PHYSICAL REVIEW C 89, 044912 (2014)

Parton shadowing and J/ψ-to-Drell-Yan ratio in nuclear collisions at energies availableat the CERN SPS and the GSI FAIR

Partha Pratim Bhaduri, A. K. Chaudhuri, and Subhasis ChattopadhyayVariable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700 064, India

(Received 23 November 2013; revised manuscript received 24 February 2014; published 29 April 2014)

We have analyzed the data on J/ψ-to-Drell-Yan production cross-section ratios in proton-nucleus (p + A) andnucleus-nucleus (A + A) collisions, measured by the NA50 Collaboration in the CERN Super Proton Synchrotronenergy domain. The adapted version of the two-component QVZ model [J. Qiu, J. P. Vary, and X. Zhang, Nucl.Phys. A 698, 571 (2002); ,Phys. Rev. Lett. 88, 232301 (2002)] has been employed to calculate J/ψ productioncross sections. For both J/ψ and Drell-Yan production, nuclear modifications to the free nucleon structurefunctions are taken into account. In heavy-ion collisions, such modifications are assumed to be proportional tothe local nuclear density resulting in centrality-dependent initial state effects. Differences in quark and gluonshadowing lead to a new source of impact parameter dependence of the J/ψ-to-Drell-Yan production ratio. ForJ/ψ , the final state interaction of the produced cc pairs with the nuclear medium is also taken into account. Asatisfactory description of the data in both p + A and A + A collisions is obtained. The role of the shadowingcorrections is investigated in detail. Model calculations are extrapolated to predict the centrality dependence ofthe J/ψ-to-Drell-Yan ratio in the GSI Facility for Antiproton and Ion Research energy regime.

DOI: 10.1103/PhysRevC.89.044912 PACS number(s): 25.75.Dw

I. INTRODUCTION

The primary objective of the relativistic heavy-ion collisionexperiments is to study the nuclear matter under extremeconditions of temperature and density in the laboratory. Ofparticular interest is the QCD predicted transition from thecolor confined hadronic phase to the color deconfined quark-gluon plasma (QGP) phase. However the transient nature of theplasma renders its identification very difficult. It necessitatesthe search for experimental evidence that would survive thecomplex evolution through the later stages of the collision.J/ψ suppression in nuclear collisions had long been identifiedas a diagnostic tool to indicate the occurrence of the decon-finement transition [1–3]. However subsequent experimentalmeasurements found a considerable reduction of the J/ψ yieldalready present in proton-nucleus (p + A) collisions, which isattributed to the cold nuclear medium of the target nucleus.It is commonly expected that in addition to the cold nuclearmatter (CNM) suppression, in nuclear collisions, formation ofQGP would lead to anomalous J/ψ suppression. At the CERNSuper Proton Synchrotron (SPS), J/ψ suppression in heavy-ion collisions is measured at a beam energy of 158 A GeV,in Pb + Pb collisions by the NA50 Collaboration [4] andin In + In collisions by the NA60 Collaboration [5], in thesame kinematic domain. Originally the NA50 Collaborationpublished their data on J/ψ suppression in terms of theJ/ψ-to-Drell-Yan (DY) ratio at different collision centralities.Due to huge statistical uncertainties in the measurement of DYdimuons, data from the NA60 Collaboration were published interms of the measured-by-expected ratio of J/ψ cross sectionsas a function of collision centrality, where expected denotesthe J/ψ production cross section evaluated incorporating thenuclear absorption scenario following the Glauber formalismof nuclear scattering theory [6]. One obvious disadvantagein this case is that the experimental data become sensitiveto the theoretical model inputs. Recently both In + In and

Pb + Pb data have been presented in terms of the nuclearmodification factor (RAA) [7] defined as the ratio of J/ψ

production cross sections in A + A (σJ/ψAA ) and p + p (σJ/ψ

pp )collisions. In this case as well, the p + p measurements werenot performed; rather σ

J/ψpp was obtained through extrapolation

of the parametrized 158 GeV p + A data up to A = 1. Inour previous work [8], we have shown that both the datasets on the centrality dependence of R

