Elastic parton scattering and non-statistical event-by-event mean-pt fluctuations in Au + Au collisions at RHIC

0.17 MB·English

by  Qing-Jun Liu

Elastic parton scattering and non-statistical event-by-event mean-p fluctuations in Au
t
+ Au collisions at RHIC
Qing-Jun Liu1,2 and Wei-Qin Zhao2,3
1Department of Mathematics and Physics, Beijing Institute of Petro-chemical Technology, Beijing 102617, P.R. China
2CCAST(World Lab.), P.O. Box 8730, Beijing 100080, P.R. China
3Institute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918(4), Beijing 100039, P.R. China
Non-statistical event-by-event mean-pt fluctuations in Au + Au collisions at √sNN = 130 and
200 GeV are analyzed in AMPT with string-melting, and the results are compared with STAR
data. Theanalysis suggests thatin-mediumelastic parton scatteringmay contributegreatly tothe
mean-pt fluctuations in relativistic heavy-ion collisions. Furthermore, it is demonstrated that non-
statistical event-by-event mean-pt fluctuations can be used to probe the initial partonic dynamics
in these collisions. The comparison shows that with an in-medium elastic parton scattering cross
8
0 section σp =10 mb, AMPT with string-melting can well reproduce √sNN =130 GeV data on the
0 centrality dependence of non-statistical event-by-event mean-pt fluctuations. The comparison also
2 shows that the fluctuation data for √sNN = 200 GeV Au + Au collisions can be well reproduced
with σp between 6 and 10 mb.
n
a PACSnumbers: 25. 75. -q,25. 75. Gz
J

4
1 I. INTRODUCTION energies[15]. The intention of this letter is to answer
these questions.
]
h
t In order to detect the production and to study
-
l the properties of Quark-Gluon-Plasma(QGP), non- II. THE AMPT MODEL AND ANALYSIS
c
statistical event-by-event mean-p fluctuations in rela- METHODS
u t
n tivistic heavy-ion collisions have been measured[1, 2,
[ 3, 4, 5, 6] at CERN SPS and BNL RHIC, and have The AMPT model is a hybrid model. It uses minijet

been extensively studied theoretically[7, 8, 9, 10, 11, partons from hard processes and strings from soft pro-
1
v 12, 13, 14, 15, 16, 17, 18, 19, 21]. While experimen- cesses in HIJING as the initial conditions for modeling
0 tal data show that a strongly interacting quark-gluon- heavy ion collisions at ultra-relativistic energies. Since
0 plasma(sQGP)hasbeenproducedinheavy-ioncollisions a phase transition of hadronic matter to quark-gluon
0 at RHIC [22, 23], a common consensus on the explana- plasma would occur [27, 28] in Au + Au collisions at
2 tionfor the dataonnon-statisticalevent-by-eventmean- RHIC, we study partoniceffects onevent-by-eventmean
.
1 pt fluctuations measured at RHIC has not been reached pt fluctuations using the AMPT model which allows the
0 yet[4, 5, 6, 15, 16, 17, 18, 19]. To be more specific, melting ofthe initialexcitedstringsintopartons[29]. In-
8 the observednon-statisticalevent-by-eventmean-pt fluc- teractionsamongthesepartonsaredescribedbytheZPC
0 tuations at RHIC currently can be explained in vari- partoncascademodel[30]. At present, the AMPT model
:
v ous physical scenarios: quenched jets/minijets produc- includes only parton-parton elastic scatterings with an
i tion[5, 15], alargedegreeofthermalization[16], percola- in-medium cross section given by:
X
tionofstrings[17],abuild-upofradialcollectiveflow[18]
r and formation of ”lumped clusters” [19, 20]. Though 9πα2
a σ s, (1)
jets/minijets contribute significantly to the event-by- p ≈ 2µ2
eventmean-p fluctuations[19]andjet-quenchingreduces
t
the fluctuations[5], as HIJING model[24] predicts[15], wherethestrongcouplingconstantα istakentobe0.47.
