Medium-modified Jets and Initial State Fluctuations as Sources of Charge Correlations Measured at RHIC

2.3 MB·English

by  Hannah Petersen

Medium-modified Jets and Initial State Fluctuations as Sources of Charge
Correlations Measured at RHIC
Hannah Petersen,1 Thorsten Renk,2,3 and Steffen A. Bass1
1Department of Physics, Duke University, Durham, North Carolina 27708-0305, United States
2Department of Physics, P.O. Box 35 FI-40014 University of Jyva¨skyla¨, Finland
3Helsinki Institute of Physics, P.O. Box 64 FI-00014, University of Helsinki, Finland
Weinvestigatethecontributionofmedium-modifiedjetsandinitialstatefluctuationstotheasym-
metry in charged particle production with respect to thereaction plane. This asymmetry has been
suggested as a compelling signature of the Chiral Magnetic Effect in QCD and make a study of
”conventional” scenarios for thecreation of such charged particle multiplicity fluctuations a timely
endeavor. The different pathlength combinations of jets through the medium in non-central heavy
ioncollisionsresultinfinitecorrelationsoflikeanddifferentchargedparticlesemittedinthedifferent
1
hemispheres. OurcalculationisbasedoncombiningjeteventsfromYaJEM(YetanotherJetEnergy
1
LossModel) andabulkmedium evolution. Itisfound thatthejet productionprobabilities are too
0
smalltoobservethiseffect. Theinfluenceofinitial statefluctuationson thisobservableis explored
2
usinganevent-by-event(3+1)dhybridapproachthatisbasedonUrQMD(Ultra-relativisticQuan-

n tum Molecular Dynamics) with an ideal hydrodynamic evolution. In this calculation momentum
a conservationandellipticflowareexplicitlytakenintoaccount. Theasymmetriesintheinitialstate
J
aretranslated toafinalstatemomentumasymmetrybythehydrodynamicflowprofile. Dependent

1 on the size of the initial state fluctuations the resulting charged particle asymmetries are in qual-
3 itative agreement with the preliminary STAR results. The multi-particle correlation as proposed
by the PHENIX collaboration can in principle be used to disentangle the different contributions,
]
however is in practice substantially affected by the procedure to subtract trivial resonance decay
h
t contributions.
-
l
c PACSnumbers: 25.75.-q,24.10.Lx,24.10.Nz,25.75.Gz
u
n
[ I. INTRODUCTION may convert topological charge fluctuations in the QCD

vacuum into global electric charge fluctuations with re-
2
spect to the reaction plane. While the magnitude of the
v Ultra-relativistic heavy-ion collisions at the Relativis-
6 charge fluctuations which can be attributed to the CME
tic Heavy-Ion Collider (RHIC) are thought to have cre-
4 is still a matter of ongoing debate [9, 10], the STAR col-
atedahightemperatureandpressurestateofQCDmat-
8 laborationhasrecentlyreportedthatchargefluctuations
3 ter termed the Quark-Gluon-Plasma (QGP) [1–5]: Two with respectto the reactionplane have indeedbeen seen
8. major discoveries stand out: (1) the emission of hadrons [11].
with a transverse momentum p of several GeV/c or
0 T In order to confirm the discovery of the CME in rel-
moreisstronglysuppressed(jet-quenching),implyingthe
0 ativistic heavy-ion collisions, one first needs to verify
1 presence of matter with a very large color opacity, and that experimental measurements cannot be understood
: (2) the anisotropic (“elliptic”) flow in non-central colli-
v in terms of ”conventional”, well-established, phenomena
sions is near the ideal hydrodynamic limit, requiring an
i observedat RHIC. It has recently been pointed out that
X early onset of the period during which the expansion is
correlationsfromchargeandmomentum conservationat
r governedbyfluiddynamics(earlierthan1fm/cafterthe freeze-out overlaid with elliptic flow may very well be
a
initialimpact)aswellasnearlyidealfluidpropertieswith
able to describethe observedphenomena [12,13]. Inad-
a viscosity-to-entropy density ratio η/s 1. The mat-
≪ dition,theexperimentalobservablesuggestedtomeasure
ter created at RHIC has been thus called the strongly
the CME has been arguedto be predominantly sensitive
interactingQuark-GluonPlasma(sQGP)[6]andquanti-
to other effects [14, 15].
