---

Nuclear Gluon Distributions in a Parton Model

arXiv:hep-ph/9301262v1 22 Jan 1993IU/NTC 92 −21October 5, 1992Nuclear Gluon Distributions in a Parton ModelS. Kumano∗Nuclear Theory Center, Indiana University2401 Milo B. Sampson LaneBloomington, Indiana 47408-0768, U.S.A.ABSTRACTGluon distributions in the carbon and tin nuclei are investigated by using a Q2 rescalingmodel with parton recombination effects.

We obtain strong shadowings in the small xregion due to the recombinations.The ratio GA(x)/GN(x) in the medium x region istypically 0.9 for medium size nuclei. At large x, the ratio becomes large due to gluonfusions from different nucleons.

Comparisons with recent New Muon Collaboration datafor GSn(x)/GC(x) indicate that more accurate experimental data are needed for testingthe model. * present address: Institut f¨ur Kernphysik, Universit¨at Mainz, 6500 Mainz, Germany.submitted to Phys.

Lett. B

Recent measurements of gluon distribution ratios GSn(x)/GC(x) by New Muon Col-laboration (NMC) [1] are the first data which could shed light on gluon distributions innuclei [2].Modifications of the structure function F2(x) in nuclei were discovered by EuropeanMuon Collaboration (EMC effect) [3]. This effect has been an interesting topic in the sensethat it may provide an explicit quark signature in nuclear phenomena.

On the contrary,“gluonic EMC effect” is little known. Gluon distribution functions in the nucleon [4] havebeen investigated by using muon (electron, or neutrino) deep inelastic scattering data [5,6],direct photon data [7,8], and muon induced J/ψ production data [9,10].

Although there aresome theoretical predictions [11,12,13,14] for gluon distributions in nuclei, we have littleexperimental data. There are direct photon data for proton reactions with nuclear targets[15,16]; however, there is no available large pT data in the WA80 case [15].

Accuracy isnot good enough for extracting a gluon distribution function of the beryllium (Be) nucleusfrom the E706 data [16]. In any case, we do not expect much modification of the gluondistribution in light nuclei such as Be.The NMC analyzed inelastic J/ψ production data by a color singlet model [17] andobtained gluon distribution ratios GSn(x)/GC(x) [1].

These are interesting data whichindicate modifications of the gluon distribution in nuclei. We should note that it is veryimportant to know the gluon distributions in nuclei.

For example, J/ψ suppressions inheavy-ion collisions were proposed as a signature of quark-gluon plasma [18]. Althoughother initial and final state interactions may explain the J/ψ suppression phenomena, it isimportant that initial conditions as local (gluonic) EMC effects [19] should be subtractedout for investigating the physics origin of the suppressions [20].

Such issues have not beenwell studied yet because there is little data for gluon distributions in nuclei.As a model for explaining the EMC effect, we take a Q2 rescaling model [21] andapply it for the gluon distribution. The model was proposed originally for the structurefunction F2(x) by considering the possibility that an effective confinement radius for quarksis changed in a nuclear environment.

In fact, strong nucleon overlaps are expected in nucleiby noting the fact that the nucleon diameter is approximately equal to the average nucleonseparation in nuclei. From this confinement-radius change and the Q2 evolution equation,2

the Q2 rescaling model was proposed [21]. In this research, we use the above simple picturealso for gluons.

Namely, the nuclear gluon distribution function in the rescaling model isgiven by GA(x, Q2) = GN(x, ξAQ2), where ξA is called as the rescaling parameter.Other new features which exist if a nucleon resides in a nucleus are parton recombina-tions (fusions). The mechanism has been investigated for explaining the shadowing regionF2(x < 0.1) in parton models [11,12,22].

The recombinations also have important effectson the gluon structure function due to processes shown in Fig. 1.

We find that there arestrong shadowings in the small x region (x < 0.05) and strong anti-shadowings in themedium x region [12]. In Ref.

22, it was shown that a model of the Q2 rescaling withthe recombination can explain experimental data of F2(x) fairly well in the wide x region(0.005 < x < 0.8).In this report, the gluonic EMC effect is investigated by the Q2 rescaling modelcombined with the parton recombinations in Ref. 22.

Using this model we calculate gluondistributions in the carbon (C) and tin (Sn) nuclei. Results in our model are comparedwith the recent NMC ratios GSn(x)/GC(x).In order to investigate recombination effects, we calculate contributions to G(x) fromprocesses in Fig.

1 as investigated by Close, Qiu, and Roberts [12]. For example, a gluonwith momentum fraction x is produced by a fusion of gluons from the nucleon 1 and 2.

