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Physics
Letters
B
www.elsevier.com/locate/physletb
Constraining
the
magnitude
of
the
Chiral
Magnetic
Effect
with
Event
Shape
Engineering
in
Pb–Pb
collisions
at
√
s
NN
=
2
.
76 TeV
.
ALICE
Collaboration
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received27September2017
Receivedinrevisedform21November2017 Accepted8December2017
Availableonline12December2017 Editor:L.Rolandi
In ultrarelativistic heavy-ion collisions, the event-by-event variation of the elliptic flow v2 reflects fluctuationsintheshapeoftheinitialstateofthesystem. Thisallowstoselectevents withthesame centrality butdifferent initial geometry. This selection technique,Event Shape Engineering, has been used inthe analysis of charge-dependent two- and three-particle correlations in Pb–Pb collisions at √s
NN=2.76 TeV.The two-particle correlatorcos(
ϕ
α−ϕ
β),calculated for differentcombinations ofcharges
α
andβ,isalmostindependentofv2(foragivencentrality),whilethethree-particlecorrelator cos(ϕ
α+ϕ
β−22)scalesalmostlinearlybothwiththeevent v2andcharged-particlepseudorapidity density.Thechargedependenceofthethree-particlecorrelatorisofteninterpretedasevidenceforthe ChiralMagneticEffect (CME),aparityviolatingeffectofthestronginteraction.However,itsmeasured dependenceonv2pointstoalargenon-CMEcontributiontothecorrelator.Comparingtheresultswith MonteCarlocalculationsincludingamagneticfield duetothespectators, theupper limitoftheCME signalcontributiontothethree-particlecorrelatorinthe10–50%centralityintervalisfoundtobe26–33% at95%confidencelevel.©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
Paritysymmetryisconservedinelectromagnetismandis max-imallyviolated inweakinteractions. Instronginteractions,global parity violation is not observed even though it is allowed by quantum chromodynamics. Local parity violation instrong inter-actions might occur in microscopic domains underconditions of finite temperature [1–4] due to the existence of the topologi-callynon-trivialconfigurationsofthegluonicfield,instantonsand sphalerons. The interactions between quarks and gluonic fields with non-zero topological charge [5] change the quark chirality. Alocal imbalance of chirality, coupled withthe strong magnetic field produced in heavy-ion collisions (B
∼
1015 T) [6–8],wouldlead to charge separation along the direction of the magnetic field,whichisonaverageperpendiculartothereactionplane(the plane of symmetry defined by the impact parameter vector and thebeamdirection),a phenomenon calledChiralMagnetic Effect (CME)[9–12].Since the sign ofthe topological charge is equally probable to be positive or negative, the charge separation aver-agedovermanyeventsiszero.Thismakes theobservationofthe CMEexperimentallydifficultandpossibleonlyviacorrelation tech-niques.
E-mailaddress:alice-publications@cern.ch.
Azimuthalanisotropiesinparticleproductionrelativetothe re-actionplane,oftenreferredtoasanisotropicflow,areanimportant observabletostudythesystemcreatedinheavy-ioncollisions[13, 14].Anisotropicflow arisesfromtheasymmetry intheinitial ge-ometry of the collision. Its magnitude is quantified via the co-efficients vn in a Fourier decomposition of the charged particle
azimuthal distribution[15,16].Local parityviolationwouldresult inanadditionalsineterm[17]
dN d
ϕ
α∼
1
+
2v1,αcos(ϕ
α)
+
2a1,αsin(ϕ
α)
+
2v2,αcos(
2ϕ
α)
+ ...,
(1)where
ϕ
α=
ϕ
α−
RP,ϕ
α istheazimuthalangleoftheparticleofcharge
α
(+,−
) andRP isthe reaction-plane angle.The first
(v1,α ) and the second (v2,α ) coefficients are called directed and
ellipticflow,respectively.Thea1,α coefficientquantifiestheeffects
fromlocalparityviolation.Sincetheaverage
a1,α=
0 overmanyevents, one can only measure
a21,α or a1,+a1,−. The charge-dependenttwo-particlecorrelatorδ
αβ≡
cos(ϕ
α−
ϕ
β)
=
cos(ϕ
α)
cos(ϕ
β)
+
sin(ϕ
α)
sin(ϕ
β)
(2) https://doi.org/10.1016/j.physletb.2017.12.0210370-2693/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
isnot convenientforsuch astudy,becausealong withthesignal
a1,α a1,β(β
denotesthecharge)thereisamuchstrongercontri-butionfromcorrelationsunrelatedtotheazimuthalasymmetryin theinitial geometry(“non-flow”).Thesecorrelationslargelycome fromthe inter-jet correlationsand resonance decays.To increase theCMEcontributionitwas proposedtousethefollowing corre-lator[17]
γ
αβ≡
cos(ϕ
α+
ϕ
β−
2RP
)
=
cos(ϕ
α)
cos(ϕ
β)
−
sin(ϕ
α)
sin(ϕ
β)
(3)that measures the difference between the correlation projected onto the reaction plane and perpendicular to it. In practice, the reaction-planeangleisestimatedby constructingtheeventplane angle
2 usingazimuthalparticledistributions,whichiswhythis
correlatorisoftendescribedasathree-particlecorrelator.This cor-relatorsuppressesbackgroundcontributionsatthelevelofv2,the
difference between the particle production in-plane and out-of-plane. Examplesof such backgroundsources are thelocal charge conservation (LCC) coupled with elliptic flow [18,19], momen-tumconservation[19–21],anddirected-flowfluctuations[22].The mostsignificantbackgroundsourceforCME measurementsisthe LCC.