fying its properties in terms of its transport coefficients
In this paper we focus on estimating various conven-
isoneofthemajortasksofthecurrentexperimentaland
tional physics mechanisms that lead to charge parti-
theoretical researchprogram.
cle number asymmetry within a realistic model, namely
OneshouldnotethatQCDmattercreatedinrelativis- medium-modifiedjetsaswellasinitialstatefluctuations,
ticheavy-ioncollisionsmaypossessaveryrichsetoffea- combined with well-known bulk physics such as momen-
tures, reflecting the fundamental symmetries (and viola- tum conservation, resonance decays and elliptic flow. In
tionsthereof)ofQCD,wellbeyondtheabovenotedchar- Section II the different observables that have been pro-
acteristicsoflargeopacityandnear-idealfluidity. Among posed are introduced. These observables are surely sen-
the more intriguing features which are currently being sitive to fluctuations ofmultiplicity (and charge)if these
searched for is the presence of the Chiral Magnetic Ef- fluctuationsarecorrelatedwiththe reactionplane. Both
fect(CME)[7–10]: aswaspointedoutin[7],non-central ofthetwoszenariosthatwearestudyinghere,in-medium
heavy-ioncollisionscreateacoherentmagneticfieldthat jets (in Section III) and initial state granularity (in Sec-
2
tion IV) give a particular mechanism to generate multi-
plicity fluctuations correlated in a peculiar way with the
rtheaectoibosnerpvleadnec.haOrgnelyd opnacrteicallel flpuocstsuibalteiocnosntwriibthutrioenspsetcot A+UD/− = ((NNU++−+NND++))((NNU−−−+NND−−)) (4)
to the reaction plane are accounted for, can we quantify U D U D
the possible contribution of the CME to the measure-
ments. and correspondingly for the LR-direction where N+
and N− are the numbers of positively and negatively
charged particles in one event.
II. DEFINITION OF OBSERVABLES The opposite chargecorrelation(A+/− andA+/−)are
UD LR
positive, if the particles tend to be aligned and negative
The standard observable used to look for the CME is forachargeseparationscenario. Withoutanycorrelation
the angular correlation coefficient thisobservablewouldbeconsistentwithzero. The(A+)2
and (A−)2 are a measure of the overall charged particle
fluctuation. The preliminary STAR results seem to be
cos(φ +φ ) positive (on the order of 1 10−3) in the out-of-plane as
γ = i∈α,j∈β i j (1) ·
α,β P M M wellasthein-planedirectionformid-centralAu+Aucol-
α β
lisionsat√sNN =200AGeV.Themaindifferenceofthis
whereαandβ representpositiveandnegativecharges, observable compared to the original angular correlation
φ measures the angle with respect to the reaction plane measurement [11, 18] is that each particle contributes
orientationandM arethemeasuredmultiplicities. Asar- with the same weight independent of its position in the
guedin[12,13,15], this observableis (contrarytoinitial respective hemisphere.
expectations) dominated by a strong in-plane like-sign
correlation which has no obvious relation with charge
separation as proposed as signal of the CME.
B. Multi-Particle Correlation
Inthepresentstudyweconsidertwoothernewlydevel-
oped observables to quantify the correlations of charged
particleswiththereactionplaneforwhichacomputation The PHENIX collaboration has recently proposed a
using a detailed framework is feasible with a reasonable different observable that is sensitive to a charge separa-
amountofCPUtime. Inaddition,theseobservablesseem tion with respect to the reaction plane as it is predicted
to have a clearer relation to out-of-plane charge separa- from the chiral magnetic effect [17]. This multi-particle
tion. correlation coefficient relies on an event-by-event mea-
surement technique and is defined as follows
A. Charge Asymmetry Observable dN/d(∆S )
ch
C = (5)
p
dN/d(∆S )
all
The first observable we focus on for measuring the
event-by-eventcharged particle asymmetry has been de- where
veloped by the Purdue group within the STAR collab-
oration [16]. The measurement is based on counting
P M
1 1
charged particles that are emitted into different hemi- ∆S = sin(φ+) sin(φ−) . (6)
spheres with respect to the reaction plane. The differ- P Xi=1 i − M Xi=1 i
ent hemispheres are defined as follows: ’Up=U’ means
p > 0, ’Down=D’ refers to p < 0, ’Left=L’ stands for
y y Here,thefirstsumrunsoverallpositivelychargedpar-
p < 0 and ’Right=R’ for p > 0. The UD-direction re-
x x ticlesinoneeventwhereasM isthenumberofnegatively
flectstheout-of-planedirectionwhereastheLR-direction
chargedparticlesinoneeventandφ isthe azimuthalan-
represents the in-plane direction.
