Quarkonium plus prompt-photon associated hadroproduction and nuclear shadowing
aa r X i v : . [ h e p - ph ] M a r Quarkonium plus prompt-photon associated hadroproduction and nuclear shadowing
C. Brenner Mariotto a and M.V.T. Machado b a Instituto de Matem´atica, Estat´ıstica e F´ısica, Universidade Federal do Rio GrandeCaixa Postal 474, CEP 96201-900, Rio Grande, RS, Brazil b Centro de Ciˆencias Exatas e Tecnol´ogicas, Universidade Federal do Pampa Campus de Bag´e,Rua Carlos Barbosa. CEP 96400-970. Bag´e, RS, Brazil
The quarkonium hadroproduction in association with a photon at high energies provides a probeof the dynamics of the strong interactions as it is dependent on the nuclear gluon distribution.Therefore, it could be used to constrain the behavior of the nuclear gluon distribution in proton-nucleus and nucleus-nucleus collisions. Such processes are useful to single out the magnitude ofthe shadowing/antishadowing effects in the nuclear parton densities. In this work we investigatethe influence of nuclear effects in the production of
J/ψ + γ and Υ + γ and estimate the transversemomentum dependence of the nuclear modification factors. The theoretical framework considered inthe J/ψ (Υ) production associated with a direct photon at the hadron collider is the non-relativisticQCD (NRQCD) factorization formalism.
PACS numbers: 12.38.Bx, 13.25Gv,13.60.Le, 13.85.Qk; 12.38.-t
I. INTRODUCTION
In recent years, quarkonium hadroproduction has be-come the subject of intense theoretical and experimentalinvestigation. The main reason is that production anddecays of heavy quarkonia have been an ideal labora-tory to investigate Quantum Chromodynamics (QCD).Their large masses provide a hard scale which allows usto use perturbative QCD techniques. Basically, thereexist three distinct formalisms for quarkonium produc-tion. The simplest one is the color evaporation model(CEM) [1], where the hadronization of the Q ¯ Q pairs intoquarkonia is assumed to be dominated by long-distancefluctuations of gluon fields which motivates a statisticaltreatment of color. In the color-singlet model (CSM) [2],quarkonium is viewed as a non-relativistic color-singletbound state of a Q ¯ Q pair with definite angular momen-tum quantum numbers. Production rates for a quarko-nium state are computed by calculating the productionof a heavy quark pair which is constrained to be in acolor-singlet state and have the same angular momentumquantum numbers as the physical quarkonium. In thenon-relativistic QCD (NRQCD) factorization formalism[3], non-perturbative aspects of quarkonium productionare organized in an expansion in powers of ν , the rela-tive velocity of the Q ¯ Q in quarkonia. For production of S -wave quarkonia, the results of the CSM are recoveredin the limit of ν →
0. In addition, in the NRQCD for-malism new quarkonium production mechanisms are nowpossible since it is no longer required that the Q ¯ Q pro-duced in the short-distance process have the same colorand angular momentum quantum numbers as the quarko-nium state. Recently, several computations of the QCDcorrections to the inclusive quarkonium hadroproductionprocesses have shed some light on the robustness and/ordeficiencies of those models. Comprehensive reviews ofrecent developments in the theory of quarkonium pro-duction can be found in Refs. [4, 5].Beside the studies of inclusive production, efforts are being made to obtain improved theoretical predictions forcomplementary observables to the inclusive yield, suchthe hadroproduction of J/ψ and Υ in association with aphoton. In the framework of CSM, the associated pro-duction of