Themeasurementsofcharge-dependentazimuthal correlations performedattheRelativisticHeavyIonCollider(RHIC)[23–26]and the LargeHadron Collider (LHC) [27,28] are inqualitative agree-ment withthe expectations for the CME. However, the interpre-tationoftheseexperimentalresultsiscomplicatedduetopossible backgroundcontributions.TheEventShapeEngineering(ESE) tech-niquewas proposedtodisentanglebackgroundcontributionsfrom thepotentialCMEsignal[29].Thismethodmakesitpossibleto se-lectevents witheccentricityvaluessignificantly largerorsmaller thantheaverageinagivencentralityclass[30,31]since v2 scales
approximatelylinearlywitheccentricity[32].Centrality estimates thedegree ofoverlapbetweenthetwocollidingnuclei, withlow percentage values corresponding to head-on collisions. The CME contribution is expectedto mainly scale with the magnetic field strength andto not have a strong dependenceon the eccentric-ity[33], while the background variessignificantly. Therefore ESE providesa uniquetoolto separatetheCME signalfromthe back-groundforthethree-particlecorrelator.
TheCMSCollaborationhasrecentlyreportedthemeasurement ofthe three-particlecorrelator
γ
αβ inp–Pbcollisions at√
sNN=
5
.
02 TeV[34],wherethedirectionofthemagneticfieldisexpected tobeuncorrelatedtothereactionplane[35].Themagnitudeofthe correlator inp–PbandPb–Pb collisions is comparableforsimilar final-statecharged-particle multiplicities.This measurement indi-catesthat thecontribution ofthe CME to thisobservable in this multiplicityrangeissmall.Inthispaperwe report themeasurements ofthetwo-particle correlator
δ
αβ, the three-particle correlatorγ
αβ, and the ellipticflowv2 ofunidentifiedchargedparticles.Thesemeasurementsare
performedforshapeselectedandunbiasedeventsinPb–Pb colli-sionsat
√
sNN=
2.
76 TeV.AnupperlimitontheCMEcontributionisdeduced fromcomparisonsof theobserved dependenceofthe correlationsontheevent v2 tothat estimatedusingMonteCarlo
(MC) simulations of the magnetic field ofspectators with differ-entinitialconditions.Whilethispaperwasinpreparation,apaper employingasimilar approachtoestimatethefractionoftheCME signal inthe three-particle correlator was submitted by the CMS Collaboration[36].
The data sample recorded by ALICE during the 2010 LHC Pb–Pb run at
√
sNN=
2.
76 TeV is used for this analysis.Gen-eral information on the ALICE detector and its performance can be found in [37,38]. The Time Projection Chamber (TPC) [37,39]
and Inner Tracking System (ITS) [37,40] are used to reconstruct charged-particle tracksandmeasure theirmomenta witha track-momentum resolution betterthan 2% forthe transverse momen-tuminterval 0
.
2<
pT<
5.
0 GeV/c [38].Thetwo innermostlayersoftheITS, theSiliconPixelDetector(SPD),are employedfor trig-gering and event selection. Two scintillator arrays (V0) [37,41], which cover the pseudorapidity ranges
−
3.
7<
η
<
−
1.
7 (V0C) and 2.
8<
η
<
5.
1 (V0A), are used fortriggering, eventselection, andthedeterminationofcentrality[42] and2.Thetrigger
con-ditions and theevent selection criteriaare described in [38]. An offline eventselection is applied to remove beam induced back-groundandpileup events.Approximately 9
.
8·
106 minimum-biasPb–Pb eventswithareconstructedprimaryvertexwithin
±
10 cm fromthenominalinteractionpointinthebeamdirection belong-ingtothe0–60%centralityintervalareusedforthisanalysis.Charged particles reconstructed using the combined informa-tion fromtheITS andTPCin
|
η
|
<
0.
8 and 0.
2<
pT<
5.
0 GeV/care selected withfull azimuthal coverage. Additional quality cuts are applied to reduce thecontamination fromsecondary charged particles (i.e. particles originating fromweak decays, conversions andsecondaryhadronicinteractionsinthedetectormaterial)and faketracks(withrandomassociationsofspacepoints).Onlytracks withatleast70spacepointsintheTPC(outofamaximumof159) withan average
χ
2 perdegree-of-freedom forthe trackfit lowerthan 2,adistanceofclosest approach(DCA) tothe reconstructed eventvertexsmallerthan2.4 cminthetransverseplane(xy)and 3.2 cm inthelongitudinaldirection(z)areaccepted.Thecharged particletrackreconstructionefficiencywas estimatedfromHIJING simulations[43,44]combinedwithaGEANT3[45]detectormodel, and found to be independent of the collision centrality. The re-construction efficiencyofprimary particlesdefinedin[46],which maybiasthedetermination ofthe pT averagedcharge-dependent
correlations and flow, increases from 70% at pT
=
0.
2 GeV/c to85% at pT
∼
1.
5 GeV/c where it hasa maximum. It thengradu-allydecreasesandisflatat80%forpT
>
3.