s
HIJING model significantly underestimates the STAR The effective screening mass µ is generated by medium
data[4, 6] on the event-by-event mean-p fluctuations. effects and given as an adjustable parameter thus it can
t
This may imply sources of the mean-p fluctuations be- beusedinstudyingeffectsofpartonscatteringcrosssec-
t
yond jets/minijets production. Taking into account the tions in heavy-ion collisions. The transition from the
fact that HIJING model includes neither partonic nor partonicmattertothe hadronicmatter isachievedusing
hadronic cascade processes, one may wonder if the HI- a simple coalescence model[26]. Following the formation
JING-based AMPT model[25, 26], which includes par- of hadrons, hadronic scatterings are then modeled by a
ton cascade together with hadronic cascade processes, relativistic transport (ART) model [31]. This version of
is able to reproduce the STAR data on non-statistical theAMPTmodelisabletoreproduceboththecentrality
event-by-event mean-p fluctuations. Additionally, how andtransversemomentum(below2 GeV/c)dependence
t
partonic and hadronic cascade processes contribute to ofthe elliptic flow[29]andpioninterferometry[32]mea-
thenon-statisticalevent-by-eventmean-p fluctuationsis sured in Au + Au collisions at RHIC [33, 34]. It has
t
an interesting question in heavy-ion collisions at RHIC been also applied for studying kaon interferometry[35],
2
charmflow[36],φmesonflow[37]andandthesystemsize evenquark-gluon-plasma;then the partonic medium un-
dependence of elliptic low[38]. dergoes hadronization to become hadrons; what follows
In this letter, ∆σ [4] and ∆p ∆p [6] are used isahadronicstagewhenthehadronsmaydecayorinter-
pt:n h t,i t,ji
in our analysis of event-by-event mean-p fluctuations. act with each other experiencing hadronic cascade until
t
According to Ref. [4, 6], they are defined as: freeze-out to produce final state particles. With AMPT,
the following three classes of AMPT events may be gen-
∆σ = ∆σp2t:n, (2) erated: class I–events with both partonic interactions
pt:n 2σ and hadronic cascade process, class II–events with par-
pˆt
tonic interactions but without hadronic cascade process,
class III–events with neither partonic interactions nor
ǫ
1 C hadroniccascadeprocess. Events ofclass III are primar-
k
∆p ∆p = , (3)
h t,i t,ji ǫ n (n 1) ily HIJING events with jet production but without jet
k k
kX=1 − quenching. Therefore, through analyzing non-statistical
event-by-event mean-p fluctuations in the aforemen-
where t
tionedthree classesofAMPT events,one canstudy how
∆σ2 = 1 ǫ n [ p pˆ]2 σ2 , (4) the non-statistical event-by-event mean-pt fluctuations
pt:n ǫ k h tik− t − pˆt are built up through aforementioned stages of particle
Xk=1 production processes. In another word, using AMPT,
one can learn to what extent jets/minijets, partonic in-
nk nk teractionsandhadroniccascadeprocesscontributetothe
Ck = (pt,i pt ) (pt,j pt ), (5) event-by-eventmean-pt fluctuations.
−hh ii −hh ii
i=1j=1,i6=j We havegeneratedeventsofthosethreeclassesforAu
X X
+ Au collisions at √sNN = 130 GeV with impact pa-
andǫ is the number ofevents,n is the number ofparti-
k rameter of 5 < b < 7 fm, and analyzed non-statistical
clesinthekthevent,pˆ andσ arethemeanandvariance
t pˆt event-by-event mean-pt fluctuations in each of the three
oftheinclusivetransversemomentumdistribution. p
h tik classes of events for charged hadrons. The results are
is the average transverse momentum for the kth event
tabulated in Table. I. From Table. I, one can see, first
defined as
of all, that in events of class III, there exist noticeable
nk non-statistical event-by-event mean-pt fluctuations due
p = p /n , (6) to production of jets/minijets[15]. It is noted that the
h tik t,i! k values of the a and b parameter for string fragmentation
i=1
X
used in AMPT[26] is different from those in the HIJING
where pt,i is the transverse momentum of the ith parti- model. Thisiswhyn¯foreventsofclassIIIisgreaterthan
cle in that event. pt denotes the mean of the pt that from HIJING without jet-quenching. Secondly, the
hh ii h i
distribution and is given by magnitudeof∆σ ineventsofclassIIismorethantwo
pt:n
times the magnitude of ∆σ in events of class III, and
ǫ pt:n
so is the magnitude of ∆p ∆p . This indicates that
hhptii= hptik!/ǫ. (7) h t,i t,ji
k=1
X
As pointed out in Ref. [4, 6, 20], both ∆σ and
ph∆t flput,ci∆tupatt,jioi,ntmogeeatshuerresw,situhchoathseFrpte[v5e]natn-bdyΦ-epvte[7np]tt,:namreeabny- T∆AσBptL:nE(MeVI:/c) ash∆wpetl,li∆aspt,tjhi(eMteoVta/lc)n2u,mbetorgeotfheevrentws(iǫt)h,
definitiondeterminedbytwo-particletransversemomen- the mean (pˆt) and variance (σpˆt) of inclusive transverse
tum correlations. When only statistical event-by-event momentum distributions, the mean (n¯) and variance (σn) of
multiplicity distributions, in-medium elastic parton scatter-
mean-p fluctuations exist, there are no two-particle
t ing cross section(σp) for four classes of mid-central AMPT
transverse momentum correlations, hence a null value
events(5<b <7fm)—Au + Au collisions at √sNN = 130
wouldbeobtainedfor ∆p ∆p and∆σ . Formore
h t,i t,ji pt:n GeV. Except for σp and ǫ, these quantities are calculated
detailsregardingthetwomeasures,interestedreadersare usingchargedhadronswith η <1and0.15<pt <2GeV/c.