J/ψ + γ at a hadron collider was first proposedas a good channel to investigate the gluon distribution inthe proton with a relatively clean signal [6]. In Ref. [7],such a process at the Tevatron energy has been consid-ered in the CSM at LO, and the results show that thecontribution from the gluon fusion sub-process is domi-nant over that from the fragmentation process (the sameoccurs at the LHC [8]). The color-octet contributionswere investigated in Ref. [9] and it was found they aredominant in the large p T region. Recently, in Ref. [10]the effect of the NLO QCD corrections to J/ψ (Υ) + γ hadroproduction at the LHC has been investigated. InRef. [11] the real next-to-next-to-leading (NNLO) orderQCD contribution to hadroproduction of a J/ψ (Υ) + γ via color singlet transitions for the inclusive case has beenaddressed. In this Letter, we examine the production ofassociated J/ψ + γ and Υ + γ at large p T within theNRQCD approach in proton-nucleus and nucleus-nucleuscollisions. Such processes are relatively clean because theproduced large p T quarkonium is easy to detect throughits leptonic decay modes and the quarkonium’s large p T is balanced by the associated high energy photon. Atthe LHC energy, the leading contributions are dominatedby gluon induced hard processes and then the quarko-nium production associated with a direct photon will bestrongly dependent on the nuclear gluon distribution.Our goal is to use the J/ψ + γ and Υ + γ processes asauxiliary observables to constrain the nuclear gluon dis-tribution. This is motivated by similar investigations oninclusive heavy quark, quarkonium and prompt photonproduction in central proton-nucleus and nucleus-nucleuscollisions (See e.g. Refs. [12–18]). One of the nuclear ef-fects which is expected to modify the behavior of gluondistribution is the nuclear shadowing. This effect hasbeen observed in the nuclear structure functions by dif-ferent experimental collaborations [19, 20] in the studyof the deep inelastic lepton scattering (DIS) off nuclei.The modifications on F A ( x, Q ) depend on the partonmomentum fraction x . While for momentum fractions x < . . < x < . . < x < .
3) it isverified an enhancement known as antishadowing. Theseexperimental results strongly constrain the behavior ofthe nuclear quark distributions, whereas the the nucleargluon distribution is still an open question due to thescarce experimental data in the small- x region and/orfor observables strongly dependent on the nuclear gluondistribution.This Letter is organized as follows. In next section,we summarize the main formulas concerning the process J/ψ + γ in the NRQCD formalism and define the nu-clear modification factors for proton-nucleus and nucleus-nucleus collisions, R pA and R AA , respectively. In lastsection we present the numerical results considering themore recent nuclear parton parameterizations and esti-mating the transverse momentum dependence of the nu-clear modification factors at the LHC energies. II. QUARKONIUM PRODUCTIONASSOCIATED WITH A DIRECT PHOTON
As long as
J/ψ + γ is produced at small longitudi-nal momentum fraction, x F ≪
1, the gluon fusion chan-nel dominates over the q ¯ q annihilation process. There-fore, at high energies and at leading order (LO), the pro-cess g + g → J/ψ + γ contributes at the partonic levelwith six Feynman diagrams, which is similar to that of g + g → J/ψ + g in inclusive J/ψ hadroproduction. Thesignal we focus on is the production of a
J/ψ and anisolated photon produced back-to-back, with their trans-verse momenta balanced. The LO cross section is ob-tained by convoluting the partonic cross section with theparton distribution function (PDF), g ( x, µ F ), in the pro-ton, where µ F is the factorization scale. At NLO expan-sion on α s , there are one virtual correction and threereal corrections processes, as shown in Ref. [10]. Inthe NRQCD formalism, the contributing subprocessesare q + ¯ q → S +1 L J + γ and g + g → S +1 L J + γ .The Fock-components that contribute to J/ψ produc-tion are the color-singlet S [1]1 state and the color-octetstates S [8]1 , S [8]0 and P [8]0 , , . The color-singlet S statecontributes at O (1) but the color-octet channels all con-tribute higher orders in ν (the relative velocity betweenthe heavy quarks).We are interested here in the quarkonium productionin a nuclear medium. In order to get the J/ψ + γ yield in pA and AA collisions, a shadowing-correction factor hasto be applied to the J/ψ yield obtained from the simplesuperposition