in the TPC larger than 0.8. The selected tracks are also required to have at least 2 ITS hits and a 𝜒2per ITS hit smaller than 36. In addition, tracks are selected with a distance of closest approach (DCA) to the reconstructed vertex position smaller than 3.2 cm and 2.4 cm in the longitudinal direction (𝑧) and transverse plane (𝑥𝑦), respectively. These selection criteria reduce the contamination from secondary charged particles (i.e., particles originating from weak decays, conversions, and secondary hadronic interactions in the detector material) and fake tracks (random associations of space points) and ensure a track momentum resolution better than 4% in the considered 𝑝Tinterval [56]. The charged-particle track reconstruction efficiency is estimated from simulations with the HIJING event generator [57,58] combined with the GEANT3 transport model [59]. These simulations include a detailed description of the detector response. The Physics Letters B 856 (2024) 138862 3 ALICE Collaboration 𝑝Taveraged charge-dependent correlations are corrected for track reconstruction efficiency. The charge-dependent correlations are measured using twoand three-particle correlators expressed as 𝛿𝛼𝛽 ≡⟨cos(𝜑𝛼−𝜑𝛽)⟩=⟨cos(Δ𝜑𝛼)cos(Δ𝜑𝛽)⟩+⟨sin(Δ𝜑𝛼)sin(Δ𝜑𝛽)⟩ =⟨𝑣1,𝛼𝑣1,𝛽 ⟩+𝐵in +⟨𝑎1,𝛼𝑎2,𝛽 ⟩+𝐵out ,(2) 𝛾𝛼𝛽 ≡⟨cos(𝜑𝛼+𝜑𝛽−2Ψ 2)⟩ =⟨cos(Δ𝜑𝛼)cos(Δ𝜑𝛽)⟩−⟨sin(Δ𝜑𝛼)sin(Δ𝜑𝛽)⟩ =⟨𝑣1,𝛼𝑣1,𝛽 ⟩+𝐵in −⟨𝑎1,𝛼𝑎2,𝛽 ⟩−𝐵out , (3) where Δ𝜑𝛼(𝛽)=𝜑𝛼(𝛽)−Ψ 2, and 𝐵in and 𝐵out denote background contributions projected onto Ψ2and perpendicular to it, respectively. The term ⟨𝑣1,𝛼𝑣1,𝛽 ⟩is expected to have negligible charge dependence at midrapidity [60]. In addition, ⟨𝑣1⟩at midrapidity is zero for a symmetric collision. While 𝛾𝛼𝛽 suppresses background contributions at the level of 𝑣2(i.e., the relative difference between the particle production in-plane and out-of-plane), 𝛿𝛼𝛽 is dominated by short-range correlations unrelated to Ψ2(“non-flow”), such as inter-jet correlations and resonance decays. The orientation of the symmetry plane Ψ2is estimated from the azimuthal distribution of the energy deposition measured by the V0A detector, with the 𝑥and 𝑦components given by 𝑄2,x=∑ 𝑗 𝑤𝑗cos(2𝜑𝑗),𝑄 2,y=∑ 𝑗 𝑤𝑗sin(2𝜑𝑗),(4) where the index 𝑗runs over the 32 sectors of the V0A detector, 𝜑𝑗is the azimuthal angle of sector 𝑗defined by the geometric centre, and 𝑤𝑗is the amplitude of the measured signal in that sector. The symmetry plane resolution is calculated from correlations between the symmetry planes determined with the TPC, the V0A, and the V0C detectors [26]. The effect of the decorrelation of Ψ2between mid and forward pseudorapidity has been estimated to be less than 3% for 𝑣2[61]. Any non-uniform detector response is taken into account by adjusting the components of the 𝐐2vector using a recentering procedure (i.e., subtraction of the 𝐐2vector averaged over many events from the 𝐐2vector of each event) [62]. The non-flow contributions to the charge-dependent azimuthal correlations are greatly suppressed by the large pseudorapidity separation between the TPC and the V0A (|Δ𝜂| >2.0). The absolute systematic uncertainties were estimated from the variation of the results with different event and track-selection criteria. The event selection contributions were determined by varying the range of the reconstructed collision vertex position from the nominal interaction point along the beam direction, estimating centrality from the number of hits in the first or second layer of the ITS, and imposing stricter pileup rejection criteria than the default selection. Systematic uncertainties related to track selection criteria were evaluated by changing the ITS hit requirements, varying the minimum number of TPC space points, changing the minimum number of crossed TPC readout rows and the ratio between the number of crossed rows and the number of findable space points in the TPC, rejecting tracks close to the TPC sector boundaries to which the sensitive readout rows do not extend, and comparing any