gle in the transverse plane in momentum space. ∆S is
The charged particle asymmetry coefficients are de- all
theanalogousquantitywheretheithparticleisrandomly
fined in the following way
chosenfromtheevent. Thisobservableisamulti-particle
correlationthat has to be measuredevent by event. The
(N+ N+)2 ratioofthechargesensitivedistributiontotheoneforall
(A+ )2 = U − D (2) chargedparticlesisflatat1,if thereis nochargespecific
UD (N++N+)2
U D correlation (e.g. elliptic flow). A concave shape indi-
cates charge separation out of plane (e.g. the presence
ofthe CME)and a convex shape arises,if positively and
(A− )2 = (NU−−ND−)2 (3) negativelychargedparticlesarepreferablyemittedinthe
UD (N−+N−)2 same direction (e.g. resonance decays).
U D
3
III. MEDIUM-MODIFIED JETS Notethatjetsleadtoanasymmetryinchargedhadron
productioneventbyeventevenwithoutamediummodi-
A. Overview fication,simplybecausethefragmentationofahardpar-
tontoahadronjetisaprobabilisticprocess,andalsobe-
cause jets in hadronic collisions may be due to a pQCD
The idea of jets as a mechanism to generate asymme-
subprocess like qg qg in which the fragmentation of
tries in the charged multiplicity distribution is based on →
the gluon in the out state is much softer from the frag-
thenotionthatin-mediumenergylossfromaleadingpar-
mentation of the quark. However, in the presence of a
tonisdominatedbyinducedgluonradiation[19,20],giv-
medium, the medium-induced radiation is expected to
ing rise to additional multiplicity production. Moreover,
dominate multiplicity production, and the vacuum case
this mechanism is predominantly active out of plane:
While radiativeenergylossasymptoticallyhasanL2 de- has no mechanism to account for a correlation with the
reaction plane. In the following, we use the in-medium
pendence in a constant medium, the actual scaling of
shower evolution code YaJEM (Yet another Jet Energy-
lost energy and produced multiplicity in a real situation
lossModel)intheRAD(radiativeenergyloss)scenarioto
is complicated and has no simple functional shape for
estimate the jet-induced event by event charged hadron
a number of reasons, among them the spacetime evolu-
multiplicity asymmetry.
tion of the bulk medium which reduces the density as a
functionofspaceandtimeandthere-interactionofradi-
atedgluons withthe medium, leadingto a cascadeofin-
B. Model Description
ducedradiationtillfiniteenergycorrectionsbecomeman-
ifest [21]. However, the multiplicity of medium-induced
hadron production is a monotonously rising function of YaJEMisaMonteCarlocodetosimulatethemedium-
both pathlength and medium density. modified evolution of a parton shower. It is based on
the PYSHOW algorithm [22, 23] for shower evolution in
vacuum,to whichitreducesinthe absenceofamedium.
A detailed description of the model is given in [24, 25],
here we just summarize the essential physics underlying
the model.
In YaJEM, the evolution from the initial parton to a
finalstatepartonshowerismodelledasaseriesofbranch-
ingprocessesa b+cwhereaiscalledtheparentparton
→
and b and c are referred to as daughters. In QCD, the
allowed branching processes are q qg, g gg and
→ →
g qq. The kinematics of a branching is described in
ter→msofthevirtualityscaleQ2andoftheenergyfraction
z, where the energy of daughter b is given by E = zE
b a
andofthedaughtercbyE =(1 z)E . Itisconvenient
c a
to introduce t = lnQ2/Λ w−here Λ is the scale
QCD QCD
parameterofQCD. ttakesa rolesimilarto atime inthe
evolution equations, as it describes the evolution from
some high initial virtuality Q (t ) to a lower virtuality
0 0
Q (t ) at which the next branching occurs. In terms
m m
FIG.1: Sketchofthehadronmultiplicityasymmetryinduced
of the two variables, the differential probability dP for
a
by medium-modified showers: for a shower evolving in the
a parton a to branch is
medium, induced gluon radiation leads to larger multiplicity
production. α
s
dPa = Pa→bc(z)dtdz (7)
2π
The basic idea how medium modified jets may gen- Xb,c
erate an asymmetry in the charged hadron multiplicity
correlated out of the reaction plane is shown in Fig. 1. where the splitting kernels Pa→bc(z) read
Letusstartwitharandominitialhardvertexpositionin 1+z2
the transverse plane: if the vertex position is such that Pq→qg(z)=4/3 (8)
1 z
one jet is close to the surface and escapes unmodified −
(1 z(1 z))2
whereastheotherjetpropagatesalongdistancethrough Pg→gg(z)=3 − − (9)
the medium, the averagemultiplicity ofchargedhadrons z(1 z)
−
for both jets is expected to be very different. Further- Pg→qq(z)=NF/2(z2+(1 z)2). (10)
more, this effect can be estimated to be stronger in the −
up-downdirectionthanintheleft-rightdirection,simply We do not consider electromagnetic branchings. N
F
because the maximum variation in pathlength is larger counts the number of active quark flavoursfor givenvir-
for out of plane emission than for in-plane emission. tuality. The resulting systemofequations describing the
4
branching processes in vacuum is solved numerically us-
ing MC techniques utilizing the Pyshow code [22, 23].
