Possible observables for the chiral electric separation effect in Cu + Au collisions

0.16 MB·English

by  Guo-Liang Ma

Possibleobservables forthechiral electric separationeffect inCu +Au collisions
Guo-Liang Ma1, and Xu-Guang Huang2,
∗ †
1Shanghai Instituteof AppliedPhysics, ChineseAcademyof Sciences, Shanghai 201800, China
2PhysicsDepartmentandCenterforParticlePhysicsandFieldTheory,FudanUniversity,Shanghai 200433,China
Thequark-gluonplasma(QGP)generatedinrelativisticheavy-ioncollisionscouldbelocallyparity-odd. In
parity-oddQGP,theelectricfieldmayinduceachiralcurrentwhichiscalledthechiralelectricseparationeffect
(CESE).WeproposetwopossibleobservablesforCESEinCu+Aucollisions: Thefirstoneisthecorrelation
ζ = cos[2(φ +φ 2Ψ )] ;thesecondoneisthecharge-dependentevent-planeangleΨqwithq= being
cαhβargeh.Nonzerαo∆ζβ=−ζ RP ζi and∆Ψ= Ψ+ Ψ maysignaltheCESEinCu+Auc2ollisions.W±ithina
opp− same h| 2 − −2|i
multiphasetransportmodel,westudyhowthefinalstateinteractionaffectstheseobservables. Wefindthatthe
correlationγ = cos(φ +φ Ψ ) issensitivetotheout-of-planechargeseparationcausedbythechiral
5 αβ h α β− RP i
1 magneticeffectandtothein-planechargeseparationcausedbythein-planeelectricfield,butitisnotsensitive
0 totheCESE.Ontheotherhand, ∆ζ and∆ΨaresensitivetotheCESE.Therefore,wesuggestthatthefuture
2 experiments measure the above observables in Cu+Au collisions in order to disentangle different chiral and
chargeseparationmechanisms.
y
a
PACSnumbers:25.75.-q,12.38.Mh,11.30.Er
M

1 I. INTRODUCTION Heavy-ioncollisionscanalsogeneratestrongelectricfields
2
due to the event-by-eventfluctuation of the proton positions

in the ions [3, 4] or due to asymmetric colliding geometry
] Relativistic heavy-ion collisions generate not only ex-
h (for example, in Cu + Au collisions [30–32]). It was pro-
tremely hot quark-gluon plasma (QGP) but also extremely
t posed that the electric fields may also induce chiral current
- large magnetic fields due to the fast motion of the colliding
l andchiralseparationinQGP,whichiscalledthechiralelec-
c ions. Recentdetailedcalculationsrevealedthatthemaximum
u magnetic fields in Au + Au collisions at energies currently tric separation effect (CESE) [33–36]. It was also proposed
n that the Cu+Au collisions may provide us a good chance to
availableattheBNLRelativisticHeavyIonCollider(RHIC)
[ can reach 5m2 1018 Gauss while in Pb + Pb collisions at detectCESE becausethereisa strongelectricfield directing
π ∼ fromAutoCuduetothechargeasymmetrybetweenAuand
2 energiesavailableattheCERNLargeHadronCollider(LHC)
v they can reach 60m2 1019 Gauss [1–5]. Under such large Cu nuclei[33]. Recently, the electromagneticfields in Cu +
3 π ∼ Aucollisionswerestudiedindetails,anditwasfoundthatthe
magnetic fields, some novelquantum phenomenacan possi-
0 largein-planechargeseparationeffect(in-planeCSE)induced
bly happen. The most intriguing ones are the so-called chi-
9 by the strong in-plane electric fields could stronglysuppress
ral magnetic effect (CME) [6–10] and chiral separation ef-
3
orevenreversesignsofγ [30].
0 fect (CSE) [11, 12]: They occur in parity- and charge-odd αβ
1. regions in QGP and can result in charge and chirality sepa- Inthispaper,weproposetwoobservablesthataredesigned
rationsalongthedirectionofthemagneticfield,respectively.