J/ψAA , in In + In and

Pb + Pb collisions, can be reasonably described by the adaptedversion of the Qiu-Vary-Zhang (QVZ) approach [9]. In thepresent article, we aim to check the viability of our modelby examining the available data corpus on J/ψ-to-DY ratiosin p + A [10,11] and Pb + Pb [4] collisions measured bythe NA50 Collaboration, at SPS energies. The advantage ofanalyzing this ratio is that the cross sections for both theprocesses are directly measured in the experiment. Moreoverbecause the muon pairs for both events were collected in thesame run, it certainly gives a better control over the systematicuncertainties. A special emphasis is put on the role of partonshadowing in deciding the behavior of the J/ψ-to-DY ratiosobserved in nucleon-nucleus and nucleus-nucleus collisionsand its sensitivity to the differences in quark and gluonshadowing parameters. Such effects of parton shadowing onthe J/ψ production in p + A and A + A collisions have alsobeen investigated earlier [12–15], within the energy domains ofthe SPS, the BNL Relativistic Heavy Ion Collider (RHIC), andthe CERN Large Hadron Collider (LHC). Shadowing factorshave been evaluated as a function of rapidity and collisioncentrality. Our analysis is motivated by and akin to suchprevious studies as far as evaluation of shadowing effects areconcerned. In addition we have also taken into account thefinal state nuclear dissociation of J/ψ in order to explain themeasured data.

Organization of the paper is as follows. In Sec. II we brieflydescribe our theoretical framework for calculation of J/ψ and

0556-2813/2014/89(4)/044912(8) 044912-1 ©2014 American Physical Society

BHADURI, CHAUDHURI, AND CHATTOPADHYAY PHYSICAL REVIEW C 89, 044912 (2014)

DY production cross sections in p + A and A + A collisions.Section III is devoted to the analysis of the relevant SPS data.In Sec. IV we give predictions for the centrality dependenceof this ratio for the upcoming Compressed Baryonic Matter(CBM) experiment [16] at the GSI Facility for Antiproton andIon Research (FAIR). In Sec. V we summarize and conclude.

II. THEORETICAL FRAMEWORK

To calculate J/ψ production, we have used the adaptedversion of the originally proposed QVZ model [9]. Details ofthe original model and its modifications as used in the presentcalculations can be found in Refs. [8,9,17–19]. Here we presenta brief description for completeness. The QVZ model assumesJ/ψ production hadronic collisions as a factorizable two-component process. Production of a cc pair in the initial hardscattering is the first stage and is accounted for by perturbativeQCD. Hadronization of the cc pair to a physical J/ψ mesonforms the second stage. This is nonperturbative in nature andcan be suitably parametrized following different hadronizationschemes. The single-differential J/ψ production cross sectionin collisions of hadrons h1 and h2, at the center-of-mass energy√

s, can be expressed as

dσJ/ψh1h2

dxF

= KJ/ψ

∫dQ2

(dσ cc

h1h2

dQ2dxF

)× Fcc→J/ψ (q2), (1)

where Q2 = q2 + 4m2C , with mC being the charm quark mass,

and xF is the Feynman scaling variable. KJ/ψ accounts foreffective higher-order contributions. Fcc→J/ψ (q2) denotes thetransition probability of a color-averaged cc pair with relativemomentum square q2 to evolve into a physical J/ψ mesonin hadronic collisions. Different parametric forms have beenformulated for the transition probability, motivated by theavailable models of color neutralization. Out of them, twofunctional forms, namely, the Gaussian form [F (G)(q2)] and thepower-law form [F (P)(q2)], respectively, bearing the essentialfeatures of the color-singlet [20] and color-octet [21] modelshave been found earlier to describe the J/ψ production crosssection data in p + A collisions reasonably well [19].

In p + A collisions, J/ψ production is affected by severalcold nuclear matter effects that become operative at differentstages of evolution. At the initial stage, nuclear modificationsof the parton densities of the target nucleons affect the ccpair production cross section. The mechanisms governingthese modifications are still largely unknown. However basedon global DGLAP analysis, several groups have producedparametrizations of the ratio Ri(A,x,Q2) that convert thefree-proton distributions for each parton i, f

pi (x,Q2), into

nuclear ones (nPDF), f Ai (x,Q2), using the available data

from deep inelastic scattering (DIS) and DY measurementsperformed with nuclear targets (see Ref. [22] for a recentcomprehensive review on nPDFs and the references therein).In our analysis, to maintain accordance with our earlier works,we opted for the leading order (LO) MSTW2008 [23] set forthe free proton PDF and the LO global EPS09 [24] interfacefor the ratio Ri(A,x,Q2).