Inordertomakethelinkfrommomentumspacewhere 0.1
the showerevolution takes place to position space where (A+UD)2 (A+LR)2
the medium perturbations evolve, we assume that the 00..0089 (AA+-/U-UDD)2 (AA+-/L-LRR)2
averageformationtimeofashowerpartonwithvirtuality
n
o
Q is developed on the timescale 1/Q, i.e. the average ati 0.07
lifetime of a virtual parton with virtuality Qb coming orrel 0.06
from a parent parton with virtuality Q is in the rest C
a e 0.05
frame of the original hard collision (the local rest frame g
of the medium may be different by a flow boost as the har 0.04
C
medium may not be static) given by 0.03
0.02
E E
b b
hτbi= Q2 − Q2. (11) 0.010 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50
b a E[GeV] E[GeV]
We assume that the actual formation time can then be
obtained from a probability distribution
FIG.2: (Color online) Contribution of medium-modifiedjets
τ to the charged particle asymmetry coefficients in the out-of-
b
P(τb)=exp (12) plane (left) and in-plane (right) direction for three different
(cid:20)− τ (cid:21)
h bi initial parton energies (10,20 and 40 GeV) for Au+Au colli-
whichwe sample to determine the actualformationtime sionsat√sNN =200AGeV.Opensymbolsdepictcentralcol-
lisions(b=2.4fm)whilefilledsymbolsrepresentmid-central
of the fluctuation in each branching.
collisions (b=7.5 fm.
ThemediummodificationintheRADscenarioappears
as a change of parton virtuality ∆Q2 dependent on a
a
medium parameter qˆwhere
and compute the asymmetry coefficients (A+)2,(A−)2
and A+−. The results are shown in Fig. 2.
τa0+τa
∆Q2 = dζqˆ(ζ). (13) The result indicates that jets are in principle capable
a Zτa0 of creating substantial charge correlations. In this sce-
nario the charge correlation arises because of an asym-
Here, the time τa is given by Eq. (12), the time τa0 metry in the particle production. The correlationshown
is known in the simulation as the endpoint of the pre- inFig. 2showsthatinadevelopingshowerthebalancing
vious branching process and the integration dζ is along chargesarepreferablyemittedinthesamehemisphere,so
the eikonal trajectory of the shower-initiating parton. If positivelyandnegativleychargedparticlestend to align.
the parton is a gluon, the virtuality transfer from the However, somewhat surprisingly, no pronounced differ-
medium is increased by the ratio of their Casimir color ence between up-down and left-right is visible. This can
factors, 3/4 = 2.25. qˆ is a function of medium energy be traced back to a number of reasons. First, Eq. (13)
3
density ǫ with the relation chosen such that the single evaluated in an expanding medium leads to small modi-
pion suppression observed in 200 AGeV central Au-Au fications at late times, i.e. for long paths, as qˆbecomes
collisions at RHIC is described [25]. very small when the energy density of the system is low.