0 GeV/c.Thesystematicuncertaintyoftheefficiencyisabout5%.
Theeventshapeselectionisperformedasin[30]basedonthe magnitude ofthe second-order reducedflow vector, q2 [47],
de-finedas q2
=
|
Q2|
√
M,
(4) where|
Q2|
=
Q22,x
+
Q22,y is themagnitudeofthesecond orderharmonic flowvector and M isthe multiplicity.The vector Q2 is
calculatedfromtheazimuthaldistributionoftheenergydeposition measuredintheV0C.Itsx and y componentsandthemultiplicity aregivenby Q2,x
=
i wicos(
2ϕ
i),
Q2,y=
i wisin(
2ϕ
i),
M=
i wi,
(5) where the sum runs over all channels i of the V0C detector (i=
1−
32),ϕ
i istheazimuthal angleofchanneli and wi istheamplitude measuredinchannel i.Thelargegapinpseudorapidity (
|
η
|
>
0.
9)betweenthechargedparticlesintheTPCusedto de-terminev2,δ
αβandγ
αβandthoseintheV0Csuppressesnon-floweffects.Tenevent-shapeclasseswiththelowest(highest)q2 value
corresponding to the 0–10%(90–100%) rangeare investigatedfor eachcentralityinterval.
The flow coefficient v2 is measured using the event plane
method [16]. The orientation ofthe eventplane
2 isestimated
fromtheazimuthaldistributionoftheenergydepositionmeasured bytheV0Adetector.Theeventplane resolutioniscalculatedfrom correlationsbetweentheeventplanesdeterminedintheTPCand
Table 1
Summaryofabsolutesystematicuncertainties.Theuncertaintiesdependon central-ityandshapeselection,whoseminimumandmaximumvaluesarelistedhere.
Opposite charge Same charge δαβ (3.4−25)×10−5 (3.1−10)×10−5 γαβ (2.6−34)×10−6 (4.1−74)×10−6
v2 (1.2−4.7)×10−3
Fig. 1. (Colouronline.) Unidentifiedchargedparticlev2forshapeselectedand un-biasedeventsasafunctionofcollisioncentrality.Theeventselectionisbasedon
q2determinedintheV0Cwiththelowest(highest)valuecorrespondingto0–10% (90–100%)q2.Pointsareslightlyshiftedalongthehorizontalaxisforbetter visibil-ity.Errorbars(shadedboxes)representthestatistical(systematic)uncertainties.
thetwo V0 detectorsseparately [16].The non-flow contributions tothe v2 coefficientandcharge-dependentazimuthalcorrelations
are greatly suppressed by the large rapidity separation between theTPCandtheV0A(
|
η
|
>
2.
0).The absolute systematic uncertainties are evaluated from the variationoftheresultswithdifferentselectioncriteriaonthe re-constructedcollision vertex, differentmagneticfield polarities, as well asby estimatingthecentrality frommultiplicities measured bytheTPCortheSPDratherthantheV0detector.Changesofthe resultsduetovariationsofthetrack-selectioncriteria(e.g. chang-ing the DCA xy and z ranges, number of the TPC space points, usingtracksreconstructedbytheTPConly)areconsideredaspart of the systematic uncertainties. The effect of reconstruction ef-ficiency on the measurements is checked by randomly rejecting trackstoensure aflat acceptancein pT.The detectorresponseis
studied using HIJING and AMPT [48] simulations, where the v2
coefficientsandthe charge-dependent azimuthal correlations ob-tained directly from the models are compared with those from reconstructedtracks.Thelargestcontributiontothesystematic un-certainties is given by the detector response. The checks related tothereconstruction efficiency,magneticfieldpolarity and track-selectioncriteriaalsoyieldsignificantdeviationsfromthenominal valuesfor v2,
γ
αβ andδ
αβ, respectively. The contributions fromall sources are added in quadrature as an estimate of the total systematicuncertainty. The resultingsystematic uncertainties are summarizedinTable 1.
Fig. 1 presents the unidentified charged particle v2 averaged
over0
.
2<
pT<
5.
0 GeV/c forshape selected andunbiasedsam-plesasafunctionofcollisioncentrality.The measured v2 forthe
shapeselectedeventsdiffersfromtheaveragebyupto25%,which demonstratesthateventswiththedesiredinitialspatialanisotropy canbe experimentallyselected.Sensitivityoftheeventshape se-lectiondeterioratesforperipheralcollisions(alreadyvisibleforthe
Fig. 2. (Colouronline.) Top:Centralitydependenceofγαβforpairsofparticleswith sameandoppositechargeforshapeselectedand unbiasedevents.Bottom: Cen-tralitydependenceofδαβforpairsofparticleswithsameandoppositechargefor shapeselectedandunbiasedevents.The eventselectionisbasedonq2determined intheV0Cwiththelowest(highest)valuecorrespondingto0–10%(90–100%)q2. Pointsareslightlyshiftedalongthehorizontalaxisforbettervisibilityinboth pan-els.Errorbars(shadedboxes)representthestatistical(systematic)uncertainties.
50–60%centralityclass)duetothelowmultiplicityandforcentral collisionsduetothereducedmagnitudeofflow[30].
The centrality dependence of
γ
αβ for pairs of particles withsameandopposite chargeforshape selectedandunbiasedevents is showninthe top panel ofFig. 2.The same charge results de-notetheaveragebetweenpairsofparticleswithonlypositiveand onlynegativechargessincethetwocombinationsarefoundtobe consistent withinstatisticaluncertainties. Thecorrelation ofpairs with the same charge is stronger than the correlation for pairs of opposite charge for both shape selected and unbiased events. The orderingof thecorrelationsofpairs withsameandopposite charge indicates a charge separation withrespectto the reaction plane.Themagnitudeofthesameandoppositechargepair corre-lations dependsweakly onthe event-shapeselection (q2,i.e. v2)
inagivencentralitybin.