In heavy-ion collisions, parton densities are modified insideboth projectile and target nuclei. Depending on the collision

geometry, either the halo or the core of the nuclei will bemainly involved in the reaction. Consequently the shadowingeffects will be more important in the core than in the periphery.Hence the shadowing factors have to be calculated for variouscentrality intervals. Different prescriptions are available in lit-erature to model the impact-parameter-dependent shadowingfactors [13,14,25]. In the present calculations we implementthe spatial dependence of shadowing functions assuming themto be proportional to the local nuclear density [13,14], withthe Woods-Saxon (WS) profile chosen for nuclear densitydistributions. Inhomogeneous shadowing effects inside thenucleus can also be invoked by postulating them to be linearlyproportional to the density-weighted longitudinal thickness ofthe nucleus at the transverse position of the binary collision(TA(rT) defined as TA(rT) = ∫

ρA(rT,z)dz, where ρA(rT,z) isthe local nuclear density at a point (rT,z) inside the nucleusA. However these two parametrizations of local shadowinghave been found to give similar results at SPS energies;their difference lies within 2% − 3% [15]. Recently spatialdependence of the nPDFs has been studied in detail usingthe A dependence of the spatially independent global EPS09and EKS98 routines [25]. Spatial dependence is modeled asa power series of TA, having terms up to (TA)4. Two spatiallydependent nPDF sets, namely, EPS09s and EKS98s, have alsobeen released for public use.

In p + A and A + A collisions, the nascent cc pairs onceproduced will pass through the nuclear medium. During theirpassage they undergo multiple collisions with the mediumand gain relative square four-momentum at a rate of ε2 perunit path length. Some of the cc pairs can thus gain enoughmomentum to cross the threshold to evolve as open charmmesons (DD pairs). This would finally result in the reductionof the J/ψ yield compared to the nucleon-nucleon collisions.The overall effect of the multiple scattering of the cc pairs canbe represented by a shift of q2 in the transition probability,

q2 −→ q2 = q2 + ε2〈L〉, (2)

where 〈L〉 denotes the average geometrical path lengthtraversed by the cc pair till it exits the medium and is calculatedusing the Glauber model. For both parametrizations of thetransition probability, F (q2), the corresponding values of ε2,extracted from the analysis of absolute J/ψ production cross-sections in p + A collisions, exhibited nontrivial dependenceon the beam energy (Eb) [19]. The lower the beam energyis, the larger the value of ε2 is, implying larger nucleardissociation.

In the DY process, a quark and an antiquark from thenucleons of the two colliding nuclei annihilate to form a virtualphoton which subsequently decays into a μ+μ− pair. Theleading-order DY cross section can be calculated by usingthe standard prescription (see, for example, Ref. [3]). Theyare not affected by any final state effect. Only the CNMeffect incorporated is the nuclear modification of the partondistribution functions. The inclusive cross sections can beobtained by integrating the double-differential cross sectionwithin the suitable mass and rapidity range as appropriate fora particular experimental setup.

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III. ANALYSIS OF SPS DATA

With this brief description of the model, we now moveforward to examine the reliability of the model calculations indescribing the available data sets on the J/ψ-to-DY ratio atSPS, available from the NA50 Collaboration. Uncertainties inthe ratio are mostly dominated by the statistical errors of theDY production cross-section data. The NA50 Collaborationmeasured J/ψ through its dimuon decay channel. For p + Acollisions the said ratio was measured with both 400 GeV[10] and 450 GeV [11] proton beams. In the case of Pb + Pbcollisions the data were collected at 158 A GeV [4]. For450 GeV, the NA50 Collaboration collected two sets of p + Adata in two independent runs with different beam intensities.The first (ever) set was collected with a high-intensity (HI)450 GeV proton beam using five different nuclear targets(Be, Al, Cu, Ag, W). Subsequently at the same beam energynew p + A data samples were collected with low beamintensity (LI) and with the same set of targets. The datasets at 450 GeV correspond to the phase space window:−0.5 < yc.m. < 0.5 and −0.5 < cos(θcs) < 0.5, where yc.m.

denotes the dimuon center-of-mass rapidity and θcs is theCollins-Soper angle. The NA50 Collaboration also took datawith a 400 GeV incident proton beam using six differenttarget nuclei (Be, Al, Cu, Ag, W, Pb). Data were selectedin the kinemtaic region: −0.425 < yc.m. < 0.575 and −0.5 <cos(θcs) < 0.5. Unlike previous measurements, in the 400 GeVrun, data for all targets were collected in the same datataking period, which significantly reduces the systematicerrors.