referred to Ref. [4, 6, 11, 13]. Errors are statistical only. | |
event class I II III IV
σp(mb) 10 10 N/A 3
III. SOURCES OF NON-STATISTICAL ǫ 50,686 50,480 45,000 31,981
EVENT-BY-EVENT MEAN-pt FLUCTUATIONS n¯ 600 607 765 616
σn 90 90 122 90
Particleproductioninultra-relativisticheavy-ioncolli- pˆt(MeV/c) 479 477 458 457
sionsinvolvethefollowingstages: theinitialstage,where σpˆt(MeV/c) 285 276 263 275
jets/minijets are produced followed by partonic interac- ∆σpt:n 70.3±1.3 79.9±1.4 29.7±1.1 31.7±1.4
tions resulting in the formation of a partonic medium ∆pt,i∆pt,j 68.5 1.3 73.9 1.3 21.1 0.8 29.0 1.2
h i ± ± ± ±
3
103 100

c) 90
) V/ 80
2
) e
c M 70
/
eV ( 60
M 102 p:nt50
(
(
> s 40
pt,j D
30
D
pt,i 20
10
D<
0
0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350
N N
part part
FIG. 1: (Color online)h∆pt,i∆pt,ji in AMPT for σp = 10 FIG. 2: (Color online)∆σpt:n as a function of centrality for
mb(dashed line) , σp = 6 mb(dash-dotted line) and σp = 3 Au + Au collisions at √sNN = 130 GeV. The dashed line,
mb(solid line) as a function of centrality for √sNN = 130 dash-dottedlineandsolidlinewitherrorbarsdisplayAMPT
GeVAu+AucollisionscomparedwithSTARdata(hollowed results for σp = 10 mb,σp = 6 mb and σp = 3 mb. STAR
squares) as reported in Ref. [6]. data(hollowed squares) are as reported in Ref.[4], being ob-
tained via extrapolating to 100% trackingefficiency with the
error bars representing 12% uncertainties.
±
inaddition to the productionofjets/minijets ofpartons,
elastic parton scatterings add significantly to the non-
statistical event-by-event mean-p fluctuations. Hence in-medium parton scattering cross section incorporates
t
elastic parton scatterings may well be among others a properties of the medium and thus represents an impor-
major source of the non-statistical event-by-eventmean- tant aspect of partonic dynamics. To study the corre-
p fluctuations. Thirdly, comparing the magnitudes of lationbetween in-medium elastic partonscattering cross
t
∆σ and ∆p ∆p for event class-I with those for section and non-statistical event-by-event mean-p fluc-
pt:n h t,i t,ji t
class-II, one notices that due to hadronic cascade pro- tuations, in Table. I we have tabulated our results for
cesses,the non-statisticalevent-by-eventmean-p fluctu- AMPT events with in-medium elastic parton scattering
t
ationsbuiltupintheinitialstage,whichischaracterized cross sections σ = 10 mb, σ = 3 mb. Comparing the
p p
bytheproductionofjets/minijetsandpartonscatterings, magnitude of ∆σ as well as ∆p ∆p calculated us-
pt h t,i t,ji
decreaseabout12%and7%for∆σ and ∆p ∆p , ing σ =10 mb with that using σ =3 mb as tabulated
pt:n h t,i t,ji p p
respectively. This reduction of the mean-p fluctuations in Table. I, one may come to the conclusion that non-
t
isanindicationthatthelatestagehadroniccascadepro- statistical event-by-event mean-p fluctuations increase
t
cessesthatfollowtheelasticpartonscatteringsdilutethe significantly with the increase of σ . This clearly in-
p
correlations established in the initial stage. Therefore, dicates that the event-by-event mean-p fluctuations as
t
onemayconcludeaccordingtoTable. Ithatinheavy-ion measuredwith ∆σ or ∆p ∆p , are rather sensitive
pt h t,i t,ji
collisions at RHIC, non-statistical event-by-event mean- to the in-medium elastic parton scattering cross section,
p fluctuations aregeneratedinthe initial stage;inaddi- and therefore are promising probes of the partonic dy-
t
tionto the productionof jets/minijets ofpartons,elastic namics in the initial stage of ultra-relativistic heavy ion
parton scatterings also contribute a large portion of the collisions.