Asaresultofthemedium-inducedchangeinvirtuality, Thismeansthatinanexpandingmedium,partonsdonot
additional gluon radiationoccurs which after hadroniza- actuallyprobethefulllengthdifferencebetweenin-plane
tion leads to an increased multiplicity in the shower. and out-of-plane emission, but rather probe pathlength
differenceduring the time periodwhenmodificationsare
significant only, i.e. the first 3-5 fm/c. Given this
C. Results ’filter’, the differences between i∼n-plane and out-of-plane
emissionareconsiderablysmallerthanestimatednaively
Inordertoestimatetheeventbyeventchargedhadron based on geometry. Furthermore, especially for low p
T
asymmetry,weembedback-to-backjetpairsofthreedif- hadron production, the angular distribution of hadrons
ferent energies (10, 20 and 40 GeV per jet) into a 3+1 around the jet axis is wide [25, 27]. Note that this can
d hydrodynamical simulation [26] on a random position happen even if the jet shape itself is rather narrow, as
sampled from the binary collision profile. The jet pair the jet shape traces the flow of momentum andnot mul-
then gets a random orientation with respect to the re- tiplicity. The fact that there can be significant multi-
action plane. We then propagate both jets through the plicity created also in the down hemisphere even from
medium and evaluate Eq.(13) to determine the medium a shower initiating parton travelling into the up hemi-
modification. After hadronizing the jets, we count the sphere further weakens the difference between in-plane
charged hadron content in the four different quadrants and out-of-plane emission.
5
So far, we have investigated the charge correlationco-
efficients created by a single jet only. This is not a very
realistic situation: First, high momentum jets of e.g. 40
GeV are very rare events, so even if they create sizeable 1.4
Jets+UrQMD,b=5-9fm,allpT
asymmetriesinchargedmultiplicity,sucheventsmaynot Jets+UrQMD,b=5-9fm,pT<1.0GeV
have much weight in an average over many events. Sec- 1.3
ond, for low momentum jets, one cannot assume that
1.2
onlyasinglejetpereventcontributes. However,itisim-
mediately clearthatembedding multiple jets inanevent
Sall1.1
weakens the asymmetry significantly. When we account
d
for these effects by mixing jets with the probability of N/
a jet with given energy being in the event determined S/dch1.0
fromaLOpQCDcalculationintoaUrQMDbackground d
N/ 0.9
[28, 29], the picture changes considerably: In Fig. 3 the d
contributionofjetsappearsasaninsignificantcorrection
0.8
to the background result.
0.7
0.6
-0.08 -0.06 -0.04 -0.02 0.0 0.02 0.04 0.06 0.08
0.005 S
(A+ud)2,UrQMD (A+lr)2,UrQMD
(A-ud)2 (A-lr)2
0.004 A+/-ud A+/-lr
+Jets +Jets
n
o FIG.4: (Coloronline)Calculationofthemulti-particlecorre-
elati 0.003 lation coefficient inmid-centralAu+Aucollisions at √sNN=
orr 200A GeV. The full squares depict the results from the full
C
e 0.002 calculation including medium-modified jets to the hadronic
g
ar transportapproach(UrQMD)backgroundevent,whereasthe
Ch 0.001 fullcirclesshowtheresultonlyforparticleswithpT <1GeV.
0.0
alone leads to the same shape as the combined events.
0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 But again, the probability for jet production is very low
b[fm] b[fm]
andthereforetheresultsresembleverymuchtheUrQMD
results that are shown in Fig. 9. Furthermore, the influ-
enceofap <1GeVcuthasbeenexplored,sincethepre-
FIG. 3: (Color online) Calculation of the charged parti- T
liminary measurements have been made in a limited p
cle asymmetry coefficients in the out-of-plane (left) and in- T
plane(right)directionfortwodifferentcentralitiesforAu+Au range and the chiral magnetic effect is mostly expected
collisions at √sNN = 200A GeV. The open circles depict in the bulk low transverse momentum region. The low
the results from the hadronic transport approach (UrQMD) p result and the result for all charged particles are the
T
that serves as a background for thefull calculation including samewithinerrorbarsandespeciallythe shapedoesnot
medium-modified jets that is represented by full squares. change. Since the distribution of the charge sensitive
averaged sine differences has a higher peak around zero
In hindsight, this could have been anticipated: While and lower flanks than the distribution that is not charge
truly hard jets are too rare to influence the result, low specific this result indicates that particles with opposite
p jets (below 5 GeV) tend to be createdfrequently, but chargesarepreferablyemittedinthesamedirectionthan
T
the presence of multiple jets in an event tends to cancel in different directions. The underlying physics mecha-
their effect. Clearly, a bulk mechanism creating charge nisminboth casesis correlatedparticle productionfrom
asymmetries is more efficient than a rare probe. ’clusters’ - in one case jets, in the other decaying reso-
Note alsothatitis apparentfromFig. 3thatUrQMD nances.
