Centrality-dependent forward $J/\psi$ production in high energy proton-nucleus collisions

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by  B. Ducloué

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Centrality-dependent forward J/ψ production in high energy
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proton-nucleus collisions
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J
5 B.Ducloué1,2,T.Lappi1,2,andH.Mäntysaari3
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1DepartmentofPhysics,UniversityofJyväskylä,P.O.Box35,40014UniversityofJyväskylä,Finland

2HelsinkiInstituteofPhysics,P.O.Box64,00014UniversityofHelsinki,Finland
]
h 3PhysicsDepartment,BrookhavenNationalLaboratory,Upton,NY11973,USA
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Abstract.ForwardJ/ψproductionandsuppressioninhighenergyproton-nucleuscolli-
e
sionscanbeanimportantprobeofgluonsaturation. Inanearlierworkwestudiedthis
h
process in the Color Glass Condensate framework and showed that using the Glauber
[
approachtoextrapolatethedipolecrosssectionofaprotontoanucleusleadstoresults

1 closer to experimental data than previous calculations in this framework. Here we in-
v vestigatethecentralitydependenceofthenuclearsuppressioninthismodelandshowa
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comparisonofourresultswithrecentLHCdata.
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1 Introduction
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The study of the nuclear suppression of forward J/ψ production in high energy proton-nucleus col-
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lisions can be a valuable tool to better understand saturation dynamics. Indeed, it probes the target
1
: nucleusatveryhighdensities,wheresaturationeffectsshouldbeenhanced,andthecharmquarkmass
v
is small enough to be sensitive to these dynamics while being large enough to provide a hard scale
i
X allowingaperturbativetreatment. J/ψmesonsalsohavecleanexperimentalsignaturesandtheirpro-
r duction and suppression have been the subject of many experimental studies. In a recent work [1]
a
were-evaluatedthenuclearsuppressionofforward J/ψproductionathighenergyintheColorGlass
Condensate(CGC)framework,showingthatusingtheopticalGlaubermodeltorelatethedipolecross
sectionofanucleustotheoneofaprotonleadstoasmallersuppressionforminimumbiaseventsthan
inpreviousworksinthesameformalism[2]andresultsclosertoexperimentaldata1. Inthisworkwe
discusstherelationbetweentheexplicitimpactparameterdependenceoftheopticalGlaubermodel
andcentralityandwecompareourresultswithrecentdataonthecentralitydependenceof J/ψsup-
pressionattheLHCpresentedbytheALICECollaboration[4].
2 Formalism
Theformalismforgluonandquarkpairproductioninthedilute-denselimitoftheColorGlassCon-
densatehasbeenstudiedinRefs.[5,6](seealsoRef.[7])andappliedinseveralworks,suchas[2,8–
11].Thisallowstocomputethecrosssectionforcc¯pairproduction,whichisthecentralobjectneeded
1Theauthorsof[2]haverecentlypresentedupdatedresults[3]similartothoseobtainedin[1].
EPJWebofConferences
tostudy J/ψproduction. TheexpressionforthiscrosssectioncanbefoundinRef.[2]. Weusethe
simplecolorevaporationmodeltodescribethehadronizationoftheproducedcc¯pairsinJ/ψmesons.
Inthismodel,afixedfractionofthecc¯pairsproducedwithaninvariantmassbetween2m and2M ,
c D
where m is the charm quark mass and m is the D-meson mass, is assumed to hadronize into J/ψ
c D
mesons. Thus the cross section for J/ψ production with transverse momentum P and rapidity Y
⊥
reads
dσJ/ψ = F (cid:90) 4MD2 dM2 dσcc¯ , (1)
d2P dY J/ψ d2P dYdM2
⊥ 4m2c ⊥
where d2P⊥dσdYcc¯dM2 isthecrosssectionfortheproductionofacc¯ pairwithtransversemomentum P⊥,
rapidityY andinvariantmass M. InthisexpressionF isanon-perturbativeconstantwhichcanbe
J/ψ
extractedfromdata. Inthefollowingwewillfocusonratiosofcrosssectionsforwhichthevalueof
thisparameterplaysnorole.