non-statistical event-by-eventmean-pt fluctuations. To estimate the in-medium elastic parton scattering
cross section σ and to test the AMPT model with
p
string melting, we studied the centrality dependence of
IV. NON-STATISTICAL EVENT-BY-EVENT non-statisticalevent-by-eventmean-p fluctuationsinAu
t
MEAN-pt FLUCTUATIONS AND σp + Au collisions at √sNN = 130 and 200 GeV based
on AMPT. The results are compared with STAR data
Taking place in the initial stage of ultra-relativistic as is shown in Fig. 1, Fig. 2 and Fig. 3. In getting
heavy-ion collisions, in-medium partonic interactions the AMPT results shown in Fig. 1, Fig. 2 and Fig. 3,
help drive the colliding system toward the formation chargedhadronswithtransversemomentum0.15 p
t
≤ ≤
of QGP. In addition, considering the possible modifica- 2.0 GeV/c and pseudo-rapidity η <1.0 are used, the
| |
tionofpartonicinteractionsinthe partonicmedium, the same cuts employed in obtaining the STAR data shown
4
in these figures[4, 6]. In calculating AMPT results for V. DISCUSSION
∆p ∆p shown in Fig. 1 and Fig. 3, the variation of
t,i t,j
h i
p withinagivencentralitybinistreatedinthe same
hh tii Jet/minijet partons may lose energy when passing
way as Ref. [6] adopted to get the STAR data: p is
hh tii throughpartonicmedium. Thispartonenergylosscalled
calculated as a function of N , the multiplicity used to
ch jet-quenching usually consists of two parts: collisional
define the centrality bin. Then this dependence is fitted
energy loss and radiational energy loss. The parton en-
and the fit is used in Eq. 5 on an event-by-event basis
ergy loss is modeled in the AMPT, as pointed out in
asa functionofN . StatisticalerrorsforAMPT results
ch Ref. [26], via elastic two-body parton scatterings. How-
are shown in Fig. 1 through Fig. 3.
ever in this treatment, the radiational energy loss is ig-
nored. Looking at the AMPT results listed in Table.
BothFig.1andFig.2demonstratethatwithanelastic
I, by comparing ∆p ∆p and ∆σ from events of
parton scattering cross section σp = 10 mb the AMPT classIIwithelasthicpta,ritont,sjciatteringtpot:nthoseofclassIII
model with string-melting can reproduce STAR data on
withoutelasticpartonscattering,wefindthattheelastic
thecentralitydependenceofthenon-statisticalevent-by-
two-body parton scattering, while adding to collisional
eventmean-p fluctuations. This conclusionis consistent
t parton energy loss, gives an additional event-by-event
withtheonedrawnthroughinterferometrystudyofAu+
mean-p fluctuations in mid-central collisions. In the
Aucollisionsatthesameenergy[32,35]. Fig. 1andFig.2 t
following a possible explanation is given for this result.
also reveal that for σ = 3 mb the AMPT model signif-
p First, based on the AMPT model, parton cascade pro-
icantly underestimates the data for non-peripheral colli-
cess due to elastic parton scattering is proposed to be a
sions. For the most peripheral collisions, Fig. 1 through
mechanism[39, 40] for producing a Mach-like cone struc-
Fig. 3 display good agreement between the data and
ture,whichhasrecentlybeenobservedinAu+Aucolli-
the AMPT model calculations with σ = 6 mb and 10
p sions at RHIC[41] and has been studied in several phys-
mb. That weak dependence on elastic parton scattering
ical scenarios[39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50].