In Fig. 1 we show the variation of the J/ψ-to-DY cross-section ratio as a function of 〈L〉 for various p + A systems.The two theory curves result from fitting the above datasets following two parametrizations of F (q2), representingtwo different physical mechanisms of J/ψ formation, asmentioned earlier. For both the cases, nuclear modificationof parton densities is taken into account. The 〈L〉 values aspublished with the data are used to generate the theoreticalcurves. Different 〈L〉 correspond to different target nuclei, forwhich the corresponding EPS09 nPDF set is implemented.Note that for a given parametrization of F (q2) (power-lawor Gaussian), our employed model contains three parameters.Two of them, namely, ε2 and αF , were already fixed earlier

[19] using inclusive data on absolute J/ψ production crosssections in p + A and p + p collisions, respectively. Theonly free parameter left for the current analysis is the Keff

defined as Keff = fJ/ψ/KDY, where fJ/ψ = KJ/ψ × NJ/ψ .KDY takes care of higher-order effects in DY production. Asevident from the figure, both the curves can give a satisfactorydescription of the data. This is of course expected from ourearlier observation, where we found that the J/ψ productionin p + A collisions at SPS energies is well described by bothforms of F (q2).

Let us now examine the ratio in Pb + Pb collisions at158 A GeV. In this case, all the model parameters, as mentionedearlier, are fixed from the p + A data. We have selected thelatest data set published by the NA50 Collaboration [4]. Datawere collected in the dimuon kinematic domain 0 < yc.m. < 1and −0.5 < cos(θcs) < 0.5. DY differential cross sections areintegrated in the mass domain 2.9–4.5 GeV/c2. Analysis hasbeen performed using three independent centrality estimators,namely, neutral transverse energy (ET ) deposited in anelectromagnetic calorimeter, forward energy (EZDC) depositedin a zero degree calorimeter, and charge particle multiplicityper unit of pseudorapidity at midrapidity (dNch/dη)max (desig-nated by Nch in the figures). For each case, the centrality classesand the corresponding values of the number of participantnucleons (Npart), of the impact parameter (b), and of theaverage path length of the nuclear matter traversed by thepreresonant cc pair (〈L〉) are also given. As earlier, we haveused those 〈L〉 values in our model calculations. It is alsoimportant to mention that, for Pb + Pb collisions, no modelparameter is tuned. All the model parameters are fixed fromthe present (keff) and previous (αF and ε2) analysis of theavailable p + A data sets.

To investigate the role played by parton shadowing in detaillet us first compare the data with our model calculationswithout incorporating the nuclear modifications of projectilenucleons. The results are illustrated in Fig. 2. The theoreticalcurves correspond to the power-law parametrization of F (q2).As evident from the figure, the theoretical curves completelyunderestimate the data (the same is true for the Gaussianthough not shown explicitly). The dominant contribution tothe J/ψ production comes from gluon fusion and at the SPSkinematic domain gluons in the projectile nucleons are heavily

<L> (fm)1 2 3 4 5

DY

/J/

B

40

45

50

55

60

d ta(P)

F(G)F

NA50-450 GeV-LI

<L> (fm)1 2 3 4 5

DY

/J/

B

40

50

60

data(P)

F(G)

F

NA50-450 GeV-HI

<L> (fm)1 2 3 4

DY

/J/

B

40

45

50

55

60

da a(P)

F(G)

F

NA50-400 GeV(a) (b) (c)

FIG. 1. (Color online) Model description of the data on the ratio of the J/ψ-to-DY production cross sections in the (a) 450 GeV high-intensity (HI) run, (b) 450 GeV low-intensity (LI) run, and (c) 400 GeV p + A collisions, measured by the NA50 collaboration at the SPS.Bμμ denotes the branching ratio of the J/ψ decaying into dimuons. The two theoretical curves represent two different parametric forms of theJ/ψ formation probability [F (q2)].

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BHADURI, CHAUDHURI, AND CHATTOPADHYAY PHYSICAL REVIEW C 89, 044912 (2014)

<L> (fm)6 8

DY

/J/

B

10

15

20

25

30

data

:w/o projectile shadowingF

NA50-158 GeV-Pb+Pb (E

<L> (fm)5 6 7 8 9

DY

/J/

B

10

15

20

25

30

data

:w/o projectile shadowingF

NA50-158 GeV-Pb+Pb (

<L> (fm)4 6 8

DY

/J/

B

10

15

20

25

30

data

:w/o projectile shadowingF

NA50-158 GeV-Pb+Pb (E

FIG. 2. (Color online) Centrality dependence of the J/ψ/DY ratio in 158 A GeV Pb + Pb collisions, measured through the dimuonchannel, within the acceptance (0 � yc.m. � 1 and −0.5 � cos(θcs) � 0.5) of the NA50 muon spectrometer. Data were published using threeindependent centrality estimators based on the measurements of: (a) transverse energy (ET ), (b) forward energy (EZDC), and (c) total chargedparticle multiplicity (Nch) (see text for details). The theoretical curve corresponds to the power law [F (p)(q2)] parametric form of the J/ψ

transition probability. Model calculations do not take into account the shadowing corrections of the projectile nucleons and thus completelyunderestimate the data.

