Effect of final state interactions on particle production in $d$+Au collisions at RHIC

0.15 MB·English

by  Xiaoping Zhang

Effect of final state interactions on particle production in d+Au collisions at RHIC
XiaopingZhanga,b,,JinhuiChenc,ZhongzhouRena,N.Xub,ZhangbuXud,QiangZhenga,e,XiangleiZhuf
∗
aDepartmentofPhysics,NanjingUniversity,Nanjing210008,China
bNuclearScienceDivision,LawrenceBerkeleyNationalLaboratory,Berkeley,CA94720,USA
cShanghaiInstituteofAppliedPhysics,CAS,Shanghai,201800,China
dBrookhavenNationalLaboratory,Upton,NewYork,11973,USA
eSchoolofMathematicsandComputerScience,GuizhouNormalUniversity,Guiyang,550001,China
fDepartmentofEngineeringPhysics,TsinghuaUniversity,Beijing100084,China
Abstract
0
1We show that particle species dependence of enhanced hadron production at intermediate transverse momentum (p ) for d+Au
T
0
collisions at RHIC can be understood in terms of the hadronic rescatterings in the final state. A multiphase transport model
2
(AMPT) with two different hadronizationmechanisms: string fragmentation or parton coalescence, is used in our study. When

nthe hadronsare formedfrom string fragmentation, the subsequenthadronicrescatteringswill result in particle mass dependence
a
of nuclearmodificationfactor R , whichis consistentwith the presentexperimentaldata. On the otherhand, in the framework
J CP
of parton coalescence, the mass dependencedisappearsand the strangenessplays an importantrole. Both mechanismsfailed to
6
2reproducethe pT dependenceofRCP ofpion,indicatingthatinitial-stateeffectsmightbealsoimportantinsuchcollisions.

Keywords: Nuclearmodificationfactor,hadronizationmechanisms,hadronicrescatterings
]
h
t
-
l1. Introduction alternate way for hadronization is string fragmentation [13–
c
u 15]. In this scenario, hadrons are formed from the decays of
TheCronineffect,whichreferstotheenhancedhadronpro-
n excited strings, which result from the recombination of ener-
[duction at intermediate transverse momentum (pT) with in- getic minijet partons and soft strings that produced from ini-

creasing targetnucleussize in proton-nucleus(pA) collisions,
1 tialsoftnucleon-nucleoninteractions. Afterthehadronization,
was first observed by Cronin et al. [1, 2] in 1975 at center
v thefollowedrescatteringsbetweenformedhadronsorbetween
4of mass energy √sNN = 27.4 GeV. Recent experimental data formed hadrons and nucleon spectators should also be taken
3in d+Au collisions from RHIC have shown that similar ef-
intoaccount.
7fect exists at higher collision energy (√s = 200 GeV) [3, 4].
4AnadequateunderstandingoftheCronineffectbecomesespe-
.
1cially importantfor makingreliable theoreticalinterpretations
0of the observationsin heavy ion collisions at RHIC, in which In this paper we study quantitatively how the two different
0the quark-gluon plasma (QGP) is thought to be created [5]. hadronizationmechanisms(stringfragmentationandpartonco-
1
Traditional explanations of the Cronin effect all involve mul- alescence)andthefollowedfinalstateinteractionswouldcon-
:
vtiple scattering of incoming partons that lead to an enhance- tributetothenuclearmodificationfactorsind+Aucollisionsat
Ximent at intermediate pT [6–11]. The models can reproduce √s=200GeV.Amultiphasetransportmodel(AMPT)[14,15]
the observedcentralitydependenceforpionsverywell. How- with two versions: default (hadronization from Lund string
r
aever,noneoftheseinitial-statemodelswouldpredictaspecies- fragmentation,mainlyhadronicrescatteringsin thefinalstate,
dependent Cronin effect, as initial state parton scattering pre- version1.11)andstringmelting(hadronizationfromquarkco-
cedesfragmentationintothedifferenthadronicspecies[4].This alescence, version 2.11) are used to study the later-stage ef-
indicatespossiblefinal-state interactions(FSI) wouldpossibly fect. The final state hadronic and/or partonic interactions are
contributetotheCronineffect. includedinthecalculations. Quarktransversemomentumkick
Recently, Hwa and Yang [12] demonstrated the recombi- duetomultiplescatteringsaretreatedinthesamewayasinRef.