differences between results with only positive and only negative charges for pairs of particles with same charge. Finally, changes of the results due to uncertainties in the tracking efficiency arising from an imperfect description in the simulation of the relative abundances of different particle species and their different reconstruction efficiencies [63]were considered as part of the systematic uncertainties. The largest contribution to the systematic uncertainties for 𝛾𝛼𝛽 and 𝛿𝛼𝛽 is given by the centrality estimation and track-selection criteria, respectively. The systematic uncertainties are evaluated for each centrality interval. The different sources are assumed uncorrelated and are added in quadrature as an estimate of the total systematic uncertainties if their deviations from the nominal values are significant according to the BarTable 1 Summary of absolute systematic uncertainties on the charge-dependent correlations. The uncertainties depend on centrality, whose minimum and maximum values are listed here. Opposite charge Same charge 𝛿𝛼𝛽 (6.8 − 33) × 10−5 (3.8 − 13) × 10−5 𝛾𝛼𝛽 (1.0−8.3) × 10−5 (1.4−5.9) × 10−5 low criterion [64]. The resulting systematic uncertainties increase from central to peripheral collisions and are summarised in Table 1. 3. Results Fig. 1compares the 𝛿𝛼𝛽 and 𝛾𝛼𝛽 correlators for sameand oppositecharge pairs in Xe–Xe collisions at √𝑠NN =5.44 TeV to those measured in Pb–Pb collisions at √𝑠NN =5.02 TeV [42]as a function of centrality and average charged-particle multiplicity density ⟨d𝑁ch∕d𝜂⟩at midrapidity [65,66]. The results for same-charge pairs denote the average between pairs of particles with only positive and only negative charges since the two combinations are consistent within statistical uncertainties. Both correlators exhibit strong dependence on the chargesign combination and qualitatively similar centrality dependence in the two systems. For 𝛿𝛼𝛽, the magnitude of the sameand opposite-charge pair correlations is positive and increases from central to peripheral collisions. In contrast to the CME expectation, the correlation for the opposite-charge pairs is stronger than for the same-charge combinations, indicating that background dominates these measurements. For 𝛾𝛼𝛽, the magnitude of opposite-charge pair correlations is close to zero within uncertainties for most of the centrality intervals, while it decreases from central to peripheral collisions becoming more negative for same-charge pairs. Thus, the correlation of opposite-charge pairs is weaker than for same-charge pairs. This ordering is compatible with a charge separation with respect to the reaction plane expected in the presence of the CME. The 𝛿𝛼𝛽 for same-charge pairs shows small (if any) differences between Xe–Xe and Pb–Pb collisions within uncertainties, while the correlations for opposite-charge pairs have larger magnitude in Xe–Xe collisions in the 10–70% centrality interval. The 𝛾𝛼𝛽 for sameand oppositecharge pairs from Xe–Xe and Pb–Pb collisions have similar magnitudes within uncertainties in the 0–10% and 50–70% centrality ranges, while the correlations are stronger in Xe–Xe collisions in the 10–50% centrality interval. These observations can be attributed to the different number of particles produced in the collision within a given centrality interval between the two systems that dilutes the correlations. This is supported by the fact that the 𝛿𝛼𝛽 and 𝛾𝛼𝛽 for sameand opposite-charge pairs from Xe–Xe collisions are consistent within uncertainties with the corresponding Pb—Pb results when reported as a function of ⟨d𝑁ch∕d𝜂⟩. The 𝛾𝛼𝛽 correlator is also investigated as a function of the pseudorapidity difference Δ𝜂=|𝜂𝛼−𝜂𝛽|, the transverse momentum difference Δ𝑝T=|𝑝T𝛼−𝑝T𝛽|, and the average transverse momentum ⟨𝑝T⟩ = (𝑝T𝛼+𝑝T𝛽)∕2 of the pair. Fig. 2presents these results for sameand opposite-charge pairs in the 20–30% centrality interval compared to measurements performed in 30–40% Pb–Pb collisions [42]. Different