In forward J/ψ production, the projectile proton is probed at relatively large x which justifies
the use of the collinear approximation on this side. The gluon density in the projectile can thus be
describedusingacollinearpartondistributionfunction. HerewewillusetheMSTW2008[12]LO
parametrization for this purpose. On the other hand, when working at forward rapidity, the target,
whichcanbeeitheraprotonoranucleus,isprobedatverysmall x. Theinformationaboutitsgluon
densityiscontainedinthefunction
1 (cid:68) (cid:69)
S (x −y )= TrU†(x )U(y ) , (2)
Y ⊥ ⊥ N ⊥ ⊥
c
where U(x ) is a fundamental representation Wilson line in the target color field. The evolution of
⊥
S (r )isgovernedbytherunningcouplingBalitsky-Kovchegov(rcBK)equation[13–15], whichis
⊥
Y
solvednumerically.WeuseasaninitialconditiontheMVeparametrization[16]whichinvolves,asthe
AAMQS[17]one,parameterswhichareextractedfromDISmeasurements. IntheMVeparametriza-
tiontheinitialconditionforaprotontargetreads
Sp (r )=exp(cid:20)− r⊥2Q2s0 ln(cid:32) 1 +e ·e(cid:33)(cid:21), (3)
Y=ln 1 ⊥ 4 |r |Λ c
x0 ⊥ QCD
withx =0.01. Theexpressionfortherunningcouplingis
0
12π
αs(r)= (cid:18) (cid:19). (4)
(33−2N )log 4C2
f r2Λ2
QCD
Inthiscasethereisnoexplicitdependenceontheimpactparameterandtheintegrationover b can
⊥
besimplyreplacedby
(cid:90)
σ
d2b → 0 , (5)
⊥
2
where σ0 corresponds to the effective proton transverse area measured in DIS experiments. The
2
valuesoftheparametersintheseexpressionsobtainedinRef.[16]byafittoHERADISdata[18]are
Q2 = 0.060GeV2,C2 = 7.2, e = 18.9and σ0 = 16.36mb. Togeneralizethedipolecrosssection
s0 c 2
from a proton to a nucleus we use, as in Ref. [16], the optical Glauber model. In this approach the
initialconditiontothercBKequationreads
SA (r ,b )=exp(cid:34)−AT (b )σ0 r⊥2Q2s0 ln(cid:32) 1 +e ·e(cid:33)(cid:35), (6)
Y=ln 1 ⊥ ⊥ A ⊥ 2 4 |r |Λ c
x0 ⊥ QCD
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wheretheonlyadditionalquantityinvolvedcomparedtotheprotoncase(3)isthestandardWoods-
SaxondistributionT (b ),whereb istheimpactparameter:
A ⊥ ⊥
(cid:90)
n
TA(b⊥)= dz (cid:34)√ (cid:35) , (7)
1+exp b⊥2+z2−RA
d
withd =0.54fm,R =(1.12A1/3−0.86A−1/3)fmandnisanormalizationconstantdefinedsuchthat
(cid:82) A
d2b T (b ) = 1. Besides T , all the parameters take the same value as in the proton case. The
⊥ A ⊥ A
rcBK equation is then solved independently for each value of b . In principle this explicit impact
⊥
parameter dependence can be related to the centrality classes used by experiments in the following
way:intheopticalGlaubermodelaclass(c −c )%wouldbedefinedbylimitingtheintegrationover
1 2
b betweenb andb definedsuchthat
⊥ 1 2
1 (cid:90) b2
(c −c )%= d2b p(b ). (8)
1 2 σpinAel b1 ⊥ ⊥
HereσpA isthetotalinelasticproton-nucleuscrosssection,givenby
inel
(cid:90)
σpA = d2b p(b ), (9)
inel ⊥ ⊥
withthescatteringprobabilityatimpactparameterb being
⊥
p(b⊥)≈1−e−ATA(b⊥)σinel, (10)
whereσ isthetotalinelasticnucleon-nucleoncrosssection. Theparticleyieldinagivencentrality
inel
classisthengivenby
dN = (cid:82)bb12d2b⊥dd2NP(⊥bd⊥Y) , (11)
d2P⊥dY (cid:82)b2d2b p(b )
b1 ⊥ ⊥
wherethevaluesofb andb aredefinedasinEq.(8).However,ifweusethisprocedureandcompare
1 2
thevaluesoftheaveragenumberofbinarynucleon-nucleoncollisions,giveninthismodelby
(cid:82)b2d2b N (b )
(cid:104)N (cid:105) = b1 ⊥ collopt. ⊥ , (12)
coll opt. (cid:82)b2d2b p(b )
b1 ⊥ ⊥
where
N (b )= AT (b )σ , (13)
collopt. ⊥ A ⊥ inel
with the values of (cid:104)N (cid:105) estimated by ALICE [4] in each centrality class, we find a disagreement
coll
betweenthetwoascanbeseenfromTable1. Inthefollowing, forafirstcomparison, wedecideto
performourcalculationineachcentralityclassatafixedimpactparameter b definedsuchthatthe
⊥
numberofbinarycollisionsintheopticalGlaubermodelcorrespondstoitsaveragevalueestimated
by ALICE, i.e. N (b ) = (cid:104)N (cid:105) . A more consistent comparison would require the use
collopt. ⊥ coll ALICE
of distributions in impact parameter space but for this one would need to have access to the N
coll
distributionsatexperimentsandnotonlyto(cid:104)N (cid:105).
coll
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Centralityclass (cid:104)N (cid:105) (cid:104)N (cid:105)
coll opt. coll ALICE
2–10% 14.7 11.7±1.2±0.9
10–20% 13.6 11.0±0.4±0.9
20–40% 11.4 9.6±0.2±0.8
40–60% 7.7 7.1±0.3±0.6
60–80% 3.7 4.3±0.3±0.3
80–100% 1.5 2.1±0.1±0.2
Table1.AveragenumberofbinarycollisionsineachcentralityclassasobtainedintheopticalGlaubermodel
comparedwiththevalueestimatedbyALICE[4].