nation of soft and shower partons in the final state could ex- [13]. Tohaveacleantestoffinalstateinteractions,weassume
plain the mass dependent Cronin effect. This model do pre- noquarkintrinsic pT broadeningduetoinitialmultipleparton
dict a larger enhancement for protons than for pions at 1 < scattering [8], and see how the final state interactions would
p < 4 GeV/c. However, the inclusion of recombination contributeto the Cronineffect observed. We show thatrecent
T
fromdeconfinedpartonsrequiresa highenergydensityinini- dataonparticlespeciesdependenceofcentral-to-peripheralnu-
tial state, which may not be justified in d+Au collisions. An clear modification factor RCP at midrapidity for d+Au colli-
sionsatRHICcanbeunderstoodintermsofthehadronization
fromstringfragmentationandthefollowedhadronicrescatter-
Correspondingauthor
∗
Emailaddress: [email protected](XiaopingZhang) ingsinthefinalstate.
PreprintsubmittedtoPhysicsLettersB January26,2010
2. TheAMPTmodel
10 10
−2 (a) d+Au 200 GeV (b)
TheAMPTmodel[14,15]isahybridmodelthatconsistsof c) 1
V/ 10−1 default −1
four main components: the initial conditions, the partonic in- e string melting
G −2
teractions,conversionfromthepartonictothehadronicmatter, y ( 10−3 −3
andthehadronicinteractions. Theinitialconditions,whichin- d −4
T
clude the spatial and momentum distributions of hard minijet dp 10−5 −5
partons and soft string excitations, are obtained from the HI- N/ −6
JINGmodel(version1.383forthisstudy). OneusesaWoods- 2)dpT10−7 π+ −−87 STAR data
Saxonradialshapeforthecollidinggoldnucleiandintroducesa π K+ (/3) π−
parameterizednuclearshadowingfunctionthatdependsonthe 1/(2 10−9 pφ ((//33000)) −−190 Kp −( /(3/30))
impactparameterofthecollision. Theratioofquarkstructure 10−11 −11
0 2 4 6 8 0 2 4 6 8
function is parameterized as the following impact-parameter-
Transverse momentum p (GeV/c)
dependentbutQ2(andflavor)-independentform[14] T
fA(x,Q2,r) Figure 1: Transverse momentum spectra of mid-rapidity (y < 0.5) pions,
RA(x,r)≡ AafN(x,Q2) kaons,protonsandφmesonsin“minimumbias”d+Aucollis|io|nsfromdefault
a AMPT(solidlines)andstringmeltingAMPT(dashedlines)versusdatafrom
=1+1.19ln1/6A(x3 1.2x2+0.21x) STARCollaboration(statisticalerroronly)[3,19].