ThebottompanelofFig. 2showsthecentralitydependenceof
δ
αβforpairsofparticleswithsameandoppositechargeforshapeselectedandunbiasedsamples.Asreportedin[27],themagnitude ofthecorrelationforthesamechargepairsissmallerthanforthe opposite charge combinations.This isin contrastto theCME ex-pectation, indicating that backgrounddominates the correlations. The sameandopposite chargepair correlationsareinsensitive to theevent-shapeselectioninagivencentralitybin.
The difference between opposite andsame charge pair corre-lationsfor
γ
αβ canbeusedto studythecharge separationeffect.This difference is presented asa function of v2 forvarious
Fig. 3. (Colouronline.) Top:Differencebetweenoppositeandsamechargepair cor-relationsforγαβasafunctionofv2forshapeselectedeventstogetherwithalinear fit(dashedlines)forvariouscentralityclasses.Bottom:Differencebetweenopposite andsamechargepaircorrelationsforγαβ multipliedbythecharged-particle den-sity[49]asafunctionofv2forshapeselectedeventsforvariouscentralityclasses. Theeventselectionisbasedonq2determinedintheV0Cwiththelowest(highest) valuecorrespondingto0–10%(90–100%)q2.Errorbars(shadedboxes) represent thestatistical(systematic)uncertainties.
for all centralities and its magnitude decreases for more central collisions and with decreasing v2 (in a given centrality bin). At
least two effects could be responsible for the centrality depen-dence: the reduction of the magnetic field with decreasing cen-tralityand the dilutionof the correlation due to the increase in the number of particles [24] in more central collisions. The dif-ferencebetweenopposite andsamecharge paircorrelations mul-tiplied by the charged-particle density in a given centrality bin, dNch
/
dη
(takenfrom[49]),to compensateforthe dilutioneffect,ispresentedasafunction ofv2 inthebottompanel ofFig. 3.All
thedatapointsfallapproximatelyontothesameline.Thisis qual-itativelyconsistentwithexpectationsfromLCC whereanincrease inv2,whichmodulatesthecorrelationbetweenbalancingcharges
withrespecttothe reactionplane [50], resultsina strongeffect. Therefore,theobserveddependenceon v2 points toalarge
back-groundcontributionto
γ
αβ.The expected dependenceof the CME signal on v2 was
eval-uated with the help of a Monte Carlo Glauber [51] calculation includingamagneticfield.Inthissimulation,thecentralityclasses are determined fromthe multiplicity of charged particles in the acceptance of the V0 detector following the method presented in [42]. The multiplicity is generated accordingto a negative bi-nomialdistributionwithparameterstakenfrom[42]basedonthe number of participant nucleons and binary collisions. The ellip-tic flow isassumed to be proportional to the eccentricity ofthe participantnucleons andapproximatelyreproduces themeasured
Fig. 4. (Colouronline.) TheexpecteddependenceoftheCMEsignalonv2forvarious centralityclassesfromaMC-Glaubersimulation[51](seetextfordetails).Noevent shapeselectionisperformedinthemodel,andtherefore alargerangeinv2 is covered.Thesolidlinesdepictlinearfitsbasedonthev2variationobservedwithin eachcentralityinterval.
pT-integrated v2 values [52]. The magnetic field is evaluated at
the geometricalcentre of theoverlap regionfromthe numberof spectator nucleons following Eq.(A.6)from [11] withthe proper time
τ
=
0.
1 fm/c. The magnetic field is calculated in 1% cen-trality classesand averaged into the centrality intervalsused for dataanalysis.Itisassumedthat theCMEsignal isproportional to|
B|
2cos(
2(
B
−
2))
,where|
B|
andB arethemagnitudeand
directionofthemagneticfield,respectively.Fig. 4presentsthe ex-pecteddependenceoftheCMEsignalon v2 forvariouscentrality
classes. Similar resultsare found using MC-KLN CGC[53,54] and EKRT[55]initialconditions.TheMC-KLNCGCsimulationwas per-formed usingversion32oftheMonteCarlokT-factorization code
(mckt) available at [56], while the TRENTO model [57] was em-ployedforEKRTinitialconditions.