3 Results
TheALICEcollaborationrecentlymeasuredthenuclearsuppressionofJ/ψproductioninproton-lead
√
collisionsindifferentcentralityclassesat s =5TeV[4]. Tocompareourresultswiththesedata
NN
weuse,asexplainedpreviously,afixedimpactparameterdefinedsuchthatN (b )=(cid:104)N (cid:105)
coll.opt ⊥ coll ALICE
ineachcentralityclassconsideredbyALICE.Thisprocedurewouldleadforthe80–100%classtoan
impactparameterforwhichthesaturationscaleofthenucleuswouldfallbelowtheoneoftheproton.
Forthisreasonwewillnotconsiderthisclassinthefollowing. InFig.1weshowthecomparisonof
ourresultsandALICEdataforthenuclearmodificationfactorQ ,definedas
pPb
dNpPb
Q = d2P⊥dY , (14)
pPb A(cid:104)T (cid:105) dσpp
A d2P⊥dY
asafunctionofP inthefivemostcentralclassesconsideredbyALICE.Weincludeintheuncertainty
⊥
band the variation of m between 1.2 and 1.5 GeV and of the factorization scale between M /2
(cid:113)c ⊥
and 2M with M = M2+P2 where M is the cc¯ pair’s invariant mass. The description of the
⊥ ⊥ ⊥
data is quite good in the first three bins but our calculation predicts values of Q which approach
pPb
unity too quickly when N decreases. This too strong dependence on centrality in our calculation
coll
can also be seen in Fig. 2, where we show the nuclear modification factor integrated over P as
⊥
wellasthetransversemomentumbroadening,definedasthedifferenceof(cid:104)P2(cid:105)inproton-leadandin
⊥
proton-protoncollisions,asafunctionN . However,oneshouldkeepinmindthatthevalueofN
coll coll
indicatedforALICEdataisanaveragewhileinourcalculationitisafixedvalue.Takingintoaccount
thefluctuationsinourcalculationcouldhaveasignificantimpact.
4 Conclusions
In this work we have studied the centrality dependence of forward J/ψ nuclear suppression in the
ColorGlassCondensate. Forthisweused,asinRef.[1],theopticalGlaubermodeltogeneralizethe
dipolecrosssectionofaprotontonuclei. InRef.[1]thismodelwasfoundtoleadtovaluesforthe
nuclear modification factor in minimum bias collisions closer to experimental results than previous
calculationsinasimilarframework.However,whenstudyingthecentralitydependenceinthismodel,
we found here that this dependence appears to be much stronger than in recent ALICE data [4].
Nevertheless,westressthattheresultsshownherehavebeenobtainedusingafixedimpactparameter
forwhich, intheopticalGlaubermodel, thenumberofbinarycollisionscorrespondstotheaverage
valueofthisquantityestimatedbyALICE.Foramoreconsistentcomparisonwithexperimentaldata,
PhysicsOpportunitiesatanElectron-IonCollider
QpPb QpPb
1.4 1.4
CGC CGC
1.2 ALICE 1.2 ALICE
1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 Ncoll=11.7 0.2 Ncoll=11
0 P [GeV] 0 P [GeV]
0 1 2 3 4 5 6 7 8 ⊥ 0 1 2 3 4 5 6 7 8 ⊥
QpPb QpPb
1.4 1.4
CGC CGC
1.2 ALICE 1.2 ALICE
1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 Ncoll=9.6 0.2 Ncoll=7.1
0 P [GeV] 0 P [GeV]
0 1 2 3 4 5 6 7 8 ⊥ 0 1 2 3 4 5 6 7 8 ⊥
QpPb
1.4
CGC
1.2 ALICE
1
0.8
0.6
0.4
0.2 Ncoll=4.3
0 P [GeV]
0 1 2 3 4 5 6 7 8 ⊥
Figure1.NuclearmodificationfactorQ asafunctionofP indifferentcentralitybinscomparedwithALICE
pPb ⊥
data[4].
itwouldbenecessarytousedistributionsinimpactparameterspace,butthiswouldrequireaccessto
the typical size of the fluctuations of the number of binary collisions in the experimental centrality
classes.
Acknowledgments
T. L. and B. D. are supported by the Academy of Finland, projects 267321 and 273464. H. M. is
supportedunderDOEContractNo. DE-SC0012704.ThisresearchusedcomputingresourcesofCSC
–ITCenterforScienceinEspoo,Finland. WewouldliketothankC.HadjidakisandI.Lakomovfor
discussionsontheALICEdata.
EPJWebofConferences
QpPb h6P⊥2ipPb−hP⊥2ipp[GeV2]
1.4
CGC 5 CGC
1.2 ALICE ALICE
4
1
0.8 3
0.6 2
0.4 1
0.2 0
0 0 2 4 6 8 10 12 14 16 Ncoll -1 0 2 4 6 8 10 12 14 16 Ncoll
Figure2.NuclearmodificationfactorQ (left)andnucleartransversemomentumbroadening(cid:104)P2(cid:105) −(cid:104)P2(cid:105)
pPb ⊥ pPb ⊥ pp
(right)asafunctionofN comparedwithALICEdata[4].
coll
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