background results show that a pure hadronic transport
approachisnotcapableoftranslatinginitialstatefluctu-
IV. INITIAL STATE FLUCTUATIONS
ations to the final state distributions effectively enough
toleadtoasignificantsignalastheA+/− coefficientsare
on the order of 1 10−6. A. Overview
·
In Fig. 4 the calculation of the multi-particle correla-
tion coefficient is shown. Medium-modified jets, embed- In the second part of this article the charged parti-
ded in a UrQMD background lead to a convex shape of cleasymmetrythatarisesfromwell-knownbulk medium
the ratio of the distributions in ∆S. The result for jets effects isinvestigated. The basicideais thatenergyden-
6
sinityhecalvuystieorns rperaocdtuiocnesdmbiyghttheleaindittioalabsyinmamryetsrcyatctoerrrienlgas- mwhaelirseatNion,=ǫ (2a1πn)d32σEG3γazussaErecfthperoevniedregsytdheenspirtoypaenrdnotor--
cf cf
tions in the particle production in different hemispheres. tal energy of the particle in the computational frame,
Duetothedevelopmentofradialflowduringthemedium while (x ,y ,z ) is the position vector of the particle.
p p p
evolutiontheinitialcoordinatespacegranularityistrans- Summing over all single particle distribution functions
lated to a resulting momentum space anisotropy. These leadstodistributionsofenergy-,momentum-andbaryon
clustersareexpectedtoenhancethemultiplicityinaspe- number-densities in each cell.
cifichemispherewhichresultsinalignmentofthecharged Thetransitionfromthehydrodynamicevolutiontothe
particleproductioninsteadofseparation. Inthispicture, transport approach when the matter is diluted in the
resonancedecaysmightexplicitlyintroduceachargecor- late stage is treated as a gradual transition on an ap-
relationoftheoutgoingparticles,ife.g. aρmesondecays proximated iso-eigentime hyper-surface (see [37, 38] for
into π+ +π− and there is enough collective flow, both details). Thefinalrescatteringsandresonancedecaysare
of the pions will preferably be have a momentum in a taken into account in the hadronic cascade.
similar direction. To investigate the effect of different initial state gran-
S. Pratt recently estimated the effects of elliptic flow, ularities the width of the Gaussian distribution (14) is
momentum and charge conservation on the observable varied from σ =0.8 2.0 fm. Please note that this
Gauss
charged particle correlation measurement [13]. Our ap- is still an event-by-events−etup and in this respectdiffer-
proach follows a similar spirit but the effect of initial entfromavergingovermanyfluctuatinginitialconditions
state fluctuations is emphasized in addition. This kind as has been done in [39]. In a hydrodynamic calculation
of event-by-event fluctuations has been found to be cru- starting from smooth initial profiles the correlation ob-
cial also for other two-particle correlationmeasurements servablewouldbe zero,sincetherearenoevent-by-event
(the ’ridge’) at the highest RHIC energies [30]. fluctuations included.
B. Model Description
8 90
The charged particle asymmetry that is generated
6 80
by clusters in the initial energy density distribution is
quantified by using a hybrid approach based on the 4 70
UrQMDhadronictransportapproachincluding a(3+1)- 60
2
dimensional one fluid ideal hydrodynamic evolution [31,
50
3ea2r]lfyornothne-ehqoutiliabnrdiudmenssteagsetaagnedoftthheefirneaalctdioencowuhpilliengthies y [fm] 0 40
-2
treated in the hadronic cascade [33, 34] [40]. 30
The event-by-event-setup that is naturally employed -4
20
in this approachis crucial for the observationof charged
particle asymmetries. For Au+Au collisions at the high- -6 10
estRHIC energythe startingtime forthe hydrodynamic -8 0
evolution has been chosen to be t = 0.3 1.8 fm -8 -6 -4 -2 0 2 4 6 8
start
− x [fm]
depending on the amount of fluctuations to fit the final
pion multiplicity at midrapidity, since this is crucial for
the present study and allows us to investigate the effect
oftheinitialstategranularityonthechargecorrelations. FIG. 5: (Color online) Energy density distribution in the
Howthechangeinthestartingtimeaffectsotherbulkob- transverse plane for a central (b=0 fm) Au+Au collision at
servables like spectra and elliptic flow will be discussed √sNN=200A GeV with σGauss =0.8 fm and tstart =0.3 fm.
in a further publication [35]. Only the matter around
midrapidity(y <2)isconsideredtobe locallythermal- Fig. 5-7 show the initial energy density distribution
| |
izedandtakespartinthe idealhydrodynamicevolution. as it is obtained from UrQMD for three different val-
The more dilute spectator/corona regions are treated in ues of the Gaussian width σ = 0.8, 1.0 and 2.0 fm.