To disentanglethe potential CMEsignal from background,the dependence on v2 of the difference betweenopposite andsame
charge pair correlationsfor
γ
αβ andthe CMEsignal expectationsare fittedwith a linear function (see lines in Figs. 3 (top panel) and4,respectively):
F1
(
v2)
=
p0(
1+
p1(
v2−
v2)/
v2),
(6)where p0 accountsfortheoverallscale,whichcannotbe fixedin
theMCcalculations,andp1reflectstheslopenormalisedsuchthat
inapurebackgroundscenario,wherethecorrelatorisdirectly pro-portionalto v2,it isequalto unity. Thepresence ofa significant
CMEcontribution,ontheotherhand,wouldresultinnon-zero in-tercepts at v2
=
0 of the linear functions shown in Fig. 3. Theranges used inthese fitsare based on the v2 variation observed
in dataandthecorresponding MC interval withineach centrality range.Thecentralitydependenceofp1 fromfitstodataandtothe
signal expectationsbasedonMC-Glauber,MC-KLNCGCandEKRT models is reportedinFig. 5.The observed p1 fromdatais a
su-perposition ofa possibleCMEsignalandbackground.Assuming a purebackgroundcase,p1 fromdataandMCmodelscanberelated
accordingto
fCME
×
p1,MC+ (
1−
fCME)
×
1=
p1,data,
(7)where fCMEdenotestheCMEfractiontothechargedependenceof
γ
αβ andisgivenbyfCME
=
(γ
opp−
γ
same)
CME(γ
opp−
γ
same)
CME+ (
γ
opp−
γ
same)
BkgFig. 5. (Colouronline.) Centralitydependenceofthe p1 parameterfromalinear fittothedifferencebetweenoppositeandsamechargepaircorrelationsforγαβ andfromlinearfitstotheCMEsignalexpectationsfromMC-Glauber[51],MC-KLN CGC[53,54]andEKRT[55]models(seetextfordetails).PointsfromMCsimulations areslightlyshiftedalongthehorizontalaxisforbettervisibility.Onlystatistical un-certaintiesareshown.
Fig. 6. (Colouronline.) CentralitydependenceoftheCMEfractionextractedfrom theslopeparameteroffitstodataandMC-Glauber[51],MC-KLNCGC[53,54]and EKRT[55]models,respectively(seetextfordetails).Thedashedlinesindicatethe physicalparameterspaceoftheCMEfraction.Pointsareslightlyshiftedalongthe horizontalaxisforbettervisibility.Onlystatisticaluncertaintiesareshown.
Fig. 6presents fCME for the three models used in thisstudy.
TheCMEfractioncannotbepreciselyextractedforcentral(0–10%) andperipheral (50–60%)collisions duetothelarge statistical un-certaintieson p1 extractedfromdata.Thenegative valuesforthe
CMEfraction obtainedforthe 40–50%centrality range(deviating fromzerobyone
σ
),ifconfirmed, wouldindicatethatour expec-tationsforthebackgroundcontributiontobelinearlyproportional to v2 are not accurate. Combining the points from 10–50%ne-glectingapossiblecentralitydependencegives fCME
=
0.
10±
0.
13, fCME=
0.
08±
0.
10 and fCME=
0.
08±
0.
11 for the MC-Glauber,MC-KLNCGCandEKRTmodels,respectively.Theseresultsare con-sistentwithzeroCMEfractionandcorrespondto upperlimitson
fCMEof33%,26%and29%,respectively,at95%confidencelevelfor
the10–50% centrality interval.The CME fraction agrees withthe observationsin[36]wherethecentralityintervalsoverlap.
Insummary,the EventShape Engineering technique hasbeen appliedtomeasurethedependenceonv2ofthecharge-dependent
two- and three-particle correlators
δ
αβ andγ
αβ in Pb–Pbcolli-sionsat
√
sNN=
2.
76 TeV.Whileforδ
αβweobservenosignificantv2 dependence in a given centrality bin,
γ
αβ is found to beal-mostlinearly dependent on v2.When the charge dependence of
γ
αβ ismultipliedbythecorrespondingcharged-particledensity,tocompensate for thedilution effect,a lineardependence on v2 is
observed consistently across all centralityclasses. Using a Monte Carlosimulationwithdifferentinitial-statemodels,wehavefound thattheCMEsignal isexpectedtoexhibit aweakdependenceon
v2 in themeasured range.Theobservationsimplythat the
dom-inant contributionto
γ
αβ is due tonon-CME effects.In order toget a quantitative estimate of the signal and background contri-butions to the measurements, we fit both
γ
αβ andthe expectedsignal dependenceon v2 witha firstorderpolynomial. This
pro-cedure allows to estimate the fraction of the CME signal in the centralityrange10–50%,butnotforthemostcentral(0–10%)and peripheral(50–60%)collisionsduetolargestatisticaluncertainties. Averaging over the centrality range10–50% gives an upperlimit of26% to33% (dependingontheinitial-statemodel)at95% con-fidence levelfor theCME contribution tothe difference between oppositeandsamechargepaircorrelationsfor
γ
αβ.Acknowledgements
The ALICE Collaboration would like to thank all its engineers andtechniciansfortheir invaluablecontributions tothe construc-tion of the experiment and the CERN accelerator teams for the outstanding performance ofthe LHC complex.The ALICE Collab-oration gratefully acknowledges the resources and support pro-videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the followingfunding agenciesfortheir supportinbuildingand run-ningthe ALICEdetector:A.I. AlikhanyanNationalScience Labora-tory(YerevanPhysicsInstitute)Foundation(ANSL),State Commit-teeofScienceandWorldFederationofScientists(WFS),Armenia; Austrian AcademyofSciences andNationalstiftungfür Forschung, Technologie und Entwicklung, Austria; Ministry of Communica-tions and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fun-dação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), Na-tional Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC), China; Ministry