of the equivalent number of pp collisions.This shadowing factor can be expressed in terms of theratios R Ai of the nuclear parton distribution functions in a nucleon of a nucleus A to the PDF in the free nucleon.Most of shadowing models provide the nuclear ratios at agiven value of Q and then evoluted through the DGLAPevolution equations [21] to LO accuracy. Only very re-cently, the nuclear PDFs have been available at NLO ac-curacy. Therefore, in what follows we will consider a LOcalculation for the nuclear modification factors in orderto be consistent with the limitation of shadowing models.In this respect our analysis cannot be considered as fullyNLO and should be updated once the NLO calculation inNRQCD approach is available for the nucleon case. Onthe other hand, this is not an important limitation to ourresults as we will discuss later on.In order to obtain the transverse momentum ( p T ) dis-tribution for the process g + g → J/ψ + γ , we express thedifferential cross section as d σdydp T = Z dx g A ( x , µ F ) g B ( x , µ F ) 4 x x p T x − ¯ x T e y d ˆ σd ˆ t , (1)where we have defined ¯ x T = 2 m T / √ s , with √ s be-ing the center of mass energy of the AB system and m T = q p T + m ψ being the transverse mass of outgoing J/ψ . The gluon distribution, g A/B ( x, Q ), in the hadronA/B is evaluated at factorization scale µ F . The commontransverse momentum of the outgoing particles is p T and y is the rapidity of outgoing J/ψ having mass m ψ . Thevariables x and x are the momentum fractions of thepartons, where M /s ≤ x < M is the invariant massof J/ψ + γ system) and x can be written in terms ofother variables as x = x ¯ x T e − y − τ x − ¯ x T e y , with τ = m ψ s . (2)In the NRQCD formalism, the cross section for theproduction of a quarkonium state H is written as σ ( H ) = P n c n h | O Hn | i , where the short-distance coefficients c n are computable in perturbation theory. The h | O Hn | i arematrix elements of NRQCD operators of the form h | O Hn | i = X X X λ h | κ † n | H ( λ )+ X ih H ( λ )+ X | κ n | i . (3)The κ n is a bilinear in heavy quark fields which cre-ates a QQ pair in a state with definite color and an-gular momentum quantum numbers. Hereafter, we willuse a shorthand notation in which the matrix elementsare given as h O H (1 , ( S +1 L J ) i . The angular momentumquantum numbers of the QQ produced in the short-distance process are given in standard spectroscopic no-tation, and the subscript refers to the color configurationof the QQ : 1 for a color singlet and 8 for a color octet.The parton level differential cross sections relevant forhadroproduction of J/ψ + γ , including both color-singlet p T (GeV) R pA DSEKSHKNEPS 5 10 15 20 25 30 p T (GeV) y=0 y=2 FIG. 1: Transverse momentum dependence of the nuclear modification factor R pA in J/ψ + γ production in central and forwardrapidities at the LHC ( √ s = 8 . and color-octet contributions are given below [9, 22]: d ˆ σ sing d ˆ t = σ (cid:20) (cid:18) ˆ s s + ˆ t t + ˆ u u s t u (cid:19) h O J/ψ ( S ) i (cid:21) ,d ˆ σ oct d ˆ t = σ (cid:20) (cid:18) ˆ s s + ˆ t t + ˆ u u s t u (cid:19) h O J/ψ ( S ) i + 6ˆ ss m c (cid:18) s + 3ˆ t ˆ u m c − t ˆ us (cid:19) h O J/ψ ( P ) i + 32 ˆ t ˆ u ˆ ss m c h O J/ψ ( S ) i (cid:21) , (4)In Eqs. (4) we have defined σ = π e c αα s m c / ˆ s (withcharm quark mass m c = 1 . s = ˆ s − m c , t = ˆ t − m c , and u = ˆ u − m c . In these formulae,ˆ s , ˆ t , and ˆ u are the Mandelstam variables, which can bewritten asˆ s = x x s, ˆ t = m ψ − x √ sm T e y , ˆ u = m ψ − x √ sm T e − y . In our numerical calculations the one loop expressionfor the running coupling, α s ( µ R ), with Λ QCD = 0 . n f = 4 is considered. The (renormalization and fac-torization) scale for the strong coupling and for the eval-uation of PDFs is µ F = µ R = ( p T + m ψ ), where m ψ isthe J/ψ mass. For numerical values of the NRQCD ma-trix elements we have used those from Ref. [23], whichare (units of
GeV ): h O J/ψ ( S ) i = 1 . h O J/ψ ( S ) i =1 . × − , h O J/ψ ( S ) i = h O J/ψ ( P ) i /m c = 0 .