0 solely for the detection of CESE. In addition, it is crucial to
Recent experimental measurements of the charge azimuthal
5 takethefinalstateinteractionsintoaccountforanymodelcal-
1 correlation[13], culationsinordertolinktheinitialanomaloustransportstothe
:
v experimentaldatasinceheavy-ioncollisionsundergocompli-
i γαβ = cos(φα+φβ 2ΨRP) , (1) cateddynamicalevolutionswhichinvolvemanyfinalinterac-
X h − i
tions. We study the effects of the final state interactions by
r where φ and φ are the emission azimuthalangles of parti- usingamulti-phasetransport(AMPT)modelwhichsuccess-
a α β
cleswithchargesαandβandΨ isthereactionplaneangle, fully describes the main evolution stages of heavy-ion colli-
RP
showedsomeconsistentfeatureswiththeexpectationofCME sions.Byintroducingappropriateinitialdipolarorquadrupole
atbothRHICandLHCenergies[14–16]. Anotherimportant charge distributions, the AMPT model can successfully de-
experimentaltest of CME and CSE is the observationof the scribeboththechargeazimuthalcorrelationγ [37,38]and
αβ
charge asymmetry in the elliptic flow of pions [17, 18] that thechargeasymmetryofthepionellipticflow[39]inAu+Au
is consistent with the expectation of a chiral magnetic wave collisionsatthetopRHICenergy. Inthiswork,weintroduce
(CMW)[19,20]—acollectivemodearisingduetotheinter- differentkindsofinitialchargeseparationswhichareusedto
playbetweenCMEandCSEinthepresenceofthemagnetic mimic differentinitial chiraleffectsinto the initialcondition
field. However, one must notice that there are other back- oftheAMPTmodel,andpredictsomeobservableswhichcan
grounds that contribute to the experimentalobservables, see be used to test whether these effects can be observed in the
Refs.[21–29]fordiscussions. finalstateofCu+Aucollisionsat √s =200GeV.
NN
Thepaperis organizedas follows. InSec. IIwe setup the
numericalsimulations, in Sec. IIIwe show our main results.
FinallywesummarizeanddiscussinSec.IV.Throughoutthis
∗[email protected]
†[email protected] paper,weusethenaturalunits~=kB =c=1.
2
II. GENERALSETUP
×10-3
>
)
A. AMPTmodel φ+β0.5 Cu+Cu 200 GeV
α
φ
(
TheAMPTmodelwithastringmeltingscenarioisutilized s
o
in this work [40]. The AMPT model is a dynamical trans- c
< 0
port model which consists of four main components: initial
condition,partoncascade,hadronization,andhadronicrescat-
terings. The initialcondition,which includesthe spatialand
opp, AMPT (Normal)
momentumdistributionofparticipantmatter,minijetpartons -0.5
opp, AMPT (CME)
productionandsoftstringexcitations,isobtainedthroughthe opp, exp. data
HIJINGmodel[41,42].Thepartoncascadestartsthepartonic same, AMPT (Normal)
same, AMPT (CME)
evolutionwithaquark-anti-quarkplasmafromthemeltingof -1 same, exp. data
strings. Parton scatterings are modelled by Zhang’s parton
0 10 20 30 40 50 60 70
cascade(ZPC),whichcurrentlyonlyincludestwo-bodyelas- % Most Central
tic parton scatterings using cross sections from pQCD with
screening masses [43]. The parton interaction cross section FIG. 1: (Color online) Centrality dependence of cos(φ +φ ) in
is set as 10 mb in our work, by which the modelhas shown Cu+Cu collisions at √s =200 GeV. The open shymbolαs reprβesient
NN
goodabilitiestodescribemanykeyexperimentalobservables theresultsfromthenormalAMPTmodelwithoutanomalouseffects
at RHIC [44–49]. A quark coalescence model is then used and the AMPT model with an initial CME-like charge separation,
tocombinepartonsintohadronswhenthesystemfreezesout. andthesolidsymbolsrepresenttheexperimentaldata[14].