antishadowed, within the EPS09 routines. Once these shadow-ing corrections of projectile partons are taken into account, amuch better description of the data is obtained, as seen in Fig. 3.Here we have contrasted the data with both forms of F (q2). Forboth the cases we have considered global shadowing, implyingthe shadowing factors are independent of the spatial location ofthe partons. In consistency with the previous observations, thepower-law form [F (P )(q2)], due to threshold effects, generatesmuch larger suppression compared to the Gaussian [F (G)(q2)]case and thus can explain the Pb + Pb data even for most cen-tral collisions. The Gaussian form on the other hand underesti-mates the suppression at least for higher centralities. Note thatsuppression for F (G)(q2) is equivalent to that generated by theGlauber model with the eikonal approximation [19]. Finallyin Fig. 4, we have examined the effects of density-dependentlocal shadowing as implemented in the model. The effect of thespatial dependence of shadowing is more visible for peripheralcollisions. As stated earlier, at the SPS energy regime gluondensities in both the target and the projectile exhibit overpopu-lation and hence when a spatial inhomogenity is incorporated,gluons at the core are more affected compared to those nearthe surface. Hence in peripheral collisions the J/ψ productioncross section is less for local shadowing compared to the globalcase (where the amount of antishadowing is independent of thespatial position of the partons and thus the same for different

centrality intervals) and for most central collisions it is more.To examine such geometrical effects in more detail, let usnow calculate the shadowing function [SJ/ψ (SDY)], defined asthe ratio between J/ψ (or DY) production cross sections inPb + Pb and p + p collisions in the absence of any final stateinteraction. Due to the difference in quark and gluon shadow-ing effects, the behavior of the resulting shadowing functionsfor J/ψ and DY productions will also be different. This isillustrated in Fig. 5, where we have plotted the variation of theshadowing functions in 158 A GeV Pb + Pb collisions as afunction of b.

As evident from the figure, in the kinematic domain probedby SPS heavy-ion collisions, J/ψ production gets enhanceddue to increasing gluon densities, whereas the shadowingeffects in the DY production can be attributed to the depletedquark densities inside the Pb nucleus. Effects are maximumfor central collisions, as expected. We have also plotted theratio RAA

J/ψ/DY defined as the ratio of the two productioncross sections in the dimuon channel, in the absence ofany final state nuclear dissociation [RAA

J/ψ/DY = BμμσAAJ/ψ (ε2 =

0)/σAADY ]. Due to the absence of any final state dissociation the

ratio exhibits a decreasing trend with a decrease in collisioncentrality. Note for b = 0, the ratio assumes a value ofRAA

J/ψ/DY � 53. It is close to the normalization factor usedin Ref. [26] to describe the J/ψ/DY ratio in 158 A GeV

<L> (fm)5 6 7 8 9

DY

/J/

B

10

15

20

25

30

data

F

F

NA50-158 GeV-Pb+Pb (E

<L> (fm)5 6 7 8 9

DY

/J/

B

10

20

30

data

F

F

NA50-158 GeV-Pb+Pb (N

<L> (fm)4 6 8

DY

/J/

B

10

15

20

25

30

data

F

F

NA50-158 GeV- Pb+Pb (E

FIG. 3. (Color online) Centrality dependence of J/ψ production in Pb + Pb collisions measured at 158 A GeV beam energy. Data analyzedwith three independent centrality estimators, namely, (a) ET , (b) EZDC, and (c) Nch, are shown independently. Data samples were collectedwithin the phase space window: 0 � yc.m. � 1 and −0.5 � cos(θcs) � 0.5. The theoretical curves correspond to the two different parametricforms of the J/ψ transition probability. Global shadowing corrections of the projectile and target nucleons are taken into account.