01. Wehave checked that using another set of color octet matrixelements, taken from [5], our results do not change con-siderably, since we only calculate the ratio between theproduction cross sections, and the dependency on thecolor octet matrix elements cancels out in those ratios.In what follows we estimate the differential cross sectionsfor central ( y = 0) and forward ( y = 2) rapidities for the pp , pA and AA collisions in order to compute the nu-clear modification factors. From Eq. (1), it implies that the differential cross section at small values of the J/ψ transverse momentum in pP b (and
P bP b ) collisions atthe LHC is determined by the behavior of the nucleargluon distribution at x > ∼ − . It is important to em-phasize that smaller values of x contribute at J/ψ + γ production in the forward rapidity region which can bemeasured, e.g., with the CMS and ALICE experimentsat LHC.The main input in the calculations of J/ψ + γ cross sec-tions is the nuclear parton distribution function (nPDF).Over last years several groups has proposed parameter-izations for the nPDFs [24–28], which are based on dif-ferent assumptions and techniques to perform a globalfit of different sets of data using the DGLAP evolutionequations. These parameterizations predict very distinctmagnitudes for the nuclear effects. For larger values of x , the EKS and the EPS nPDFs show antishadowing,while this effect is absent for the HKN and DS parame-terizations in the x ≤ − domain. While the nuclearshadowing is moderate for DS and HKN parameteriza-tions and somewhat bigger for EKS one, the EPS predic-tion has a much stronger suppression compared with theother parameterizations. For smaller x around x ≃ − ,while DS and HKN parameterizations have about 20%suppression and EKS one have about 40% suppression,for the EPS parameterization this effect goes to almost80% suppression in the nuclear gluon compared with the A scaled gluon content in the proton.In what follows we calculate the quarkonium produc-tion in association with a direct photon in pA and AA collisions, considering the nuclear parton distributionsdiscussed above. We then estimate the nuclear modi-fication factor for these predictions. These factors couldbe measured at the LHC and we analyze the transversemomentum dependence of them. Since the full NLO cal-culation of J/ Ψ(Υ) + γ including the COM contributionsis not available yet, and for the sake of simplicity, the cal- p T (GeV) R AA DSEKSHKNEPS 5 10 15 20 25 30 p T (GeV) y=0 y=2 FIG. 2: Transverse momentum dependence of the nuclear modification factor R AA in J/ψ + γ production in central and forwardrapidities at the LHC ( √ s = 5 . culation of the cross sections is here done at LO accuracy.In order of to be consistent, we consider only the LO ver-sion of the nPDFs employed (besides, the EKS nPDF isonly evolved to leading order). As we are calculating ra-tios between cross sections, common uncertainties on thenormalization of the pA , AA and pp cross sections, e.g.due to higher order contributions, are expected to cancelout in the nuclear modification factors.In Fig. 1 we present our estimates for the transversemomentum dependence of the ratio R pA for central andforward rapidities, defined by R pA ≡ dσ ( pA ) dyd p T (cid:12)(cid:12)(cid:12)(cid:12) y = 0 , / A dσ ( pp ) dyd p T (cid:12)(cid:12)(cid:12)(cid:12) y = 0 , , (5)in pA collisions at the LHC ( √ s = 8 . R pA for different nPDF’s. Thedifference between central and forward rapidities for R pA comes from the kinematical x range probed in the twocases. While for central rapidities the values of x areever larger than 10 − , in the forward case the minimumvalue could be 10 − , increasing with p T . Consequently,the effects in the nuclear gluon distribution which con-tribute for the quarkonium production are different in thetwo rapidities. In the p T interval shown in Fig. 1, anti-shadowing effect is not observed as x < .