Theevolutiondynamicsofthehadronicmatterisdescribedby
arelativistictransport(ART)model[50]. Becausethecurrent
implementationoftheARTmodeldoesnotconservetheelec- with the factthatthe averagedmagneticfield is proportional
tric charge, we in this study consider only resonancedecays to b [3, 4]. Comparing with the normal AMPT result, the
andhadronicscatteringsareswitchedofftoensurethecharge AMPTresultwiththeinitialCME-likechargeseparationcan
conservation. welldescribeCu+Cudatameasuredbythesolenoidaltracker
atRHIC(STAR)experiment.
We now turn to study the Cu + Au systems. The co-
B. IntroducingtheinitialchargeseparationsintotheAMPT ordinate system of Cu + Au is set up similarly to that of
model Cu+Cu, but the Au nucleus is set to the left of the Cu nu-
cleus,i.e.,thedirectionofthetotalelectricfieldisrightward.
Let us consider the chiral magnetic effect (CME) in Cu Figures2 (a)-(f)show the netelectric chargedistributionsin
+ Cu collisions first. This can serve as a test of the AMPT the transverse momentum space of the initial partonic states
model.Thecoordinatesystemissetupsothatthex-axisisin in the AMPT models with different kinds of initial charge
thereactionplane,i.e.,Ψ = 0,andthey-axisisperpendic- separationsforcentralitybinof30-40%inCu+Aucollisions
RP
ular to the reaction plane with the z-axis being the direction √s =200 GeV. After introducing the CME effect into the
NN
of the projectile nucleus. To mimic the CME, we introduce normal AMPT model, the net electric charge distribution is
aninitialchargeseparationintotheinitialstateoftheAMPT changed from that in Fig. 2 (a) to that in Fig. 2 (b). Due
model,sincethechargesarenotseparatedbutdistributedran- to the strong electric fields in the in-plane direction in Cu +
domly in the normal AMPT model. To separate a percent- Aucollisions,theremayappearalsothein-planechargesep-
ageoftheinitialcharges,wefollowtheprocedureofaglobal aration effect (in-plane CSE) [30]. To simulate the in-plane
chargeseparation scenario, which has been employedin Ma CSE, we take an analogoussetup as above by switching the
and Zhang’spreviouswork [37]. We switch a percentageof p values of a percentage of the leftward moving u quarks
x
thedownwardmovinguquarkswiththoseoftheupwardmov- with those of the rightward moving u¯ quarks, and likewise
ing u¯ quarks in such a way that the total momentumis con- for d¯ and d quarks. The b dependence of the percentage is
served,andlikewiseford¯anddquarks,wherethepercentage assumed to be the same as that for the out-of-plane separa-
shouldpresumablydependontheimpactparameterborcen- tion. The corresponding net electric charge distribution is
trality,becausethemagnitudeoftheaveragedmagneticfield shown in Fig. 2 (c). Now we take the chiral electric sepa-
isbdependent. rationeffect(CESE) into account. We considerthe situation
In Fig. 1 we show our AMPT results of the charge az- wheretheCESE, CME andin-planeCSE happensimultane-
imuthal correlation γ (from the normal AMPT model and ously (denotedas CESE+CME+in-plane CSE) [33]: For the
αβ
the AMPT model with the initial CME-like charge separa- quarkswithp >0weswitchapercentage f%oftheleftward