cross section σ exists because in these peripheral colli-
p Secondly, the Mach-like cone structure consists of clus-
sionselasticpartonscatteringscontributetriviallytothe
tersoffinalstatechargedparticlesandeachofthecluster
mean-p fluctuations due to a very low partondensity in
t isconsistentwithconicemissionofparticlesfromjets,in
these collisions. From Fig. 3, one may infer that for Au
this sense it is jet-like and its formation represents an
+ Au collisions at √sNN = 200 GeV, the STAR data increase of the number of jet-like clusters. Thirdly, in
can also be well reproduced by the AMPT model and
a recent study based AMPT, the number of correlated
support an estimate of σ to be between 6 and 10 mb.
p final state charged particles within the clusters of the
Mach-like cone structure is reported to increase with σ
p
changingfrom3mbto10mb[40]. Furthermore,stronger
partoncascadedue to greaterσ alsoincreasesthe num-
103 p
berofcorrelatedhadronsonthenear-sideofanenergetic

) particle as one may infer according to Ref. [40]. To be
2
c) brief, an energetic parton through successive elastic col-
V/ lisions with surrounding medium may couple many par-
e tons together therefore more partons are correlatedwith
M
the increase of parton scattering cross section. Besides,
(
>( according to Ref. [19, 20], the event-by-event mean-pt
pt,j fluctuationswouldincreasewithboththenumberofclus-
ters and the number of charged particles in the clusters.
D pt,i102 cSliunscteeras laanrdgetrhσepnuinmcrbeearseosf cbhoatrhgetdhepnarutmicbleesrionftjheet-ljiekte-
likeclusters,itisnaturalthattheevent-by-eventmean-p
D< t
fluctuationsbecomesgreaterwithσ changingfrom3mb
p
to10mbasseeninTable. IandinFig.1throughFig.3.
Now we turn to the other energy loss mechanism, the
radiationalenergy loss. A study by PHENIX Collabora-
0 50 100 150 200 250 300 350
N tion atRHIC and a study basedonHIJING support the
part idea that partonenergyloss tends to decreasethe mean-
p fluctuationsatRHIC[5,15]. IntheHIJINGmodel,the
t
FIG.3: (Coloronline) ∆pt,i∆pt,j inAMPTforbothσp =10 jet-quenching mechanism includes only radiational par-
h i
mb(dashed line) and σp = 6 mb(solid line) as a function of ton energy loss. Therefore it seems that the radiational
centralityfor√sNN =200GeVAu+Aucollisionscompared parton energy loss causes the decrease of the mean-pt
with STARdata (hollowed squares) as reported in Ref. [6]. fluctuations. Nevertheless, it would be worthwhile to in-
vestigateandcomparethetwomechanismsoftheparton
energyloss,namely,thecollisionalenergylossandthera-
5
diational energy loss, and their implementation in both mb, predictions of the AMPT model are in good agree-
AMPT and HIJING more thoroughly before making fi- ment with the √sNN = 130 data on the centrality de-
nal conclusions about the effect of parton energy loss on pendence of non-statistical event-by-event mean-p fluc-
t
themean-p fluctuationsinheavy-ioncollisionsatRHIC. tuations. The comparison also shows that to reproduce
t
the mean-pt fluctuation data at √sNN =200 GeV, σp is
approximately between 6 and 10 mb.
VI. SUMMARY
Based on AMPT model with string-melting an analy-
Acknowledgments
sis of non-statisticalevent-by-eventmean-p fluctuations
t
in Au + Au collisions at √sNN = 130 and 200 GeV is
presented. The analysis suggests that in-medium elas- We acknowledge Professor C.M. Ko, Z.W. Lin, B.
tic parton scatterings can contribute significantly to the Zhang,B.A. Li for using their AMPT code. We appreci-
mean-p fluctuationsandthemean-p fluctuationscanbe atehelpfuldiscussionswithProfessorsC.M.KoandT.A.
t t
usedasgoodprobestostudythe initialpartonicdynam- Trainor. ThisworkispartlysupportedbyNationalNatu-
ics in these collisions. The AMPT results are compared ralScienceFoundationofChina(Wei-QinZhao);SRFfor
with STAR data. This comparison shows that using an ROCS, SEM; Beijing Institute of Petro-chemical Tech-
in-mediumelasticpartonscatteringcrosssectionσ =10 nology and Supercomputing Center, CNIC, CAS.
p
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