1. We havethat the nuclear factor is substantially suppressed in theEPS (EKS) case, going down an 0 . − . p T ≃ p T range. Moreover, dif-ferently from the DS and HKN predictions, the EKS andEPS parameterizations lead to a strong transverse mo-mentum dependence. Consequently, the determinationof the magnitude and p T dependence of the this nuclearmodification factor at the LHC could be useful to deter-mine the properties of the shadowing in the gluon distri-bution.The production of J/ψ + γ can also be studied in the collision of two heavy nuclei. In what follows we presentour estimates for the transverse momentum dependenceof the nuclear modification factor R AA for central andforward rapidities defined by R AA ≡ dσ ( AA ) dyd p T (cid:12)(cid:12)(cid:12)(cid:12) y = 0 , / A dσ ( pp ) dyd p T (cid:12)(cid:12)(cid:12)(cid:12) y = 0 , , (6)in AA collisions at the LHC ( √ s = 5 . pA case, we can see in Fig. 2 that the factor R AA isstrongly modified by the shadowing effects. For low p T the suppression is stronger than in the pA case. We cansee an anti-shadowing effect appearing in central rapidityfor EPS and EKS nPDFs in the region of larger p T ≃
30 GeV. Our results indicate that
J/ψ + γ productionwith p T ≤
20 GeV can be used to determine the gluonshadowing effect.The production of Υ(1 S ) + γ can be obtained from theexpression (4) above, by replacing the charm mass andcharge by the bottom ones, m b = 4 . GeV , e b , the J/ψ mass by the Υ(1 S ) mass, and by using the correspond-ing color octet matrix elements. We use the values takenfrom [29], namely (units of GeV ): h O Υ1 ( S ) i = 10 . h O Υ8 ( S ) i = 0 . h O Υ8 ( S ) i = 0 .
136 and h O Υ8 ( P ) i =0. We notice that using the alternative set for thecolor octet matrix elements [29]: h O Υ8 ( S ) i = 0 . h O Υ8 ( S ) i = 0 and 5 h O Υ8 ( P ) i /m b = 0 . R for larger p T ).In Fig. 3 we present our estimates for the transversemomentum dependence of the ratio R pA for central andforward rapidities, in pA collisions at the LHC ( √ s = 8 . S ) + γ . In this case the p T range isextended to 100 GeV, since the distributions tend to beshifted to larger values of p T due to the larger Υ mass,which makes larger values of x to be accessed, and sug-
20 40 60 80 p T (GeV) R pA DSEKSHKNEPS 20 40 60 80 100 p T (GeV) y=0 y=2 FIG. 3: Transverse momentum dependence of the nuclear modification factor R pA in Υ(1 S ) + γ production in central andforward rapidities at the LHC ( √ s = 8 . gests the existence of antishadowing. As in the previouscases the results show distinct behaviors of R pA for dif-ferent nPDF’s. For central rapidities, the EKS and EPSshow antishadowing for larger p T , while this effect is ab-sent for forward rapidities and for the other distributions.For lower p T , the suppression is different for the differentnPDFs, being stronger in the forward case. This effectcould then be used to discriminate among the nuclearPDF’s.The results for the production of Υ(1 S ) + γ in AA collisions are shown in Fig. 4, where we present our re-sults for the transverse momentum dependence of theratio R AA for central and forward rapidities at the LHC( √ s = 5 . pA case. The EPS parameterizationshows the steepest behavior, presenting shadowing (sup-pression) for low p T and antishadowing (enhancement)for larger p T and central rapidities. The EKS has a sim-ilar although less pronounced behavior, and the HKN,which presented an almost flat behavior in the J/ψ case,it now grows steeper. Thus, the HKN versus DS couldbe discriminated at low p T and central rapidities, and athigh p T and forward rapidities. In the forward case, anti-shadowing behavior at high p T tend to be less importantfor the EKS and EPS nPDF’s as p T grows. We