Amodification of a parton distribution p3(x3), due to the process of producing the partonp3 with the momentum fraction x3 by a fusion of partons p1 and p2, is given by [12,22]∆p3(x3) = KZdx1dx2 p1(x1) p2(x2) Γp1p2→p3(x1, x2, x3 = x1 + x2) δ(x, x1, x2) , (1)where K is given by K = 9A1/3αs/(2R20Q2) with R0=1.1 fm and the strong-interactioncoupling constant is αs(Q2) = 4π/[9 ln(Q2/Λ2)]. The δ function is given by δ(x −x1 −x2)for the processes in Figs.

1a, 1d, and 1e and δ(x −x1) for Figs. 1b, 1c, 1f, 1g, 1h, and1i.

The parton fusion function Γ(x1, x2, x3) is a probability for producing a parton p3with momentum fraction x3 by a fusion of partons p1 and p2 with momenta x1 and x2respectively.Now, we discuss numerial analysis. In evaluating recombination contributions ∆G(x)by using Eq.

(1) [23], we assume that a leak-out parton (we denote p∗(x)) is a sea quark3

or a gluon and that the momentum cutofffunction [12,24] for this parton is taken asw(x) = exp(−m2Nz20x2/2) with z0=0 or 2 fm. Then, distributions for the leak-out partonsare q∗(x) = w(x)qsea(x), ¯q∗(x) = w(x)¯q(x), and G∗(x) = w(x)G(x).Input partondistributions are given by a recent parametrization in Ref.

4. Q2 = 5 GeV2 is used in theparametrization and for calculating K in Eq.

(1). The QCD scale parameter Λ in αs(Q2)is taken as Λ=0.2 GeV.

In our theoretical analysis, targets nuclei are assumed as 12C or118Sn. The rescaling parameters for these nuclei are taken from Ref.

21, and they areξA(C)=1.60 and ξA(Sn)=2.24.Before discussing the gluon distributions in C and Sn, we first check that our modelcan explain structure functions F A2 (x) of these nuclei. As shown in Ref.

22, our results areconsistent with SLAC, EMC, and E665 experimental data for F A2 (x) of C, Ag, Sn, and Xenuclei in the wide x range (0.005 < x < 0.8). In explaining these data, the most importantfactor is the gluon shadowing.

Taking modified parton distributions due to the recombina-tions at small Q2, we should calculate distributions at large Q2, where the structure func-tions were measured. Instead of solving the evolution exactly, we simply used a solution[25] for the Altarelli-Parisi equation in the small x region (xδqseai(x) = −x12∂∂x[x∆G(x)],where i=u, d, or s).

This approximate way of treating the evolution violates the momen-tum conservation even though it is satisfied in the recombinations. The effect due to thisextra term is given by 6Zdx x δqseai(x)= +12 limx→0 x2∆G(x) + 12Zdxx∆G(x).

The firstterm vanishes if the input gluon distribution satisfies, for example, limx→0 xG(x) =constant.Dominant contributions to ∆G(x) come from the gluon-gluon fusion processes; however,they satisfy the momentum conservation by themselves (Rdxx∆GGG→G(x) = 0). There-fore, the violation is a small effect due to q¯q →G, Gq →q, and G¯q →¯q processes.

Anumerical evaluation for the Ca nucleus indicates that such violation effect is less than 1%(6Rdxxδqseai(x) = −0.005); hence it is not a serious effect on the momentum conservation.Using our model, which can explain at least the structure function F A2 (x), we predictGC(x) and GSn(x). We take the same rescaling parameter for all partons by taking anaive consideration that the confinement radius change modifies all parton momenta atthe same rate.

Predicted gluon distributions for C and Sn are shown in Figs. 2a and 2b.4

In these figures, the dashed curves are recombination effects shown byRA(recombination) = 1 + ∆GA(x, Q2)GN(x, Q2),(2)∆GA(x, Q2) is calculated by using Eq. (1) (note that no Q2 rescaling is used) and explicitexpressions are given in Ref.

22. Solid curves are combined contributions from the rescalingand recombinations and they are shown by the ratioGA(x, Q2)GN(x, Q2)=˜GA(x, Q2) + ∆˜GA(x, Q2)GN(x, Q2).

(3)In these equations, ˜GA(x, Q2) and ∆˜GA(x, Q2) are given by the rescaling model, ˜GA(x, Q2)=GN(x, ξAQ2) and ∆˜GA(x, Q2) = ∆G(x, ξAQ2). The recombination mechanism producesstrong shadowing effects in the small x region due to gluon-gluon and gluon-quark fusionprocesses in Fig.