of Science, Edu-cation and Sportand Croatian Science Foundation, Croatia; Min-istryofEducation,YouthandSportsoftheCzech Republic,Czech Republic; The Danish Council for Independent Research – Natu-ral Sciences, the Carlsberg Foundation and Danish National Re-search Foundation (DNRF), Denmark; HelsinkiInstitute of Physics (HIP),Finland;Commissariatàl’EnergieAtomique(CEA)and Insti-tut National de Physique Nucléaire et de Physique des Particules (IN2P3) andCentre Nationalde la Recherche Scientifique(CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schw-erionenforschung GmbH, Germany; General Secretariat for Re-search and Technology, Ministry of Education, Research and Re-ligions, Greece; National Research, Development and Innovation Office,Hungary; DepartmentofAtomicEnergy,Governmentof In-dia (DAE)andCouncilofScientificandIndustrialResearch(CSIR), NewDelhi, India;IndonesianInstitute ofScience,Indonesia; Cen-tro Fermi – MuseoStorico della Fisica e CentroStudi e Ricerche EnricoFermiandIstitutoNazionalediFisicaNucleare(INFN),Italy; Institute forInnovativeScienceandTechnology, NagasakiInstitute of AppliedScience (IIST),Japan Societyforthe Promotion of Sci-ence(JSPS)KAKENHIandJapanese MinistryofEducation,Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional
deCiencia(CONACYT)yTecnología,throughFondodeCooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; NederlandseOrganisatievoorWetenschappelijkOnderzoek(NWO), Netherlands; The Research Council of Norway, Norway; Commis-sion on Science and Technology for Sustainable Development in theSouth(COMSATS),Pakistan;PontificiaUniversidadCatólicadel Perú,Peru;MinistryofScienceandHigherEducationandNational Science Centre, Poland; Korea Institute of Science and Technol-ogyInformationandNationalResearchFoundationofKorea(NRF), Republicof Korea; Ministryof Education andScientific Research, InstituteofAtomicPhysicsandRomanianNationalAgencyfor Sci-ence,Technology andInnovation,Romania; JointInstitute for Nu-clearResearch(JINR),MinistryofEducationandScienceofthe Rus-sian FederationandNationalResearchCentre KurchatovInstitute, Russia;Ministry ofEducation, Science,Research andSportofthe Slovak Republic, Slovakia; NationalResearch Foundation ofSouth Africa,SouthAfrica; Centrode AplicacionesTecnológicasy Desar-rolloNuclear(CEADEN),Cubaenergía,Cuba,MinisteriodeCienciae InnovacionandCentrodeInvestigacionesEnergéticas, Medioambi-entalesyTecnológicas(CIEMAT),Spain;SwedishResearchCouncil (VR)andKnut&AliceWallenbergFoundation(KAW),Sweden; Eu-ropean Organization for Nuclear Research, Switzerland; National Science andTechnology DevelopmentAgency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Educa-tionCommissionunderNRUprojectofThailand,Thailand;Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sci-encesofUkraine,Ukraine;ScienceandTechnologyFacilities Coun-cil (STFC), United Kingdom; National Science Foundation of the UnitedStatesofAmerica(NSF)andU.S.DepartmentofEnergy, Of-ficeofNuclearPhysics(DOENP),UnitedStatesofAmerica.
References
[1]T.D. Lee, A theory of spontaneous T violation, Phys. Rev. D 8 (1973) 1226–1239. [2]T.D. Lee, G.C. Wick, Vacuum stability and vacuum excitation in a spin 0 field
theory, Phys. Rev. D 9 (1974) 2291–2316.
[3]P.D. Morley, I.A. Schmidt, Strong P, CP, T violations in heavy ion collisions, Z. Phys. C 26 (1985) 627.
[4]D. Kharzeev, R.D. Pisarski, M.H.G. Tytgat, Possibility of spontaneous parity vio-lation in hot QCD, Phys. Rev. Lett. 81 (1998) 512–515, arXiv:hep-ph/9804221. [5]S.-S. Chern, J. Simons, Characteristic forms and geometric invariants, Ann. Math.
99 (1974) 48–69.
[6]A. Bzdak, V. Skokov, Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions, Phys. Lett. B 710 (2012) 171–174, arXiv:1111.1949 [hep-ph].
[7]W.-T. Deng, X.-G. Huang, Event-by-event generation of electromagnetic fields in heavy-ion collisions, Phys. Rev. C 85 (2012) 044907, arXiv:1201.5108 [nucl-th]. [8]U. Gursoy, D. Kharzeev, K. Rajagopal, Magnetohydrodynamics, charged currents
and directed flow in heavy ion collisions, Phys. Rev. C 89 (5) (2014) 054905, arXiv:1401.3805 [hep-ph].
[9]D. Kharzeev, Parity violation in hot QCD: why it can happen, and how to look for it, Phys. Lett. B 633 (2006) 260–264, arXiv:hep-ph/0406125.
[10]D. Kharzeev, A. Zhitnitsky, Charge separation induced by P-odd bubbles in QCD matter, Nucl. Phys. A 797 (2007) 67–79, arXiv:0706.1026 [hep-ph].
[11]D.E. Kharzeev, L.D. McLerran, H.J. Warringa, The effects of topological charge change in heavy ion collisions: ‘event by event P and CP violation’, Nucl. Phys. A 803 (2008) 227–253, arXiv:0711.0950 [hep-ph].
[12]K. Fukushima, D.E. Kharzeev, H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033, arXiv:0808.3382 [hep-ph].
[13]S.A. Voloshin, A.M. Poskanzer, R. Snellings, Collective phenomena in non-central nuclear collisions, arXiv:0809.2949 [nucl-ex].
[14]U. Heinz, R. Snellings, Collective flow and viscosity in relativistic heavy-ion col-lisions, Annu. Rev. Nucl. Part. Sci. 63 (2013) 123–151, arXiv:1301.2826 [nucl-th]. [15]S. Voloshin, Y. Zhang, Flow study in relativistic nuclear collisions by Fourier
expansion of Azimuthal particle distributions, Z. Phys. C 70 (1996) 665–672, arXiv:hep-ph/9407282.