concludethat shadowing and antishadowing effects could be testedin different p T and rapidity regions and therefore help indiscriminating among the different nuclear PDF’s.Finally, we discuss qualitatively the results and com-ment on the limitations of present calculations. Let usfirst concentrate on the pA case where cold matter effectsalso play an essential role. At leading order, the differ-ential cross section is simply proportional to the product of gluon densities dσdx dx ( pA → J/ψ + γ ) ∝ g p ( x , Q ) g A ( x , Q ) × δ ( x x s − m ψ ) , where x , are the projectile and target-parton momen-tum fractions. In this kinematics, the nuclear modifi-cation factor reduces to R pA ≃ R Ag ( x ). In our analy-sis above we did not take into account the nuclear ab-sorption. In the framework of the probabilistic Glaubermodel, this effect refers to the probability for the pre-resonant Q ¯ Q pair to survive to the propagation throughthe nuclear medium. Therefore, the J/ψ may be sensi-tive to inelastic rescattering processes in a large nuclei,which spoil the simple relationship between R pA and R Ag .Assuming the factorization between the quarkonium pro-duction process and the subsequent possible J/ψ inelasticinteraction with nuclear matter, we can write the produc-tion cross section as dσdx ( pA → J/ψ + γ ) ∝ S abs ( A, σ
J/ψN ) × dσ prod dx ( pA → J/ψ + γ ) , where S abs denotes the probability for no interaction, orsurvival probability, of the meson with the nucleus target.In a Glauber model it depends on the J/ψ − N inelasticcross section, σ J/ψN , and reads as (for large nucleus): S abs ≃ Aσ J/ψN Z d b (cid:2) − exp (cid:0) − T A ( b ) σ J/ψN (cid:1)(cid:3) , (7)with the thickness function T A ( b ). As σ J/ψN is not wellconstrained from data, this is additional uncertainty en-tering on the nuclear modification factor. In a roughestimation we have R pA ≃ S abs ( A, σ
J/ψN ) R Ag . The cor-responding expression for AA collision can be obtainedusing similar methods. We quote Ref. [30] as an exam-ple where the magnitude of these corrections has beenstudied for the J/ψ production in proton-nucleus andnucleus-nucleus collisions.Concerning nucleus-nucleus collisions, the situation ismore complicated as final state effects can not be disre-garded. For instance, the processes of dissociation andrecombination of c ¯ c pairs in the dense medium can becomputed through the co-movers interaction model [31],which also incorporates also the recombination mecha-nism [32]. As mentioned for pA case, nuclear effects innucleus-nucleus collisions are usually expressed throughthe so-called nuclear modification factor, R J/ψAB ( b ), de-fined as the ratio of the J/ψ yield in AA and pp scaled bythe number of binary nucleon-nucleon collisions, N coll ( b ).A similar factor can be defined in our case of J/ Ψ + γ production, having in mind that the prompt photon isinsensitive to nuclear matter effects. We have then forsymmetric nuclei, R J/ψAA ( b ) = d N J/ψAA / d yN coll ( b ) d N J/ψpp / d y = R d s σ AA ( b ) n ( b, s ) P sup ( b, s ) R d s σ AA ( b ) n ( b, s ) . (8)where σ AA ( b ) = 1 − exp[ − σ pp A T AA ( b )] and T AA ( b ) = R d sT A ( s ) T A ( b − s ) is the nuclear overlapping function.One has that T A ( b ) is obtained from Woods-Saxon nu-clear densities, and P sup ( b, s ) = S shJ/ψ ( b, s ) S abs ( b, s ) S co ( b, s ) , (9) n ( b, s ) = σ pp A T A ( s ) T A ( b − s ) /σ AA ( b ) , (10)where the number of binary nucleon-nucleon collisions atimpact parameter b is given by, N coll ( b ) = R d s n ( s, b ).The three factors appearing in Eq. (9), S sh , S abs and S co , denote the effects of shadowing, nuclear absorption,and interaction with the co-moving matter, respectively.As