y
tion) as well as the experimental data for Cu+Cu collisions movinguquarkswiththoseoftherightwardmovingu¯ quarks
at √sNN = 200 GeV. We find that, to fit the Cu+Cu experi- (likewise for d¯and d quarks); while for quarkswith py < 0
mentaldata, the percentageof initial CME-like chargesepa- weswitchhalfofthepercentage(i.e. 0.5f%)fortheleftward
ration f% should be proportionalto the impact parameter b movingu¯ (d)quarkswiththoseoftherightwardmovingu(d¯)
with a slope of 1.56, i.e. f = 1.56b/fm. This is consistent quarks. For the initial charge separation f%, we apply the
3
)
V/c 1 (a) AMPT (Normal) 1 (b) AMPT (CME) 1 (c) AMPT (in-pla. CSE)
e
G
(
y0.5 0.5 0.5
p
0 0 0
-0.5 -0.5 -0.5
-1
V/c) 1 (d) AMPT (CESE+CME+in-pla. CSE)1-1(e) AMPT (CESE+2xCME+in-pla.CSE)--111(f) AM-P0T.5(CESE+0CME+20xi.n5-pla.CSE1)
e
G
(y0.5 0.5 0.5
p
0 0 0
-0.5 -0.5 -0.5
Cu+Au 200 GeV (30-40%)
-1 -1 -1
-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1
p (GeV/c) p (GeV/c) p (GeV/c)
x x x
FIG.2:(Coloronline)Thenetelectricchargedistributionsinthetransversemomentumplaneintheinitialpartonicstatesfordifferentsettings
of AMPTmodelsfor centralitybinof 30-40% inCu+Aucollisions √s =200 GeV.(a) Normalsettingwithout anyanomalous effect. (b)
NN
AMPTwithout-of-planechargeseparationwhichmimicthechiralmagneticeffect(CME).(c)AMPTwithin-planechargeseparationeffect
(in-plane CSE) caused by the in-plane electric field. (d) AMPT with in-plane CSE plus a quadrupolar distribution due to chiral electric
separationeffect(CESE)andCME.(e)Thesameas(d)butwiththestrengthofCMEdoubled.(f)Thesameas(d)butwiththestrengthofthe
in-planeCSEdoubled.
same b-dependentinitialchargeseparationasthatof Cu+Cu
collisions at √s =200 GeV. In this case, this b-dependent
NN
percentageisexpectedtoprovidealowerlimitfortheinitial
chargeseparationpercentage,since the Cu+Au system hasa
littlebitstrongermagneticfieldthantheCu+Cusystematthe
same impact parameter [30]. The net effect is equivalent to
a configuration with a in-plane dipole plus a quadrupole as
illustrated in Fig. 3. The net electric charge distribution for
CESE+CME+in-planeCSE is shownin Fig. 2 (d). To study
the case where the CME is much stronger, we do the CME FIG. 3: (Color online) Illustration of the charge configuration of
switching once more after the above CESE+CME+in-plane chiral magnetic effect (CME) plus chiral electric separation effect
CSE switching, whichis shownin Fig. 2(e). Ifthe in-plane (CESE)plusin-planechargeseparationeffect(in-planeCSE)inCu
+Aucollisions.
CSE effect is much larger, we do the in-plane CSE switch-
ingoncemoreaftertheCESE+CME+in-planeCSEswitching,
see Fig. 2 (f). In these ways, we have six differentkinds of
III. RESULTSANDDISCUSSIONS
initial charge distributions which mimic different initial chi-
raleffects. We usethemasthedifferentinputsfortheinitial
condition of the AMPT model, and then we extract various A. Correlationγαβ
hadronic observables to test whether the initially embedded
effects can survive after the final state interactions. The re- We first consider the correlationγ as definedin Eq. (1).