Gauss
the hadronic cascade approach. To map the point parti- A smaller width leads to entropy production during the
cles from the UrQMDinitial state to energy,momentum ideal hydrodynamic evolution indicating that the solu-
and net baryon density distributions three-dimensional tion of the differential equation is not stable anymore.
Gaussiandistributionsareusedthatrepresentoneparti- Therefore,thehighestfluctuationsaregeneratedwiththe
cle each [36]. smallest width of 0.8 fm, while for larger widths the ini-
tialfluctuationsaremoreandmoresmearedout. Smaller
ǫcf(x,y,z)=Nexp−(x−xp)2+(y2−σy2p)2+(γz(z−zp))2 , ccholaorracfltuexritsutibcespiziecstucroeuwldhebreespthruycsticuarlelsyinmtohteivtartaendsvbeyrsae
Gauss
(14) plane on the order of 0.3 fm would be expected. Our
7
parameter choices stay in a regime where the implemen- on event-by-event particle production in different hemi-
tation is technically stable and the characteristic sizes spheres. Initial state clusters and a coordinate space
correspond to typical sizes of a proton. -momentum space correlation due to radial flow leads
to observable differences in the charged particle pro-
duction in different parts of the system (see Fig. 8).
b=0 fm; |y|<2.0; t =0.5 fm; σ=1.0 fm The UD and LR chargedparticle asymmetry coefficients
start
have been calculated for four different initial granulari-
8 45 ties in the hybrid approach. The open symbols depict
6 40 the results for central (b < 3.4 fm) Au+Au collisions
35 at √sNN = 200A GeV and the filled symbols represent
4 mid-central(b=5 9fm)Au+Aucollisions. Theoverall
2 30 fluctuationsofchar−gedparticlesarelargerinnon-central
y [fm] 0 2205 cmoulllitsiipolnicsittyhaisnsminaclleenr.traTlhceoollpispioonsistebcehcaaurgsee athsyemomveertarlyl
-2 is positive and similar in the out-of-plane and the in-
15
plane direction. This confirms the expectations that in
-4
10 this scenario the particles tend to align independent of
-6 5 their charge. Within our limited statistics, the absolute
value of the difference between UD and LR can be con-
-8-8 -6 -4 -2 0 2 4 6 8 0 strained to be smaller than 1 10−3.
·
x [fm]
FIG. 6: (Color online) Energy density distribution in the 5
transverse plane for a central (b=0 fm) Au+Au collision at 2 ((AA+-uudd))22 ((AA+-lrlr))22
√sNN =200A GeV with σGauss =1.0 fm and tstart =0.5 fm. 10-2 A+/-ud A+/-lr
n
o
ati 5
el
orr 2
C
e10-3
g
8 8 har 5
C
6 7 2
4 6 10-4
5
2 5 0.0 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
[fm] [fm]
Gauss Gauss
y [fm] 0 4
-2 3
FIG. 8: (Color online) Calculation of the charged particle
asymmetrycoefficients in theout-of-plane(left) andin-plane
-4 2
(right) direction for four different values of σGauss. The open
-6 1 symbolsdepicttheresultsforcentral(b<3.4fm)Au+Aucol-
lisionsat√sNN =200AGeVandthefilledsymbolsrepresent
-8 0
mid-central(b=5 9 fm) Au+Aucollisions.
-8 -6 -4 -2 0 2 4 6 8 −
x [fm]
Higher granularity in the initial state leads to higher
opposite charge asymmetry coefficients that are on the
FIG. 7: (Color online) Energy density distribution in the order of the preliminary STAR data [16]. This physics
transverse plane for a central (b=0 fm) Au+Au collision at mechanism will contribute to the background of a po-
√sNN =200A GeV with σGauss =2.0 fm and tstart =1.8 fm. tential measurement of the chiral magnetic effect and
needs to be taken into account, before trying to look for
a potentially much smaller signal. On the other hand,
the comparison of hybrid calculation with different ini-
C. Results tial state granularities to event-by-event correlation and
fluctuation measurements might be helpful to constrain
The hybrid approach provides the opportunity to the structure of the initial state of relativistic heavy ion
study the influence of initial state fluctuations that can reactions.