−
1.08(A1/3 1)√x
−[αA(r)− ln(A+−1) ]e−x2/0.01, (1)
parametersarechosentobethesameasinRef. [15]. Thepar-
where x is the light-conemomentumfractionof partona, and tonicscatteringcrosssectionischosentobe3mb. Theevents
f is the parton distribution function. The impact-parameter areseparatedintodifferentcentralitybinsusingthenumberof
a
dependenceofthenuclearshowingeffectiscontrolledby participantnucleonssufferinginelasticcollisions. Fig. 1shows
themid-rapidity(y <0.5)transversemomentumspectraofpi-
| |
α (r)=0.133(A1/3 1) 1 r2/R2, (2) ons, kaons, protons and φ mesons for “minimum bias” d+Au
A − q − 0
collisions from default AMPT (solid line) and string melting
withrdenotingthetransversedistanceofaninteractingnucleon (dashed line). It is seen that both default and string melting
from the center of the nucleuswith radiusR0 = 1.2A1/3. The AMPT can reproducethe π± and K± spectra well. For proton
structureofdeuteronisdescribedbytheHulthenwavefunction. and antiproton production, the default version works well for
Scatteringsamongpartonsare modeledbythe Zhang’sparton p > 1 GeV/c, but underestimatesthe low p proton and an-
T T
cascade (ZPC) [16], which at present includes only two-body tiprotonyields. The stringmelting versionunderestimatesthe
elasticscatteringswithcrosssectionsobtainedfromthepQCD proton and antiproton production in the whole p range. For
T
withscreeningmasses. InthedefaultAMPTmodel,afterpar- φmesonspectrum,thedefaultversionworkswellinthewhole
tonsstopinteracting,theyrecombinewith theirparentstrings, p range,whilethestringmeltingoneoverestimatesthelowp
T T
which are producedfrom initial soft nucleon-nucleoninterac- φmesonyieldsinthe“minimumbias”d+Aucollisions.
tions. Theresultingstringsareconvertedtohadronsusingthe
Lund string fragmentation model. In case of string melting,
tihnestepardodtuocethdehiradvraolennscferoqmuasrtkrisnagnfdraagnmtieqnutaartkiosn.,Tarheecfoonlvloewrteedd Rcp11..68 (a) deπfa−ult (φNo FSI) dN/dy0.3 (b)default (No FSI) KK+−
pfraeretzoeniocuitn,ttehreayctiaornesreacroemmboindeedleidntboyhZadPrCo.nsAtfhterorutghheapaqrutoanrks 1.4 pK− ΛΞ+ 00..21 ΛΛ
coalescenceprocess. Thedynamicsofthesubsequenthadronic
1.2 0.0
matterisdescribedbyahadroniccascade,whichisbasedona −6 −4 −2 0 2 4 6
Rapidity
relativistic transportmodel(ART). Finalhadronicobservables 1.0 dy (c)before coalescence
including contributions from the strong decays of resonances N/6 u
0.8 d u
aredeterminedwhenthehadronicmatterfreezesout. s×3
4 s×3
0.6 0−20%
40−100% 2
3. Results
0.40 1 2 3 4 5 6 0−6 −4 −2 0 2 4 6
p (GeV/c) Rapidity
We learn that Lin and Ko have done a nice study [15] T
on global properties of deuteron-gold collisions with default
+
AMPT model, whichshows goodagreementwith later exper- Figure2: (Coloronline)(a)RCP forπ−,K−, p¯,φ,ΛandΞ ind+Au √sNN
imental data [17, 18]. Their study on nuclear effects is up to =200GeVcollisions fromdefaultAMPTwithoutfinalstateinteractions in-
cluded. (b)KaonandΛrapiditydistributionin“minimumbias”d+Aucolli-
p =2GeV/c. Herewefocusontheintermediatetohigher p
T T sionsfromdefaultAMPTwithoutfinalstateinteractionsincluded.(c)quark(u,
range where the Cronin effect exists. We study the deuteron- u¯,s,ands¯)rapiditydistributionbeforecoalescencein“minimumbias”d+Au
goldcollisionsat √s = 200GeV.The stringfragmentation collisionsfromstringmeltingAMPT.