αβ
sultsarepresentedinthefollowing. The centrality dependence of γ in Cu+Au collisions at
αβ
√s =200 GeV from different settings of the AMPT model
NN
areshowninFigs.4(a)-(f),wherethecentralitybinsarede-
fined by using different ranges of impact parameter. Also
4
×10-3
>
) (a) AMPT (Normal) (b) AMPT (CME) (c) AMPT (in-pla. CSE)
β
φ
+ 0.5
α
φ
(
s
o 0
c
<
-0.5
-1
×10 ×10 ×10
> 0 10 20 30 40 50 60 70
)β (d) AMPT (CESE+CME+in-pla. CSE) (e) AMPT (CESE+2xCME+in-pla. CSE) (f) AMPT (CESE+CME+2xin-pla. CSE)
φ
+
α 0.5 0.5 0.5
φ
(
s
o
c 0 0 0
<
-0.5 -0.5 -0.5
opp, AMPT (Cu+Au)
same, AMPT (Cu+Au)
opp, exp. data (Cu+Cu)
-1 -1 -1 same, exp. data (Cu+Cu)
0 10 20 30 40 50 60 700 10 20 30 40 50 60 700 10 20 30 40 50 60 70
% Most Central % Most Central % Most Central
FIG.4:(Coloronline)Centralitydependenceofγ = cos(φ +φ ) fromdifferentinitialsettingsofAMPTmodels(opensymbols)inCu+Au
αβ h α β i
collisionsat √s =200GeV.AlsoshownaretheexperimentaldataforCu+Cucollisionsat √s =200GeV(solidsymbols)[14]. Different
NN NN
panelsareinone-to-onecorrespondencewithFig.2.
shownistheexperimentaldatafromCu+Cucollisionswhich lationsarestronglysuppressedto the levelsclose to thenor-
are used as the baseline for comparison. Figure 4 (a) shows mal AMPT model [Fig. 4 (a)], which indicates the three ef-
thatthenormalAMPTmodelwithoutanyinitialchargesep- fectsalmostcancelout. Thiscanbeunderstoodbyconsider-
aration gives a zero opposite-charge correlation and a nega- ing a limiting case in which the emitting angles for positive
tive same-chargecorrelationwhich have much smaller mag- chargesareπ/4and5π/4whilefornegativechargestheyare
nitudes than the experimental data for Cu+Cu collisions at 3π/4 and 7π/4. In this special limit, one can easily check
√sNN=200 GeV. After introducing the chiral magnetic effect that both γsame and γopp vanish. If the initial strength of the
(CME) into the AMPT model, as shown in Fig. 4 (b), the CME-like charge separation gets larger, e.g. if it is doubled
opposite-charge correlation becomes positive and the same- (denoted as CESE+2 CME+in-plane CSE), the magnitudes
×
chargecorrelationbecomesmorenegative,whichpresentsim- forbothopposite-chargeandsame-chargecorrelationsarebe-
ilar magnitudesas the Cu+Cu data. It is consistent with the tweenthosefortheCMEandforCESE+CME+in-planeCSE,
previousAMPT works aboutAu+Au collisions [37] and the whichisshowninFig.4(e). Ontheotherhand,ifwedouble
aboveresultsaboutCu+Cucollisions.Iftheinitialchargesare the strength of the initial in-plane charge separation, e.g. in
separated along the reaction plane direction [mimicking the thecaseofCESE+CME+2 in-planeCSE[Fig.4(f)],thein-
×
in-plane charge separation effect (in-plane CSE) caused by planeCSEwilldominatethefinalsignal,whichshowssimilar
the strong in-plane electric field], comparing with the CME magnitudesas those for the in-planeCSE effectonly [Fig. 4
case, opposite-charge and same-charge correlations reverse (c)]. Fromthesesimulations,wefindthatthecorrelationγ
αβ
their signs, i.e. a negative opposite-chargecorrelation and a isverysensitivetoCMEandin-planeCSEbutnotsensitiveto
positivesame-chargecorrelationareobservedandtheirmag- CESE.Totestthechiralelectricseparationeffect,weneedto
nitudesarecomparabletotheCu+Cudata,asshowninFig.4 lookforotherobservables.