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PARTON SHADOWING AND J/ψ-TO-DRELL-YAN . . . PHYSICAL REVIEW C 89, 044912 (2014)

σψ

σ μμ

data

:local shadowing (ws)F

:global shadowingF

σψ

σ μμ data

:local shadowing (ws)F

:global shadowingF

σψ

σ μμ

data

:local shadowing (ws)F

:global shadowingF

FIG. 4. (Color online) Model calculation of the centrality dependence of J/ψ production contrasted with the data for Pb + Pb collisionsmeasured by the NA50 Collaboration at 158 A GeV beam energy and in the kinematic domain: 0 � yc.m. � 1 and −0.5 � cos(θcs) < 0.5.Data sets corresponding to all three independent centrality estimators, (a) ET , (b) EZDC, and (c) Nch, are shown. Shadowing corrections of theprojectile and target nucleons as incorporated in the model are assumed to be proportional to the local nuclear density. For comparison globalshadowing corrections are also shown.

Pb + Pb collisions. It might also be interesting to look at therapidity dependence of the shadowing function. In Fig. 6, wehave shown the rapidity dependence of the shadowing functionfor J/ψ production. The contributions arising from thegluon-gluon (gg) fusion and quark-antiquark (qq) annihilationare plotted separately along with their sum. The shadowingeffects for quark annihilation at forward rapidity are morethan compensated for by gluon fusion.

The reader may note that all our present calculations arebased on the default EPS09 nPDF sets. With this parametriza-tion, we are able to describe the entire Pb + Pb data within theQVZ approach. However there are many other parametriza-tions of nuclear parton densities for which, in particular,the gluon distributions that cannot be probed directly inexperiments are of a very different nature. One can perform asystematic study with different nPDF sets as inputs to checkwhether all of them can reproduce the Pb + Pb data equallywell by compensating for the difference in shadowing effectsby adjusting the model parameter ε2 that accounts for the finalstate nuclear dissociation. Earlier we have seen that the p + Adata at different SPS energies can also be described withinthe QVZ model using free proton pdf [19]. In that case onegets relatively smaller values of ε2 (provided all other modelparameters are fixed from p + p data) due to the absence ofantishadowing effects. In Ref. [27], the authors analyzed theJ/ψ production cross sections in p + A collisions at different

fixed target experiments within the Glauber model framework.They used several sets of nuclear parton distributions having alarge difference in the gluon densities for a given x. All of themwere found to reproduce the data with different values of thefinal state J/ψ absorption cross section (σJ/ψ

abs ). The strongerthe antishadowing enhancement in the initial state gluon pdf,the larger the extracted σ

J/ψabs is. Similar effects might be seen

in the case of heavy-ion data as well, but one certainly needs aquantitative check to make any robust conclusion and we planto do so in a future communication. In this context, we wouldalso like to point out that in the original proposition of theQVZ model nuclear effects on parton densities were not takeninto account. Even then the model was found to describe thethen available NA50 Collaboration data on J/ψ suppression inPb + Pb collisions. In that case the value of ε2 was tuned fromthe heavy-ion data itself. Unfortunately a direct comparisonwith our ε2 value is not possible due to differences in the othermodel parameters.

IV. PREDICTION AT FAIR

In this section we extrapolate our model to make predictionson parton shadowing and the resulting centrality dependenceof theJ/ψ-to-DY ratio in nuclear collisions at the FAIR. As abaseline we choose the Au + Au collisions at a beam energy of25 A GeV, which is within the reach of the FAIR accelerators.

b (fm)0 5 10 15

AA

DY

S

0.77

0.78

0.79

0.8

(b)

b (fm)0 5 10 15

AA ψ

J/S

1.1

1.15

(a)

b (fm)0 5 10 15

AA

/DY

ψJ/

R

46

48

50

52(c)

FIG. 5. (Color online) Centrality dependence of the shadowing function for (a) J/ψ , (b) DY productions, and (c) the ratio of the twoproduction cross sections in the dimuon channel, in the absence of any final state nuclear dissociation of J/ψ (RAA

J/ψ/DY = BμμσAAJ/ψ (ε2 =

0)/σAADY ), estimated for 158 A GeV Pb + Pb collisions. Total cross sections are obtained by integrating the differential cross section in the

rapidity range 0 < yc.m. < 1, which corresponds to the rapidity coverage of the NA50 dimuon system for the Pb-Pb run.

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BHADURI, CHAUDHURI, AND CHATTOPADHYAY PHYSICAL REVIEW C 89, 044912 (2014)

c.m.y

0 0.2 0.4 0.6 0.8

)c.

m.

(y

AA ψ

J/S

1

1.2

1.4

gg

total

qq

FIG. 6. (Color online) Rapidity dependence of the shadowingfunction for J/ψ in 158 A GeV Pb + Pb collisions within the cov-erage of the NA50 Collaboration’s muon system. The contributionsfrom quark-antiquark (qq) annihilation and gluon-gluon (gg) fusionare shown separately along with the total cross section.