NN
2
Tostudythefinalstateeffectonthenuclearmodificationfac- andresonancedecays. Forπ and K ,theR decreasesafter
− − CP
torR ,wefirstcalculatetheR (0-20%/40-100%centrality) includingthefinalstate interactionsfromintermediateto high
CP CP
of different hadrons without including the final state hadronic p . Andthissuppressionincreaseswith p . Sincemostofthe
T T
interactions and resonance decays in the default AMPT. The producedparticlesarepionsatmid-rapidity,thescatteringsare
R , which compares particle yield from central collisions to mainlytheparticle-pioninteractionsfor p m , wherem is
CP 0 0
≫
that of peripheral collisions, is defined as the ratio of particle themassofcorrespondingparticles.Forπ πelasticcollisions,
−
yieldsincentralcollisionsoverthoseinperipheralonesscaled the resonance peak centers at the position of π π center-of-
−
bynumberofinelasticbinarycollisionsNbin,thatis, mass energy √sππ close to ρ meson rest mass. Since most of
the outgoing particles which probably scatter with each other
[dN/(N p dp )]
bin T T central
R = . (3) areinthesimilardirections,theopenanglebetweentwoscat-
CP [dN/(N p dp )]
bin T T peripheral teringparticlesissmall. In ourstudied p andrapidityrange,
T
HereweusethesameNbin valueasSTARCollaborationatthe foroneparticleatlow pT,andanotherparticlewithhigheren-
correspondingcollisioncentrality[3]. OnecanseeinFig. 2(a) ergy,thecalculated √sππ isclosertotheresonancepeak. Asa
that there are only slight differences for the RCP of different result,thishadroniceffectonRCPisenhancedwith pT forpion.
particle species. This is because hadrons are produced from SimilarargumentisalsovalidforK πscatterings. Forheavier
−
string fragmentation in the Lund model, and the fragmenta- particleslikeantiproton,φmeson,Λ, theRCP increasesatlow
tion patterns for different particle species in central collisions pT accordingtotheircorrespondingproductionchannelsordue
and in peripheral collisions are set to be the same. We note to diffusionsinto mid-rapidityregion,butchangesslightly for
+
that the R ofprotonand Λ would be largerdueto the asso- p > 3 GeV/c. For even heavier particle, like Ξ , there is no
CP T
ciateproductionN+N N+Λ+K+ frominitial-statemultiple obviouschangeofR duetothefinalstateinteractions. Here
→ CP
scatterings in the gold beam direction (y < 0) at large rapid- particle mass plays important roles in the hadronic rescatter-
ity, as shown in Fig. 2(b) the enhanced production of Λ and ings. Itwilldeterminethespace-timeconfigurationofformed
K+ in “minimum bias” d+Au collisions. Some of the parti- hadrons[20].
cles are scattered into mid-rapidityregion. The strange quark
enhancementinthelargerapidityregion(goldbeamdirection)
willcausethecorrespondingincreaseofs¯quarkatotherrapid-
ity regionsduetonetstrangenessconservation. Thisisshown
iinnF“img.in2im(cu):mthbeiaqsu”ardk+rAapuidciotyllidsiisotnrisbuftrioomnbtehfeorsetrcinogalemsceeltnincge Rcp11..68 (a) deπf−aulΛt Rcp11..68 (b) string melting
K− Ξ+
AMPT.
1.4 p Ω+ 1.4
φ
1.2 1.2
Factor R (cid:9)cp11..46 (a )ππ−− wwA/.o MF FSPSITI (default) 11..46(b KK)−− ww/.o F FSSII 11..46(c )pp ww/.o F FSSII 0.81 0.81
on 1.2 1.2 1.2 0−20%
cati1.0 1.0 1.0 0.6 40−100% 0.6
difi0.8 0.8 0.8 0 1 2 3 4 5 0 1 2 3 4 5
ar Mo0.6 400−−2100%0% 0.6 0.6 pT (GeV/c) pT (GeV/c)
o−Peripheral Nucle1111....4602 (d )φφ ww/.o F FSSII 1111....4026(e )ΛΛ ww/.o F FSSII 1111....4602(f) ΞΞ++ ww/.o F FSSII Rcp111...4682(c) Exp. data (STAR) π−)()/Rp(Rcpcp111...468(d) SdsdteeTrffAiaanRuugll ttm (Neloti nFgSI)
al−t0.8 0.8 0.8 1.2 1.2
entr0.6 0.6 0.6 1
C 1
0.8
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 π−
Transverse momentum p (GeV/c) 0.6 0.8
T p
0.4
Figure3: Mid-rapidityRCP (y < 0.5)ind+Au √sNN =200GeVcollisions 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8
from default AMPT with (red| |circles) and without (black circles) final state p (GeV/c) p (GeV/c)
T T
interactions.