(c). This result is consistent with recent study in Ref. [30]
and more discussions can be found there. It is also consis-
tent with the charge asymmetry of direct flow v suggested
1 B. TwoobservablesforCESE
in Ref. [31]. If the chiral electric separation effect (CESE),
CME, and in-plane CSE happen together in the initial stage
Inthissubsection,weproposetwoobservablesforthechi-
[Fig.4(d)],boththeopposite-chargeandsame-chargecorre-
ral electric separation effect (CESE) in Cu + Au collisions.
5
×10-3
0.4
ame AMPT (Normal) ad) AMPT (Normal)
ζ-sp AMPT (CME) > (r AMPT (CME)
ζop00..23 Cu+AAu M20P0T G (CeVESE+CME+in-pla.CSE) -ΨΨ+|-<|220.2 AAAAMMMMPPPPTTTT ((((CCCinEEE-pSSSlaEEE.+++C2CCSxMMEC)EEM++E2in+x-iipnnl--app.llCaaS..CCESS)EE))
Cu+Au 200 GeV
0.1
0.1
0
0
-0.1
0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70
% Most Central % Most Central
FIG.5: (Color online) Centralitydependence of the difference be- FIG.6: (Color online) Centralitydependence of the difference be-
tweenopposite-charge(ζ )andsame-charge(ζ )correlationsof tweenevent planeanglesreconstructedfromthepositivelycharged
opp same
ζαβ = hcos[2(φα+φβ)]iforthreedifferentinitialsettingsofAMPT hadronsandnegativelychargedhadrons,h|Ψ+2 −Ψ−2|i,forsixinitial
models in Cu+Au collisions at √s =200 GeV. Some points are settingsofAMPTmodelsinCu+Aucollisionsat √s =200GeV.
NN NN
slightlyshiftedalongthehorizonalaxisforclearerrepresentation.
peripheralCu+Au collisions, where the signal becomesvery
Let us first consider the following charge azimuthal correla-
clearinthemostperipheralcentralitybin.
tion:
As discussed above, the chiral electric separation effect
ζ = cos[2(φ +φ 2Ψ )] . (2) (CESE)combinedwiththechiralmagneticeffect(CME)can
αβ h α β− RP i lead to a quadrupolar charge distributions in Cu + Au col-
We will set Ψ = 0 in the following. For a CESE + CME lisions, see Fig. 3. Therefore, we propose another observ-
induced chargRePdistribution [see Fig. 3 for illustration], sup- able for CESE: ∆Ψ = h|Ψ+2 − Ψ−2|i, where Ψ+2 and Ψ−2 are
pose the positive charges fly out along the azimuthal angles thesecondharmonicanglesoftheeventplanesreconstructed
ψ andψ +πandthenegativechargesflyoutalong ψ and by final positively charged hadrons and negatively charged
c c c
ψ + π, where ψ is a deformation angle due to th−e CESE hadrons. If we follow the above assumption for the CESE,
c c
−efeffreecntt.frTomhusζζsame ∼1. hOcons(t4hψeco)ithsehrohualdndb,efoirnpguerneelyraldidpiof-- othfe∆nΨ∆Ψfo∼rs2ixhψdciif.feIrneFnitgi.n6itiwalessehtotiwngtsheofcethnetraAliMtyPdTepmenoddeenlcine
opp
larchargedistribu∼tion(duetothein-planeCSEorduetothe Cu+Aucollisions.Asweexpected,oncetheCESEhappens,it
CME),ζ = ζ cos(4ψ ) ,whereψ isthedipolaran- leadstoasizable∆Ψwhichshowsalineardependenceonthe
same opp d d
gle(ψ =0forin-pl∼anhedipoleaindψ = π/2forout-of-plane centrality. More importantly, for those initial settings which
d d
dipole). Therefore,∆ζ,thedifferencebetweenζ andζ , do not include the CESE, we do not observe a nonzero ∆Ψ
opp same
can be an observable for the CESE since the in-plane CSE forthewholecentralitywindow. Itshouldbementionedthat
or the CME does not contribute to it. In real experiments, our results are based on the fact that in each eventwe know
the dominant background of ζ may be the elliptic flow v whichsideistheAunucleusandwhichsideistheCunucleus
αβ 2
because, if we turn off all the anomalous effects, ζ v2. inthetransverseplane,i.e. thedirectionoftheelectricfield.