1. In the medium-large x region, contributions are dominated by thegluon-gluon fusion process in Fig.

1a. It is interesting to note in our model that gluondistributions at x > 1 could be produced in the fusion process.

This is the reason whythe ratio goes to infinity at x →1 in Figs. 2a and 2b.

The Q2 rescaling contributions areopposite to the recombination. The rescaling effects are positive in the small x region andare negative in the medium-large x region.

Combined contributions shown by the solidcurves in Figs. 2a and 2b indicate strong shadowings in the very small x (x < 0.02) region,depletions (0.8−1.0) in the medium x (0.2 < x < 0.6), and large ratios in the large x(x > 0.7).In investigating shadowings in F2(x) in Ref.22, we used the rescaling for partondistributions at x < 0.1.

Although the rescaling produces large positive contributions,they are counterbalanced by the large shadowings produced through gluon distributions(δF2 in Ref. 22).

Therefore, combined contributions are not very dependent (about 5%differences) whether or not the rescaling is used in the region (0.005 < x < 0.1). On thecontrary, gluon distributions at small x are very sensitive to whether or not the rescalingis used as shown in Figs.

2a and 2b. If there is no rescaling at x < 0.1, we should havestrong gluon shadowings in the region x < 0.1 as shown by the dashed curves.

However,if the rescaling is used, gluon distributions are shadowed only in the very small x region(x < 0.02) as shown by the solid curves.5

The nuclear gluon distributions in the medium-large x region are very sensitive to themomentum cutoffas shown in Figs. 2a and 2b.

For example, GSn(x)/GN(x) = 1.02 (forz0 = 0) at x = 0.4, but it is 0.87 if z0 = 2 fm. Because GN(x) itself is very small atx = 0.4, it may seem to be an insignificant problem.

However, it is important for describinge.g. pT dependence of J/ψ in heavy-ion collisions.

The rapid increase of GA(x)/GN(x)in the medium x region could be responsible for the pT dependence of J/ψ suppressionsobserved by NA38 [26], although the pT slope obtained in the local gluonic EMC effect israther small [20] compared with the NA38 data at this stage. The gluon distributions atthe medium x are so sensitive to the momentum cutoffw(x) that we need to study moreabout the cutoff[24].

We leave the problem of the cutoffas a future research topic.Calculated gluon distributions are compared with the NMC data for GSn(x)/ GC(x)[1] in Fig. 3.

The dashed curve shows recombination results with z0=0 and the solid(dash-dot) curve shows combined results of the Q2 rescaling and the recombinations withz0=0 (z0 = 2 fm). Our theoretical results shown by the solid and dash-dot curves indicateratios GSn(x)/GC(x) < 1 at x < 0.03 due to the gluon shadowing.The ratios areabout 1.03 in the region (0.05 < x < 0.20) and are dependent on the momentum cutoffw(x) in the medium x (x > 0.2).

We notice that experimental errors are very large incomparison with typical theoretical modifications. Because our model predictions for themodifications are less than 5% in the range 0.05 < x < 0.2, we need accurate data betterthan 5% accuracy in order to test the model.

Because the NMC data for GSn(x)/GC(x)are not accurate enough, we should wait for better measurements of GA(x), for examplea proposed experiment at RHIC [27], in the small x region for investigating details ofthe gluon shadowing. It is also important to know gluon distributions in the medium xregion (0.3 < x < 0.6), although distributions themselves are very small, for studyingJ/ψ productions in heavy-ion collisions [20].In summary, we investigated gluon distributions in the nuclei C and Sn by the rescalingmodel with parton recombinations effects.

We obtained shadowings in the nuclear gluondistributions in the small x region due to the recombinations and depletions [typicallyGA(x)/GN(x) ∼0.9] in the medium x region. The ratio GA(x)/GN(x) becomes largeat x > 0.6 due to gluon fusions from different nucleons.

The ratio in the medium-largex region is very sensitive to the momentum cutofffor leak-out partons in our model.6

Comparisons with the NMC data indicate that more accurate experimental data are neededfor testing the model.This research was supported by the NSF under Contract No. NSF-PHY91-08036.

S.K.thanks Drs. F. E. Close, J. Qiu, and R. G. Roberts for discussions and suggestions aboutparton recombinations and direct photon experiments; Drs.G.

K. Mallot and G. vanMiddelkoop for discussions about the J/ψ production experiment by NMC; Drs. T. C.Awes and S. P. Sorensen for communications about WA80 and RHIC experiments.7

References1. P. Amaudruz et al., (NMC collaboration), Nucl.

Phys. B371, 553 (1992); M. deJong, Ph.D thesis, Free University of Amsterdam (1991).2.