Xe–Xe and Pb–Pb centrality intervals are selected since they have similar transverse densities (1∕𝑆d𝑁ch∕d𝜂∼10fm−2 with 𝑆being the transverse area) and transverse sizes (𝑅 =√𝑆∕𝜋∼4fm) [44], thus the contribution from dilution effects is comparable. In addition, the value of 𝑣2∕𝜀2(𝜀2is the second-order eccentricity coefficient and characterises the elliptic shape of the initial geometry) and the influence of radial flow are similar in the two systems for these centrality classes [44,56]. The opposite-charge pair correlations from Xe–Xe collisions show a weak dependence on Δ𝜂and ⟨𝑝T⟩, while they increase with increasing Δ𝑝T of the pair. The correlations for the same-charge pairs do not exhibit any significant dependence on Δ𝑝Tand ⟨𝑝T⟩within uncertainties. These Physics Letters B 856 (2024) 138862 4 ALICE Collaboration Fig. 1. The 𝛿𝛼𝛽 (top panels) and 𝛾𝛼𝛽 (bottom panels) correlators as a function of centrality (left panels) and charged-particle density [65,66] (right panels) for pairs of particles with same (closed markers) and opposite (open markers) charges from Xe–Xe collisions at √𝑠NN =5.44 TeV (red circles) compared to Pb–Pb collisions at √𝑠NN =5.02 TeV (black squares) [42]. The Pb–Pb points are slightly shifted along the horizontal axis for better visibility in the left panels. Bars (boxes) denote statistical (systematic) uncertainties. Fig. 2. The dependence of 𝛾𝛼𝛽 on the pseudorapidity difference |𝜂𝛼−𝜂𝛽|(left panel), the transverse momentum difference |𝑝T𝛼−𝑝T𝛽|(middle panel), and the average transverse momentum (𝑝T𝛼+𝑝T𝛽)∕2 (right panel) for pairs of particles with same (closed markers) and opposite (open markers) charges from 20–30% Xe–Xe collisions at √𝑠NN =5.44 TeV (red circles) compared to results from 30–40% Pb–Pb collisions at √𝑠NN =5.02 TeV (black squares) [42]. The Pb–Pb and Xe–Xe same-charge points are slightly shifted along the horizontal axis for better visibility in all panels. Bars (boxes) denote statistical (systematic) uncertainties. correlations show a strong dependence on Δ𝜂with a width of approximately one unit in pseudorapidity difference. The Xe–Xe and Pb–Pb results are compatible within uncertainties demonstrating similar behaviour of this observable despite the differences in the magnetic field. To get insight into the origin of the charge-dependent effects observed in Xe–Xe collisions, two different approaches were investigated. The first one relies on a blast wave (BW) model based on a parameterisation from Ref. [67]. Input parameters of the model are tuned to describe the 𝑝Tspectra [68]and the 𝑝T-differential 𝑣2values [69]of charged pions and kaons, as well as of protons and antiprotons, measured in the same collision system and centre-of-mass energy. To account for the main source of background in the measurements reported in this article, the model was further extended by including effects from local charge conservation (LCC). This was done by generating sources uniformly at the surface of the ellipse that surrounds the centre of the system and allowing them to decay into particles with opposite charge. In this extension of the BW model, the number of sources that emit oppositely-charged pairs is tuned separately for each centrality interval to reproduce the centrality dependence of Δ𝛿𝛼𝛽 ≡𝛿opp. 𝛼𝛽 −𝛿same 𝛼𝛽 , the correlator that is mainly sensitive to background effects. This is illustrated in the upper panel of Fig. 3, where the BW curve is represented by the blue, solid line that goes through the experimental data points. The tuned model is then used to extract the expectation for the centrality dependence of Δ𝛾𝛼𝛽 ≡𝛾opp. 