[16]A.M. Poskanzer, S.A. Voloshin, Methods for analyzing anisotropic flow in rel-ativistic nuclear collisions, Phys. Rev. C 58 (1998) 1671–1678, arXiv:nucl-ex/9805001.
[17]S.A. Voloshin, Parity violation in hot QCD: how to detect it, Phys. Rev. C 70 (2004) 057901, arXiv:hep-ph/0406311.
[18]S. Schlichting, S. Pratt, Charge conservation at energies available at the BNL Relativistic Heavy Ion Collider and contributions to local parity violation ob-servables, Phys. Rev. C 83 (2011) 014913, arXiv:1009.4283 [nucl-th].
[19]S. Pratt, S. Schlichting, S. Gavin, Effects of momentum conservation and flow on angular correlations at RHIC, Phys. Rev. C 84 (2011) 024909, arXiv:1011.6053 [nucl-th].
[20]J. Liao, V. Koch, A. Bzdak, On the charge separation effect in relativistic heavy ion collisions, Phys. Rev. C 82 (2010) 054902, arXiv:1005.5380 [nucl-th]. [21]A. Bzdak, V. Koch, J. Liao, Azimuthal correlations from transverse momentum
conservation and possible local parity violation, Phys. Rev. C 83 (2011) 014905, arXiv:1008.4919 [nucl-th].
[22]D. Teaney, L. Yan, Triangularity and dipole asymmetry in heavy ion collisions, Phys. Rev. C 83 (2011) 064904, arXiv:1010.1876 [nucl-th].
[23]STAR Collaboration, B.I. Abelev, et al., Azimuthal charged-particle correlations and possible local strong parity violation, Phys. Rev. Lett. 103 (2009) 251601, arXiv:0909.1739 [nucl-ex].
[24]STAR Collaboration, B.I. Abelev, et al., Observation of charge-dependent az-imuthal correlations and possible local strong parity violation in heavy ion collisions, Phys. Rev. C 81 (2010) 054908, arXiv:0909.1717 [nucl-ex].
[25]STAR Collaboration, L. Adamczyk, et al., Fluctuations of charge separation per-pendicular to the event plane and local parity violation in √sNN=200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C 88 (6) (2013) 064911, arXiv:1302.3802 [nucl-ex].
[26]STAR Collaboration, L. Adamczyk, et al., Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC, Phys. Rev. Lett. 113 (2014) 052302, arXiv:1404.1433 [nucl-ex].
[27]ALICE Collaboration, B. Abelev, et al., Charge separation relative to the reaction plane in Pb–Pb collisions at √sNN=2.76 TeV, Phys. Rev. Lett. 110 (1) (2013) 012301, arXiv:1207.0900 [nucl-ex].
[28]ALICE Collaboration, J. Adam, et al., Charge-dependent flow and the search for the chiral magnetic wave in Pb–Pb collisions at √sNN=2.76 TeV, Phys. Rev. C 93 (4) (2016) 044903, arXiv:1512.05739 [nucl-ex].
[29]J. Schukraft, A. Timmins, S.A. Voloshin, Ultra-relativistic nuclear collisions: event shape engineering, Phys. Lett. B 719 (2013) 394–398, arXiv:1208.4563 [nucl-ex].
[30]ALICE Collaboration, J. Adam, et al., Event shape engineering for inclusive spec-tra and elliptic flow in Pb–Pb collisions at √sNN=2.76 TeV, Phys. Rev. C 93 (3) (2016) 034916, arXiv:1507.06194 [nucl-ex].
[31]ATLAS Collaboration, G. Aad, et al., Measurement of the correlation between flow harmonics of different order in lead-lead collisions at √sNN=2.76 TeV with the ATLAS detector, Phys. Rev. C 92 (3) (2015) 034903, arXiv:1504.01289 [hep-ex].
[32]F.G. Gardim, F. Grassi, M. Luzum, J.-Y. Ollitrault, Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions, Phys. Rev. C 85 (2012) 024908, arXiv:1111.6538 [nucl-th].
[33]A. Bzdak, Suppression of elliptic flow induced correlations in an observable of possible local parity violation, Phys. Rev. C 85 (2012) 044919, arXiv:1112.4066 [nucl-th].
[34]CMS Collaboration, V. Khachatryan, et al., Observation of charge-dependent azimuthal correlations in p–Pb
collisions
and its implication for the search for the chiral magnetic effect, Phys. Rev. Lett. 118 (12) (2017) 122301, arXiv: 1610.00263 [nucl-ex].[35]R. Belmont, J.L. Nagle, To CME or not to CME? Implications of p+Pb measure-ments of the chiral magnetic effect in heavy ion collisions, Phys. Rev. C 96 (2) (2017) 024901, arXiv:1610.07964 [nucl-th].
[36]CMS Collaboration, A.M. Sirunyan, et al., Constraints on the chiral magnetic ef-fect using charge-dependent azimuthal correlations in pPb and PbPb collisions at the LHC, arXiv:1708.01602 [nucl-ex].
[37]ALICE Collaboration, K. Aamodt, et al., The ALICE experiment at the CERN LHC, J. Instrum. 3 (2008) S08002.