referred above, the nuclear absorption is usually in-terpreted as suppression of J/ψ yield because of multiplescattering of a c ¯ c pair within the nuclear medium. At lowenergies the primordial spectrum of particles created inscattering off a nucleus is mainly altered by interactionswith the nuclear matter they traverse on the way out tothe detector and energy-momentum conservation (it hasbeen shown that it becomes a minor effect at AA colli-sions at LHC). For nucleus-nucleus collisions these effectscan be combined into the generalized suppression factor S abs = [1 − exp ( − β ( x ) σ c ¯ c AT A ( b ))] β ( x ) β ( x ) σ c ¯ c A T A ( s ) T A ( b − s ) × [1 − exp ( − β ( x ) σ c ¯ c AT A ( b − s ))] , (11)where x , = ( p x − M /s ± x F ) /
2, and β ( x , ) =(1 − ǫ ) + ǫx γ , determines both absorption and energy-momentum conservation. The parameters γ , ǫ and σ c ¯ c can be adjusted to describe collider data. Secondly, co-herence effects will lead to nuclear shadowing for both soft and hard processes and therefore for the productionof heavy flavor. Shadowing factor S shJ/ψ ( b, s ) can be cal-culated within the Glauber-Gribov theory, and here it isalready included in the nuclear PDF ratios.The final state effects can be addressed taking, for ex-ample, the co-movers interaction model [32]. Assuming apure longitudinal expansion and boost invariance of thesystem, the rate equation which includes both dissocia-tion and recombination effects for the density of charmo-nium at a given production point at impact parameter s reads dN J/ψ ( b, s, y ) dτ = − σ co τ h N co ( b, s, y ) N J/ψ ( b, s, y ) − N c ( b, s, y ) N ¯ c ( b, s, y ) i , (12)where N co , N J/ψ and N c (¯ c ) is the density of comovers, J/ψ and open charm, respectively, and σ co is the inter-action cross section for both dissociation of charmoniumwith co-movers and regeneration of J/ψ from c ¯ c pairsin the system averaged over the momentum distributionof the participants. It is the constant of proportionalityfor both the dissociation and recombination terms dueto detailed balance N J/ψ N co = N c N ¯ c . The solution ofEq. (12) can be approximated by S co = exp (cid:26) − σ co (cid:2) N co ( b, s, y ) − N sh ( b, s, y ) (cid:3) ln (cid:20) N co N pp (0) (cid:21)(cid:27) ,N sh = (cid:0) dσ c ¯ cpp (cid:14) dy (cid:1) σ NDpp dσ J/ψpp (cid:14) dy N bin ( b, s ) S shad ( b, s, y ) . (13)Details of the model can be found in [32] and the quan-tities in Eq. (13) are all related to pp collisions at thecorresponding energy and should be taken from exper-iment (the extrapolation for LHC is quite uncertain).The magnitude of recombination effect is controlled bythe total charm cross section in pp collisions and thendissociation-recombination effects will be of crucial im-portance in PbPb collisions at LHC.At this stage is difficult to single out the size of eachcontribution at the LHC for the J/ Ψ (Υ) + γ . For suchphoton-associated high- p T quarkonium production, thefinal production cross section is modified by nuclearabsorption, or final-state interaction between the pre-resonance state and the nuclear medium as discussedabove. Notice that the Glauber absorption model is onlyvalid for total production cross section which is domi-nated by low- p T quarkonium production. Here, we fo-cus on the transverse momentum dependence of the nu-clear modification factor due to gluon shadowing and itis timely to discuss the p T dependence of the final-stateinteraction. To address this issue, we can do an educatedguess by verifying what we learn from RHIC. The mod-ification factor R J/ψAA has been determined as a functionof p T in the central rapidity region, analyzed both by thePHENIX [33] and STAR [34] collaborations. The fac-tor increases with p T and STAR data indicate a nuclearmodification factor larger than one for p T ≈