𝛼𝛽 −𝛾same 𝛼𝛽 , shown in the lower panel of Fig. 3. The width of the band reflects the uncertainty obtained by propagating the corresponding uncertainties of the model parameters using a sub-sampling method. It can be seen that the BW model describes fairly well the measured data points for all centrality intervals. This is in contrast to the picture that emerged in Pb–Pb collisions, where following a similar procedure the same model underestimated the measurements of Δ𝛾𝛼𝛽 by as much as ≈40%[42]. Additional insight can be obtained by comparing the results with calculations from the Anomalous Viscous Fluid Dynamics (AVFD) model [46–48]. It relies on a Glauber model description of the initial state of the collision and accounts for the development of the earlystage electromagnetic fields as well as for the propagation of anomalous fermion currents. The expanding medium is described using a 2+1 dimensional viscous hydrodynamics (VISH2+1) code [70] which is coupled to a hadron cascade model (UrQMD) [71,72]. Within AVFD, the final-state CME signal induced by the initial chirality imbalance is controlled by the axial current density 𝑛5∕s. At the same time, the relevant background in AVFD is governed by the amount of positive and nega- Physics Letters B 856 (2024) 138862 5 ALICE Collaboration Fig. 3. Centrality evolution of the difference between oppositeand same-charge pair correlations for 𝛿𝛼𝛽 (top panel) and 𝛾𝛼𝛽 (bottom panel) compared to model calculations: blast wave (BW) parameterisation [67] coupled to local charge conservation (LCC) effects (blue curves) and Anomalous Viscous Fluid Dynamics (AVFD) [46,47] (green curves). The BW+LCC model is tuned to reproduce the centrality dependence of Δ𝛿𝛼𝛽 , while AVFD is tuned to describe simultaneously the centrality dependence of Δ𝛿𝛼𝛽 and Δ𝛾𝛼𝛽. Bars (boxes) denote statistical (systematic) uncertainties on the data points, while the thickness of the curves represents the uncertainties on the model calculations. tive charged partners emitted from the same fluid element relative to the total multiplicity of the event, i.e., the LCC percentage. The model was first calibrated to describe the centrality dependence of both the charged-particle density [66]and the elliptic flow [44]. As a second step, the dependence of Δ𝛿𝛼𝛽 and Δ𝛾𝛼𝛽 on both the CME signal and the background was determined, by analysing samples with either increasing values of 𝑛5∕s or LCC percentage, respectively [45]. These results made it possible to extract the combination of 𝑛5∕s and LCC percentage that describes the data and led to a quantitative simultaneous description of the centrality dependence of Δ𝛿𝛼𝛽 and Δ𝛾𝛼𝛽 [45]. This is illustrated in the two panels of Fig. 3. Also in this case, the width of the band reflects the uncertainty obtained by propagating the corresponding uncertainties of the model parameters using a sub-sampling method. The experimental data points can be described by large values of LCC contribution, between 40%and 60%for peripheral and more central Xe–Xe collisions, respectively. In addition, the values of 𝑛5∕s extracted from this procedure did not exhibit any significant centrality dependence and were compatible with zero within uncertainties [45]. Similar to the conclusion extracted from the BW model, the study within the AVFD framework indicates that the experimental measurements in Xe–Xe collisions are dominated by background. The charge separation effect can be further studied using the difference between oppositeand same-charge pair correlations Δ𝛾𝛼𝛽 and the CME signal expectations from MC calculations employed as guidance. A comparison between Δ𝛾𝛼𝛽 divided by 𝑣2[44]in Xe–Xe collisions and that measured in Pb–Pb collisions [42]is presented as a function of centrality and charged-particle density [65,66]in Fig. 4. The value of Δ𝛾𝛼𝛽∕𝑣2is positive for all centralities and its magnitude increases from central to peripheral collisions. Furthermore, it is slightly higher in Xe–Xe than Pb–Pb collisions in the 10–60% centrality interval. However, the Xe–Xe and Pb–Pb data points fall approximately onto the same curve when reported as a function of ⟨d𝑁ch∕d𝜂⟩. The expected centrality dependence of the CME signal in Xe–Xe and Pb–Pb collisions is estimated from MC Glauber [73] simulations including a magnetic field [39]. In these calculations, the 208Pb