[38]ALICE Collaboration, B.B. Abelev, et al., Performance of the ALICE experiment at the CERN LHC, Int. J. Mod. Phys. A 29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].
[39]J. Alme, et al., The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events, Nucl. Instrum. Methods Phys. Res., Sect. A, Accel. Spectrom. Detect. Assoc. Equip. 622 (2010) 316–367, arXiv:1001. 1950 [physics.ins-det].
[40]ALICE Collaboration, K. Aamodt, et al., Alignment of the ALICE Inner Tracking System with cosmic-ray tracks, J. Instrum. 5 (2010) P03003, arXiv:1001.0502 [physics.ins-det].
[41]ALICE Collaboration, E. Abbas, et al., Performance of the ALICE VZERO system, J. Instrum. 8 (2013) P10016, arXiv:1306.3130 [nucl-ex].
[42]ALICE Collaboration, B. Abelev, et al., Centrality determination of Pb–Pb col-lisions at √sNN=2.76 TeV with ALICE, Phys. Rev. C 88 (4) (2013) 044909, arXiv:1301.4361 [nucl-ex].
[43]X.-N. Wang, M. Gyulassy, HIJING: a Monte Carlo model for multiple jet produc-tion in p p, p A and A A collisions, Phys. Rev. D 44 (1991) 3501–3516. [44]M. Gyulassy, X.-N. Wang, HIJING 1.0: a Monte Carlo program for parton and
particle production in high-energy hadronic and nuclear collisions, Comput. Phys. Commun. 83 (1994) 307, arXiv:nucl-th/9502021.
[45]R. Brun, F. Bruyant, F. Carminati, S. Giani, M. Maire, A. McPherson, G. Patrick, L. Urban, GEANT detector description and simulation tool, CERN-W5013 1 (1994) 1.
[46] ALICECollaboration,S.Acharya,etal.,TheALICEdefinitionofprimaryparticles, ALICE-PUBLIC-2017-005,https://cds.cern.ch/record/2270008.
[47]STAR Collaboration, C. Adler, et al., Elliptic flow from two and four particle correlations in Au+Au collisions at √sNN=130 GeV, Phys. Rev. C 66 (2002) 034904, arXiv:nucl-ex/0206001.
[48]Z.-W. Lin, C.M. Ko, B.-A. Li, B. Zhang, S. Pal, A multi-phase transport model for relativistic heavy ion collisions, Phys. Rev. C 72 (2005) 064901, arXiv:nucl-th/ 0411110.
[49]ALICE Collaboration, K. Aamodt, et al., Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb–Pb collisions at √sNN= 2.76 TeV, Phys. Rev. Lett. 106 (2011) 032301, arXiv:1012.1657 [nucl-ex].
[50]Y. Hori, T. Gunji, H. Hamagaki, S. Schlichting, Collective flow effects on charge balance correlations and local parity-violation observables in √sNN=2.76 TeV Pb+Pb collisions at the LHC, arXiv:1208.0603 [nucl-th].
[51]M.L. Miller, K. Reygers, S.J. Sanders, P. Steinberg, Glauber modeling in high en-ergy nuclear collisions, Annu. Rev. Nucl. Part. Sci. 57 (2007) 205–243, arXiv: nucl-ex/0701025.
[52]ALICE Collaboration, K. Aamodt, et al., Elliptic flow of charged particles in Pb– Pb collisions at 2.76 TeV, Phys. Rev. Lett. 105 (2010) 252302, arXiv:1011.3914 [nucl-ex].
[53]H.-J. Drescher, Y. Nara, Eccentricity fluctuations from the color glass condensate at RHIC and LHC, Phys. Rev. C 76 (2007) 041903, arXiv:0707.0249 [nucl-th]. [54]J.L. Albacete, A. Dumitru, A model for gluon production in heavy-ion collisions
at the LHC with rcBK unintegrated gluon densities, arXiv:1011.5161 [hep-ph]. [55]H. Niemi, K.J. Eskola, R. Paatelainen, Event-by-event fluctuations in a
perturba-tive QCD + saturation + hydrodynamics model: determining QCD matter shear viscosity in ultrarelativistic heavy-ion collisions, Phys. Rev. C 93 (2) (2016) 024907, arXiv:1505.02677 [hep-ph].
[56]http://faculty.baruch.cuny.edu/naturalscience/physics/dumitru/CGC_IC.html. [57]J.S. Moreland, J.E. Bernhard, S.A. Bass, Alternative ansatz to wounded nucleon
and binary collision scaling in high-energy nuclear collisions, Phys. Rev. C 92 (1) (2015) 011901, arXiv:1412.4708 [nucl-th].
ALICECollaboration
![Fig. 4. (Colour online.) The expected dependence of the CME signal on v2 for various centrality classes from a MC-Glauber simulation [51] (see text for details)](https://thumb-eu.123doks.com/thumbv2/123dokorg/4809428.49776/4.918.54.431.105.602/colour-expected-dependence-various-centrality-glauber-simulation-details.webp)
![Fig. 5. (Colour online.) Centrality dependence of the p1 parameter from a linear fit to the difference between opposite and same charge pair correlations for γ αβ and from linear fits to the CME signal expectations from MC-Glauber [51] , MC-KLN CGC [53,54] a](https://thumb-eu.123doks.com/thumbv2/123dokorg/4809428.49776/5.918.68.448.108.366/centrality-dependence-parameter-difference-opposite-correlations-expectations-glauber.webp)