Such extrapolations are of course based on the hope thatperturbative calculations are still valid at the FAIR energydomain. However in such low-energy collisions quarkoniumproduction would occur close to the threshold and factorizationof the initial state into parton distribution functions may not bevalid (see, for example, Ref. [28] for an alternative approachto calculate near-threshold quarkonium production based onscaling theory). But the test of the QCD factorization in thenear-threshold production can only be performed once we havedata. Let us first investigate the behavior of the shadowingfunctions for J/ and DY productions in the FAIR energydomain. Inclusive cross sections for J/ψ production areobtained by integrating the single-differential distribution overthe rapidity range −0.5 � yc.m. � 0.5. For the DY process,the double-differential cross section is integrated over themass range 2.9 � mμμ � 4.5 GeV/c2 and the rapidity range−0.5 � yc.m. � 0.5. As illustrated in Fig. 7, both the J/ψ aswell as the DY productions exhibit shadowing, with the DYproduction showing stronger effects, where the productioncross sections in the central Pb + Pb collisions reduce byalmost 50% compared to the p + p collisions. The way theseshadowing and antishadowing corrections affect the J/ψ-to-DY ratio at different collision energies can be understoodbetter if one looks at the evolution of the nuclear partondensities. Figure 8 shows the variation of EPS09 nuclear

x−310 −210 −110

Au

iR

0.8

1

1.2

1.4 g

vu

su

vd

sd

Q=3.1 GeV

FIG. 8. (Color online) Variation of the nuclear parton distribu-tion, inside a Au nucleus, as a function of the momentum fractionx. Parton densities are evaluated following the LO EPS09 defaultparametrization at a momentum scale of Q = 3.1 GeV, appropriatefor J/ψ production. The uncertainties in the nPDF sets are not takeninto consideration.

PDFs inside a Au nucleus, evaluated at a momentum scaleof Q = 3.1 GeV, suitable for J/ψ production, as a functionof the momentum fraction x. At the energies available atthe SPS and FAIR, production is dominantly at midrapidity;therefore let us consider the region yc.m. ≈ 0, which wouldcorrespond to the domain x1 = x2 = x = Q/

√sNN . Hence at

SPS (√

sNN ≈ 17.3 GeV), we have xSPS ≈ 0.18, where boththe gluons and valence quarks densities exhibit antishadowing,whereas the sea quarks show shadowing effects. This is finallyreflected in SJ/ψ > 1 and SDY < 1 at SPS energies. On theother hand, the upcoming CBM experiment at the FAIRenergies (

√sNN ≈ 6.9 GeV) will probe the kinematic region

xFAIR ≈ 0.45. In this regime, gluon, valence quark as well assea quark densities inside the nuclei get depleted (the EMCeffect). Due to higher depletion of sea quarks, the DY processshows stronger reductions. Also even in the absence of thefinal state dissociation of the preresonance cc pairs, the initialstate shadowing effects alone lead to a 10%–15% suppressionof J/ψ production in Pb + Pb collisions. Eventually this alsoleads to lower values for the ratio RAA

J/ψ/DY compared to thoseat SPS.

We end this section with quantitative predictions for theJ/ψ-to-DY ratio in the presence of CNM suppressions, whichcan be directly contrasted with the data when available. In

b (fm)0 5 10 15

AA

DY

S

0.55

0.6

(b)

b (fm)0 5 10 15

AA

/DY

ψJ/

R

37

37.5

(c)

b (fm)0 5 10 15

AA ψ

J/S

0.85

0.9(a)

FIG. 7. (Color online) Impact parameter dependence of the shadowing functions for (a) J/ψ , (b) DY productions, and (c) the ratio of thetwo production cross sections in the absence of any final state interaction of J/ψ in the nuclear medium. Shadowing factors were evaluated atmidrapidity in 25 A GeV Au + Au collisions.