nucleus is spherical while the 129Xe nucleus is deformed with a deformation parameter 𝛽2=0.18 ±0.02 [55]. The centrality classes are determined from the multiplicity of charged particles in the acceptance of the V0 detector, which is generated according to a negative binomial distribution with parameters taken from Ref. [74]. The magnetic field is calculated at the origin from the number of spectator protons using Eq. (A.6) from Ref. [19]with the proper time 𝜏=0.1fm/𝑐. Fig. 5shows the centrality dependence of ⟨(𝑒𝐵)2cos(2(ΨB−Ψ 2))⟩(ΨBis the direction of the magnetic field  𝐵), which is the expected CME signal contribution in 𝛾𝛼𝛽 , for the two collision systems. The expected CME signal is stronger in Pb–Pb than Xe–Xe collisions in a given centrality interval due to the smaller magnetic field strength and a larger decorrelation between ΨBand Ψ2 in Xe–Xe collisions. Similar results are found using TRENTo [75] initial conditions. This observation coupled to the agreement of Δ𝛾𝛼𝛽 between the two collision systems (see Fig. 4) points to a large background contribution to 𝛾𝛼𝛽 in Xe–Xe collisions. The large differences in the CME signal expectations and the small variations in 𝑣2(<10% for the 5–70% centrality interval) [44]between the two collision systems can be used to disentangle the potential CME signal from the background in Xe–Xe and Pb–Pb collisions. Assuming that both the CME signal and the background scale with d𝑁ch∕d𝜂, the charge dependence of 𝛾𝛼𝛽 for the two collision systems can be exFig. 4. Difference between oppositeand same-charge pair correlations for 𝛾𝛼𝛽 divided by 𝑣2[44]as a function of centrality (left) and charged-particle density (right) compared to results from Pb–Pb collisions at √𝑠NN =5.02 TeV [42]. The Pb–Pb points are slightly shifted along the horizontal axis for better visibility in the left panel. Bars (boxes) denote statistical (systematic) uncertainties. Physics Letters B 856 (2024) 138862 6 ALICE Collaboration Fig. 5. The expected CME signal as a function of centrality from MC Glauber simulations for Xe–Xe and Pb–Pb collisions [73](see text for details). pressed using a two-component approach similar to the one proposed in Ref. [76] ΓXe−Xe =𝑠𝐵Xe−Xe +𝑏𝑣Xe−Xe 2,(5) ΓPb−Pb =𝑠𝐵Pb−Pb +𝑏𝑣Pb−Pb 2,(6) where Γ ≡𝛾𝛼𝛽 d𝑁ch∕d𝜂, 𝐵≡⟨(𝑒𝐵)2cos(2(ΨB−Ψ 2))⟩, and 𝑣2is taken from Ref. [44]and 𝛾Pb−Pb 𝛼𝛽 from Ref. [42]. The 𝑠and 𝑏parameters quantify the signal and background contributions, respectively, and do not depend on collision system within a given centrality interval as a result of the assumption that both scale with d𝑁ch∕d𝜂. While the d𝑁ch∕d𝜂 scaling is expected for 𝑏since it is dominated by flowing clusters [25], the domains responsible for 𝑠can be considered small and thus they can be regarded as “usual” clusters which scale with d𝑁ch∕d𝜂. This scaling is further supported by the AVFD calculations performed for Pb–Pb and Xe–Xe collisions [45]. The 𝑠and 𝑏parameters can be used to calculate the fractions of the CME signal (denoted as 𝑓CME) in Xe–Xe and Pb–Pb collisions as 𝑓CME =𝑠𝐵 𝑠𝐵 +𝑏𝑣2 .(7) The smaller CME signal in Xe–Xe collisions also results in a tighter limit on 𝑓CME in Xe–Xe than in Pb–Pb collisions. It is worth noting that the CME fractions in the two collision systems are correlated because both are calculated with the same 𝑠and 𝑏parameters, extracted from the data using Eqs. (5) and (6). Fig. 6presents the centrality dependence of 𝑓CME in Xe–Xe and Pb– Pb collisions for the two models used in this study. The uncertainties in the CME fractions are obtained adding in quadrature the statistical and systematic uncertainties in Eqs. (5) and (6). The 𝑓CME does not depend significantly on the proper time used to calculate the magnetic field since varying the value from 0.1 fm/𝑐to 0.01 fm/𝑐, 0.5 fm/𝑐, and 1 fm/𝑐yields similar CME fractions. Furthermore, the dependence on the centrality range used in Pb–Pb collisions has been studied. The analysis was performed using only a single centrality interval of