EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN-EP-2022-220 20 October 2022

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20 October 2022

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Search for the Chiral Magnetic Effect with charge-dependent azimuthal

correlations in Xe–Xe collisions at √sNN =5.44 TeV

ALICE Collaboration*

Abstract

Charge-dependent two- and 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|<

0.8 and transverse momentum interval 0.2≤pT<5.0 GeV/cfor different collision centralities. The

three-particle correlator γαβ ≡⟨cos(ϕα+ϕβ−2Ψ2)⟩, 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 non-CME

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.

*See Appendix A for the list of collaboration members

arXiv:2210.15383v2 [nucl-ex] 27 Sep 2024

CME in Xe–Xe collisions ALICE Collaboration

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 glu-

onic 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 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,αin a Fourier decomposition

of the particle azimuthal distribution [24, 25]

d∆ϕα∼1+2v1,αcos(∆ϕα) + 2a1,αsin(∆ϕα) + 2v2,αcos(2∆ϕα) + ..., (1)

where ∆ϕα=ϕα−ΨRP,ϕαis the azimuthal angle of the particle of charge α(+, −), and ΨRP is the re-

action plane angle. The coefﬁcients vn,αcharacterise 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 cor-

responding to head-on collisions. The ﬁrst- and second-order ﬂow coefﬁcients (v1,αand v2,α) are called

directed and elliptic ﬂow, respectively. Since a1,αchanges 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 the reaction plane [25] of the

form γαβ ≡⟨cos(ϕα+ϕβ−2ΨRP)⟩. 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 sym-

metry plane angle Ψ2using azimuthal particle distributions [26], which is why γαβ is often referred to as

a three-particle correlator. The γαβ correlator measures the difference between the correlations projected

onto the reaction plane and perpendicular to it. The contributions from correlations in- and 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 col-

lision √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)scal-

ing [19]. This effect will be referred to as dilution in the following. The similarity of the two measure-

ments 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.

CME in Xe–Xe collisions ALICE Collaboration

To study background effects, the CMS Collaboration performed measurements of charge-dependent cor-

relations in p–Pb collisions at √sNN =5.02 TeV [37] and the STAR Collaboration in p–Au and d–Au

collisions at √sNN =0.2 TeV [38]. The results suggest that these correlations are similar to those mea-

sured 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 back-

ground. 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 sys-

tem 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 rel-

ative 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 per-

formed 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 iso-

bar 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 con-

ditions 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

CME in Xe–Xe collisions ALICE Collaboration

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 tungsten-

quartz 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 back-

ground 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 in-

terval, 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|<0.8 and 0.2≤pT<

5.0 GeV/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 asso-

ciations of space points) and ensure a track momentum resolution better than 4% in the considered pT

interval [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 pTaveraged charge-dependent correlations

are corrected for track reconstruction efﬁciency.

The charge-dependent correlations are measured using two- and three-particle correlators expressed as

δαβ ≡ ⟨cos(ϕα−ϕβ)⟩=⟨cos(∆ϕα)cos(∆ϕβ)⟩+⟨sin(∆ϕα)sin(∆ϕβ)⟩

=⟨v1,αv1,β⟩+Bin +⟨a1,αa2,β⟩+Bout,(2)

γαβ ≡ ⟨cos(ϕα+ϕβ−2Ψ2)⟩=⟨cos(∆ϕα)cos(∆ϕβ)⟩−⟨sin(∆ϕα)sin(∆ϕβ)⟩

=⟨v1,αv1,β⟩+Bin −⟨a1,αa2,β⟩−Bout,(3)

where ∆ϕα(β)=ϕα(β)−Ψ2, 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=∑

wjcos(2ϕj),Q2,y=∑

wjsin(2ϕj),(4)

where the index jruns over the 32 sectors of the V0A detector, ϕjis the azimuthal angle of sector j

deﬁned by the geometric centre, and wjis the amplitude of the measured signal in that sector. The sym-

metry plane resolution is calculated from correlations between the symmetry planes determined with

CME in Xe–Xe collisions ALICE Collaboration

Table 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

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 re-

sponse 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 (|∆η|>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 Barlow criterion [64]. The resulting systematic uncertainties increase from central to peripheral

collisions and are summarised in Table 1.

3 Results

Figure 1 compares the δαβ and γαβ correlators for same- and opposite-charge 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 cen-

trality 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 charge-sign combination and qualitatively similar centrality dependence in the

two systems. For δαβ , the magnitude of the same- and 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

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