be varied in size without adjusting any other parameter Fig. 9 shows the result for the multi-particle correla-
8
to isolate the effect of initial state fluctuations by sub-
tractingtheUrQMDdistributionsin∆S fromthehybrid
model distributions. It turns out that the procedure is
1.4 very sensitive to the subtraction - we were able to ob-
UrQMD,b=5-9fm,pT<1.0GeV
UrQMD,allpT serve even qualitative differences in shape which could
1.3 Hybrid,b=5-9fm,allpT potentially mock up the CME signal.
Hybrid,b=5-9fm,pT<1.0GeV
V. SUMMARY AND CONCLUSIONS
1.2
Sall1.1 We have investigated charge asymmetry and multi-
d particlecorrelationswiththe reactionplanegeneratedin
N/
S/dch1.0 rtrealantsipviosrtticahpeparvoya-cihonccoonltliasiinoinnsgaatRfuHllICmweditiuhminaevroealulitsitoinc
d
N/ 0.9 and medium-modified jets. While jets are in principle
d
capable of generating the aforementioned multi-particle
0.8 correlations, we were able to rule them out as a signifi-
cant contributor to such correlations due to the low jet
0.7 production rate. However,we find that initial state fluc-
tuations can generate values for the charge asymmetry
0.6-0.08 -0.06 -0.04 -0.02 0.0 0.02 0.04 0.06 0.08 coefficients on the same order of magnitude as seen by
S experiment. Our results were obtained within a hybrid
transportapproach,basedonanevent-by-eventhydrody-
namic evolution, with fluctuating initial conditions and
microscopic hadronic afterburner for the realistic treat-
FIG.9: (Coloronline)Calculationofthemulti-particlecorre-
ment of hadronic final state effects, including resonance
lation coefficient inmid-centralAu+Aucollisions at√sNN =
decays. The precision of our calculation was not suf-
200A GeV. The open symbols depict the results from the
ficient to quantify the difference between in-plane and
hadronic transport approach (UrQMD) (circles indicate an
additional pT <1 GeV cut) and the filled symbols represent out-of-plane, due to the very large computational effort
calculations within the hybridapproach. involved. However, the coefficients themselves show no
sign of charge separation. The multi-particle correlation
measurementproposedbythePHENIXcollaborationap-
tioncoefficientthathasbeendefinedinSectionIIBfrom pears to be potentially the most suitable of the studied
theUrQMDhadronictransportapproach(opensymbols) observables for differentiating a CME from other mech-
and the hybrid approach (filled symbols). It has been anisms. However, due to the need of subtracting known
checkedthattheresultsforthisobservabledonotdepend background effects like resonance decays, it is currently
on the choice of σ . The low transverse momentum unclear whether the predicted concave shape as a signal
Gauss
region shows the same behaviour as without p cut. If for the CME can be robustly established.
T
one reduces the number of particles by acceptance (or
other) cuts, the distribution broadens, however does not
change qualitatively in shape. Again the correlationsin-
VI. ACKNOWLEDGEMENTS
duced by these approaches lead to a convex shape and
can be attributed to resonance decays whereas a charge
separationscenarioasexpectedfromthechiralmagnetic WearegratefultotheOpenScienceGridandtheCen-
effect leads to a concave shape in this observable. The ter for the Scientific Computing (CSC) at Frankfurt for
initial state fluctuations have to be considered as a non- the computing resources. The authors thank Fuqiang
trivialsource of correlationsofthe particles emitted in a Wang, Roy Lacey and Berndt Mu¨ller for helpful discus-
heavy ion reaction. sions and Dirk Rischke for providing the 1 fluid hydro-
It is likely that any measurement of the observable is dynamics code. H.P. acknowledges a Feodor Lynen fel-
dominated by resonance decay effects which are known lowshipoftheAlexandervonHumboldtfoundation. This
to be present in nature. In order to observe a different workwassupportedinpartbyU.S.departmentofEnergy
mechanism(liketheCME)atwork,this distributionhas grantDE-FG02-05ER41367andbyproject133005ofthe
to be subtracted. In order to get an idea of the sen- Academy of Finland. T.R. is supported by an Academy
sitivity of the results to the subtraction, we have tried Research Fellowship of the Academy of Finland.
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