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<L> (fm)5 6 7 8 9

DY

σ/ψ

J/σ μμB

5

10

15

20(G)

F(P)

F(a)

partN100 200 300

ψJ/ A

A,C

NM

R

0.1

0.2

0.3

0.4

0.5 (P)F

(G)F

(b)

FIG. 9. (Color online) Model prediction for centrality dependence of the (a) J/ψ-to-DY ratio and (b) nuclear modification factor of J/ψ

(RJ/ψAA ), in 25 A GeV Au + Au collisions at mid-rapidity. The CNM effects incorporated in the model calculations include the density-dependent

shadowing corrections in the initial state and final state dissociation of the preresonant cc pairs inside the nuclear medium. No hot mediumeffect is taken into account. Two theory curves, as usual, correspond to the two different parametric forms of the J/ψ transition probability,representing different color neutralization mechanisms.

case the data for the DY production suffer from lack of sizablestatistics, the suppressions can also be characterized in termsRAA. Most of the present day experiments like those at theRHIC or the LHC are publishing their results on charmoniumsuppression in terms of RAA. At FAIR energies also one canexpress the data in terms of RAA, though our wish in that casewould be a direct measurement of charmonium productioncross sections in p + p collisions, rather than the extrapolationof the p + A results. In Fig. 9 we thus present our modelpredictions for the centrality dependence of J/ψ suppressionin Au + Au collisions in terms of both the J/ψ/DY ratioand RAA. The two theory curves, as usual, correspond totwo different parametrizations of F (q2). The correspondingvalues of ε2 accounting for final state dissociation are obtainedfrom the beam energy dependence of ε2(Eb), parametrized inRef. [19]. Note that at the SPS energy domain, the entire datacorpus for 158 A GeV Pb + Pb collisions can be describedby CNM effects alone, provided we opt for the power-law[F (P )(q2)] form for the J/ψ transition probability. If thedata that will be collected at the FAIR shows smaller valuesof the ratio compared to the present estimations, then suchadditional suppressions can be attributed to the presence of asecondary medium, the characterization of which will be offurther theoretical interest.

V. SUMMARY

In summary, we have discussed the J/ψ-to-DY ratioin p + A and A + A collisions, measured by the NA50Collaboration at the SPS, indicating a significant role thatthe nuclear modification of the parton densities may have onthese ratios. The J/ψ cross sections are mainly sensitive tothe gluon distributions, whereas the DY cross sections aredominated by qq annihilation. Because the nuclear effects inparton distributions are in general different for quarks andgluons, they are found to induce a relatively large effect on theJ/ψ-to-DY ratio. The nuclear dissociation of the preresonantcc pairs is also taken into account by our calculations. Oncethe nuclear-modified parton densities inside the target andprojectile nuclei are correctly taken into account, our analysis

gives a reasonable description of data for both p + A andPb + Pb collisions. Thus it leaves no room for any additionalsuppression mechanism to set in even for most central Pb + Pbcollisions, where formation of a hot and dense secondarymedium is highly envisaged. One might note that, althoughthe pattern describing the centrality dependence of σJ/ψ/σDY

remains essentially unaffected, the numerical values of theratio are somewhat sensitive to the specific choice of the PDF.This happens because different PDFs give slightly differentshapes of DY dimuon mass distributions and consequently leadto different DY yields in the region 2.9 � mμμ � 4.5 GeV/c2.For consistency one should use a single set of PDFs forall data samples. In our calculations, we have used the LOcentral MSTW set for free proton PDFs and the LO EPS09default interface for the nuclear effects. The errors in the PDFsets are ignored in the present calculations. More detailedcalculations should take such uncertainties into account thoughthey are not expected to produce large effects so to changeour main results. The MSTW set takes into account theisospin asymmetry of the quark sea (u �= d). In the case ofnuclear collisions, the shadowing factors are assumed to beproportional to the local nuclear density, which gives rise tothe new source of impact parameter dependence of the J/ψ-to-DY ratio. Explicit evaluation of the shadowing factors inPb + Pb collisions shows that, in the kinematic domain probedat the SPS, J/ψ production is antishadowed whereas DYproduction undergoes shadowing. The model is extrapolatedto predict the centrality dependence of the J/ψ-to-DY ratioin Au + Au collisions at the FAIR. In this regime both J/ψand DY productions are found to undergo suppression dueto depletion of nuclear parton densities. To determine thefinal state effects in charmonium production, such initialstate modifications must evidently be brought under control.Data from the future FAIR accelerators with unprecedentedhigh-beam intensities are thus highly welcome. One can behopeful to minimize statistical errors prevalent for DY pairs atthe FAIR, provided the data will be collected for a fairly longperiod. A precise determination of the nuclear effects willalso help to distinguish the possible effects of a compressedbaryonic matter anticipated at FAIR energy collisions.

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ACKNOWLEDGMENTS

It is a pleasure to thank Prithwish Tribedy for his kind helpduring the preparation of the manuscript. P.P.B. would also like

to acknowledge the services provided by the grid computingfacility at VECC-Kolkata, India for facilitate the performingof a major part of the computation used in this work.

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