Pb–Pb collisions and all Xe–Xe centrality classes. For all eight Pb–Pb centrality intervals, a good agreement is found with the nominal 𝑓CME. The 𝑓CME is compatible with zero up to 30% centrality in both systems and then becomes positive for midcentral and peripheral collisions with larger values in Pb–Pb than in Xe–Xe. The CME fraction for the 0–30% centrality interval in Pb–Pb collisions agrees with the one reported in Ref. [42]. Fitting the data points in the centrality range 0–70% with a constant function neglecting any centrality dependence gives 𝑓CME =−0.003 ±0.010 (𝑓CME =−0.001 ±0.012) and 𝑓CME =0.147 ±0.061 (𝑓CME =0.150 ±0.062) for MC Glauber (TRENTo) initial conditions in Xe–Xe and Pb–Pb collisions, respectively. These results are consistent with zero CME fraction in Xe–Xe collisions and correspond to upper limits on 𝑓CME of 2% (3%) and 25% (32%) at 95% (99.7%) confidence level for the 0–70% centrality interval in Xe–Xe and Pb–Pb collisions, respectively. The limits are estimated assuming Gaussian uncertainties. 4. Summary The charge-dependent twoand three-particle correlators 𝛿𝛼𝛽 and 𝛾𝛼𝛽 have been measured in Xe–Xe collisions at √𝑠NN =5.44 TeV. The charge dependence of these correlators is strongly correlated with centrality, increasing from central to peripheral collisions, and is qualitatively similar to those reported in Pb–Pb collisions. The difference between the Xe–Xe and Pb–Pb results mostly arises from dilution effects since the data points from both collision systems fall approximately onto the same curve when presented as a function of charged-particle density. Monte Carlo simulations with different initial state models predict a significantly larger magnitude of the CME signal in Pb–Pb than Xe–Xe collisions, which implies that the dominant contribution to 𝛾𝛼𝛽 in Xe–Xe collisions is due to background effects. The magnitude of the charge dependence of 𝛾𝛼𝛽 is described over the entire centrality range by a blast wave parameterisation that incorporates local charge conservation tuned to reproduce the components of the background. This magnitude is also reproduced by Anomalous Viscous Fluid Dynamics calculations with large contributions from local charge conservation effects and values of the CME signal close to zero, thus indicating that the background is the dominant contribution to the three-particle correlaFig. 6. Centrality dependence of the CME fraction extracted using Eq. (7)with the expected CME signal from MC Glauber [73](closed markers) and TRENTo [75] (open markers) models (see text for details). The TRENTo points are slightly shifted along the horizontal axis for better visibility. Physics Letters B 856 (2024) 138862 7 ALICE Collaboration tor. In order to get a quantitative estimate of the signal and background contributions, the measured values of 𝛾𝛼𝛽 in Xe–Xe and Pb–Pb collisions are compared using a two-component approach. This procedure allows one to estimate the fraction of the CME signal in both collision systems. Averaging over the 0–70% centrality interval, an upper limit of 2% (3%) and 25% (32%) is estimated at 95% (99.7%) confidence level for the CME contribution to the charge dependence of 𝛾𝛼𝛽 in Xe–Xe and Pb–Pb collisions, respectively. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability This manuscript has associated data in a HEPData repository at: https://www .hepdata .net /record /ins2172062. Acknowledgements The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 20202027 (object CERN), Bulgaria; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; The Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the Villum Fonden and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Énergie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy, Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Académico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut and Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. 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