Another backgroundmay be the transverse momentαuβm∼con2- In realexperiments,itbecomesverycomplexto identifythe
servation[25]whichcausesacontributionζ v /Mwithv relativelocationsofAuandCuandonehastoreconstructthe
αβ 4 4
thefourthharmonicflowand M themultiplici∝ty. In∆ζ these firstharmoniceventplaneinordertodistinguishtheAuside
charge-blindv andv backgroundsaresubtracted. However, fromtheCu side,whichwillbehopefullyachievedbyusing
2 4
theremayremainotherbackgrounds,forexample,duetothe some event plane detectorssuch as zero degree calorimeters
local charge conservation [26] (which leads to ζ v /M (ZDCs)infutureexperiments.
opp 4
andζ 0andthus∆ζ v /M)orduetothechir∝almag-
same 4
∼ ∝
netic wave induced quadrupole. Because we do not encode
these effects into our AMPT model, the following result is IV. SUMMARY
supposed not to be related to the local charge conservation
andchiralmagneticwave. InFig.5wepresentthecentrality Insummary,wehaveintroducedvariousinitialchargesepa-
dependenceof∆ζ in Cu+ Aucollisionsfromthreedifferent rationeffects,includingthechiralmagneticeffect(CME),in-
initialsettingsintheAMPTmodel. Onecanseethatthenor- planechargeseparationeffect(in-planeCSE),andchiralelec-
malAMPTcaseandtheCMEcannotyieldavisiblesignalfor tricseparationeffect(CESE),intotheAMPTmodeltostudy
allcentralitybins,whiletheresultforCESE+CME+in-plane howthefinalstateinteractionsrendertheinitialchargesepa-
CESE case shows an increasing trend of ∆ζ from central to ration effects.To distinguish these initial effects, three possi-
6
ble observablesare tested in Cu+Au collisions at √s =200 ACKNOWLEDGMENTS
GeV.Thechargeazimuthalcorrelation cos(φ +φ N2NΨ )
α β RP
h − i
is sensitive to the CME and the in-plane CSE but not to the
CESE. The CME resultsin a positiveopposite-chargecorre-
lation and a negative same-charge correlation, while the in- DiscussionswithJ.LiaoandG.Wangareappreciated. G.-
plane CSE reverse their signs relative to those for the CME L.M.issupportedbytheMajorStateBasicResearchDevel-
case. However,theζ ζ isanobservablethatissensi- opmentProgramin China underGrantNo. 2014CB845404,
opp same
−
tivetotheCESEbutnotsensitivetoCMEandin-planeCSE the National Natural Science Foundation of China under
which makes it be a possible observablefor the detection of Grants No. 11375251, No. 11175232, and No. 11421505,
CESE. The difference between the second harmonic angles andtheKnowledgeInnovationProgramofChineseAcademy
ofeventplanesreconstructedbyfinalpositive-chargehadrons of Sciences under Grant No. KJCX2-EW-N01. X. -G. H.
or negative-chargehadrons, Ψ+ Ψ , is also sensitive to is supported by Shanghai Natural Science Foundation under
h| 2 − −2|i
theCESEandissizableinveryperipheralCu+Aucollisions. GrantNo. 14ZR1403000and Fudan UniversityunderGrant
We thus propose that future experimentscan take advantage No. EZH1512519. We also acknowledge the support from
ofCu+Aucollisionstomeasuretheseobservablesinorderto the Innovation Fund of Key Laboratory of Quark and Lep-
identify or distinguish different chiral and charge separation ton Physics (MOE), CCNU (Grant No. QLPL2011P01 and
mechanisms. QLPL20122).
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