After including the final-state hadronic interactions and Figure 4: (Color online) Mid-rapidity (y < 0.5) RCP in d+Au √sNN =
| |
strong decays of resonances, the R of different particle 200 GeV collisions: (a) default AMPT with final state interactions; (b)
CP
string melting AMPT with final state interactions; (c) experimental data of
species will change differently, as they have different masses
RCP from STARCollaboration (statistical error only) [3]. (d) The ratios of
and scattering cross sections. We show in Fig. 3 the com- RCP(p¯)/RCP(π−)fromSTARCollaboration, fromdefaultAMPT,fromstring
parisons of R with and without the final state rescatterings meltingAMPT,andfromdefaultAMPTwithoutfinalstateinteractions.
CP
3
Accordingto aboveanalysis, thefinalstatehadronicrescat- Issues associated with the initial condition such as gluon
teringswillleadtoparticlemassdependenceofR . InFig. 4, saturation [22–24], parton intrinsic p broadening [6–11]
CP T
wecomparethedatawithmodelcalculations. Atintermediate and so on were not addressed in this paper. The future more
p , the R of heavier particles like antiproton, φ meson, Λ, completeanalysisshouldincludetheseeffects. Incomparison,
T CP
Ξ+ willbelargerthanthoseofπ andK . Theresultisquali- if the hadron is formed from quark coalescence, it is difficult
− −
tativelyconsistentwithexperimentaldata[3],asshowninFig. to explain antiproton transverse momentum spectra and the
4(c).AtintermediatepT,theRCPofantiprotonissystematically particle species dependence of RCP. On the other hand, the
larger than that of π . In Fig. 4(d), the ratio R (p¯)/R (π ) strangenesseffectplaysanimportantrole. Moreprecisiondata
− CP CP −
from the default AMPT model also agrees very well with ex- inthefuturewilltestthefindingsinthispaper.
perimental data. We note that the present calculation without
including the possible quark intrinsic p broadening at initial Acknowledgements
T
state can not reproduce the p dependence of R . This dif-
T CP WearegratefultoX.Dong,C.Jena,H.Masui,B.Mohanty,
ference between data and model results may indicate that the
Z.Lin,L.Ruan,andZ.B.Tangforvaluablediscussions. This
initial state effect is important. The year 2008 data of RHIC
work is supported by the U.S. Department of Energy under
with higher statistics will providemore precise measurements
ContractNo. DE-AC03-76SF00098,theNationalNaturalSci-
andtestourpredictionsforotherhadronspecieslikeφmeson,
ence Foundation of China (Grant Nos. 10535010, 10775123,
+
Λ,Ξ ,etc.
10865004,10905029,and10905085),bythe973NationalMa-
For comparisons, the R from string melting AMPT with
CP jorStateBasicResearchandDevelopmentofChina(GrantNo.
quark coalescence is also studied. We have shown in Fig.
G2000077400),bytheCASKnowledgeInnovationProjectNo.
2(c) that the excess of s¯ quark over s quark at mid-rapidity
KJCX2-SW-N02,andbytheResearchFundofHighEducation
is partly due to associate production from initial multiple in-
undercontractNo. 20010284036.
teractions. Combiningthis effectwith the coalescenceof par-
tons, there are enhancements of corresponding hadrons at in-
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T CP
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d+Au collisions at RHIC can be understood in terms of this
final-statehadronicrescatterings.Thisshowstheimportanceof
finalstatehadronicinteractionsind+Aucollisions,sincenone
of the initial-state models would predict a species-dependent
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CP
the p dependence of R with only final state interactions,
T CP
this indicates the initial state effects might be also important.
4