20 40 60 80 p T (GeV) R AA DSEKSHKNEPS 20 40 60 80 100 p T (GeV) y=0 y=2 FIG. 4: Transverse momentum dependence of the nuclear modification factor R AA in Υ(1 S ) + γ production in central andforward rapidities at the LHC ( √ s = 5 . If this non-suppression of
J/ψ at large p T is confirmed itdoes not seem to behave as the other hadrons, which aresignificantly suppressed in central collisions and for in-creasing p T . This behavior is closer to the one observedin prompt photons production. In the case of quarko-nium plus a prompt photon, we then would expect thesame non-suppresion pattern, since the hard photon isnot affected by nuclear matter effects.As a final comment, we notice that the present calcula-tion can be also extended for the RHIC kinematic region,where the q ¯ q annihilation processes could also contribute.For instance, a study has been done in Ref. [35] for theinclusive J/ψ production in pp collisions at RHIC withinthe PHENIX detector acceptance range using the colorsinglet and the color octet mechanisms based on NRQCDformalism. The calculations reproduce the RHIC datawith respect to the p T distribution, the rapidity distri-bution and the total cross section at √ s = 200 GeV. InRef. [30], the authors have considered the CSM approach(taking into account the s -channel cut contributions [36])and cold nuclear matter effects to compute the J/ψ nu-clear modification factor for dAu and
AuAu/CuCu col-lisions at RHIC energies. The data description is quitesatisfactory. Therefore, this indicates the robustness ofthe framework in describing the high energy data. Ofcourse, we are aware of the limitations of present calcula-tion. The picture of a
J/ψ exactly recoiling back to backwith the photon is simplified, since possible contributionsof the color-octet channel would lead to a fragmentationof the gluon into the meson, which would not be exactlyrecoiling against the photon. The experimental detectioncould be an additional concern. For example, ALICE [37]can tag the muons in the forward region, where howeverthere is no photon reconstruction, while it can detect the photons in the central region, where however the muondetection is not as good. In the case of CMS [38], thethresholds in p T both for muons and for the photon ap-pear quite low to ensure an efficient triggering.In summary, in this letter we have investigated thequarkonium production in association with a isolatedphoton in pA and AA collisions at the LHC, consideringthe NRQCD factorization formalism and some of the pa-rameterizations for the nuclear parton distributions avail-able in the literature. Our results show that the nuclearmodification factors R pA and R AA are useful observablesto discriminate among the different parton distributionsin the nuclear medium. In particular, the predicted shad-owing by the EPS parameterization is considerably largerthan in the previous nuclear PDF’s. The nuclear effectsare different at central and at forward rapidities, so mea-suring the nuclear production of J/ψ + γ and Υ + γ inthese two regions could give additional insights about thecorrect nuclear gluon distribution. These complemen-tary observables to the inclusive production are usefulto shed light on quarkonium production where the lackof a good benchmark, both for proton-proton collisions,where the actual mechanism of quarkonium productionis not known, and proton-nucleus collisions where the rel-ative magnitude of the different effects (shadowing, nu-clear absorption) cannot be fixed by present experimentaldata. Acknowledgments
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