For recent J/ψ production experiments for nuclei, see D. M. Alde et al. (E772collaboration), Phys.

Rev. Lett.

66, 133 (1991).3. J. J. Aubert et al.

(EMC collaboration), Phys.Lett 123B, 275 (1983); forsummaries, see E. L. Berger and F. Coester, Annu. Rev.

Nucl. Part.

Sci. 37,463 (1987); R. P. Bickerstaffand A. W. Thomas, J. Phys.

G 15, 1523 (1989).4. For recent parametrizations of parton distributions, see P. N. Harriman, A. D.Martin, W. J. Stirling, and R. G. Roberts, Phys.

Lett. 243B, 421 (1990); Phys.

Rev.D42, 798 (1990); J. Kwiecinski, A. D. Martin, W. J. Stirling, and R. G. Roberts,Phys.Rev.D42, 3645 (1990); the KMRS-B0 parametrization is used for inputparton distributions in this investigation.5. M. Gl¨uck, E. Hoffmann, and E. Reya, Z. Phys.

C13, 119 (1982).6. F. Bergsma et al.

(CHARM collaboration), Phys. Lett.

123B, 269 (1983); A. C.Benvenuti et al. (BCDMS collaboration), Phys.

Lett. 223B, 490 (1989).7.

M. Bonesini et al. (WA70 collaboration), Z. Phys.

C38, 371 (1988) and referencestherein.8. E. N. Argyres, A. P. Contogouris, N. Mebarki, and S. D. P. Vlassopulos, Phys.

Rev.D35, 1584 (1987); P. Aurenche, R. Baier, M. Fontannaz, J. F. Owens, and M. Werlen,Phys. Rev.

D39, 3275 (1989).9. D. Allasia et al.

(NMC collaboration), Phys. Lett.

258B, 493 (1991).10. C. S. Kim, Nucl.

Phys. B353, 87 (1991); M. Dress and C. S. Kim, Z. Phys.

C53,673 (1992).11. A. H. Mueller and J. Qiu, Nucl.

Phys. B268, 427 (1986); J. Qiu, Nucl.

Phys. B291,746 (1987).12.

F. E. Close, J. Qiu, and R. G. Roberts, Phys. Rev.

D40, 2820 (1989).8

13. L. L. Frankfurt and M. I. Strikman, Phys.

Rev. Lett.

65, 1725 (1990).14. J. Kwiecinski, Z. Phys.

C45, 461 (1990); J. Collins and J. Kiecinski, Nucl. Phys.B335, 89 (1990).15.

R. Albrecht et al. (WA80 collaboration), Phys.

Lett. 201B, 390 (1988); Z. Phys.C51, 1 (1990).16.

G. Alverson et al. (E706 collaboration), Phys.

Rev. Lett.

68, 2584 (1992).17. E. L. Berger and D. Jones, Phys.

Rev. D23, 1521 (1981); A. D. Martin, C. K. Ng,and W. J. Stirling, Phys.

Lett. 191B, 200 (1987).18.

T. Matsui and H. Satz, Phys. Rev.

178B, 416 (1986).19. S. Kumano and F. E. Close, Phys.

Rev. C41, 1855 (1990).20.

S. Kumano, Indiana University preprint IU/NTC92-02; talk given at the 13thInternational Conference on Few Body Problems in Physics, Adelaide, Australia,Jan. 5−11, 1992; in Proceedings of the International Workshop on Gross Propertiesof Nuclei and Nuclear Excitations, Hirschegg, Austria, Jan. 20−25, 1992, edited byH.

Feldmeier; to be submitted for publication.21. F. E. Close, R. G. Roberts, and G. G. Ross, Phys.

Lett. 129B, 346 (1983); Nucl.Phys.

B296, 582 (1988); F. E. Close, R. L. Jaffe, R. G. Roberts, and G. G. Ross,Phys. Rev.

D31, 1004 (1985).22. S. Kumano, preprint IU/NTC92-20 (1992), submitted to Phys.

Rev. C.23.

For evaluating the modifications ∆G(x), see comments in the appendix of Ref. 22.24.

C. H. Llewellyn Smith, Nucl. Phys.

A434, 35c (1985).25. J. P. Ralston, Phys.

Lett. 172B, 430 (1986).26.

M. C. Abreu et al. (NA38 collaboration), Z. Phys.

C38, 117 (1988).27. P. Braun-Munzinger and G. David, in Proceedings of the International Workshop onGross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria, Jan. 20−25,1992, edited by H. Feldmeier.9

Figure Captions1. Modifications of G(x) due to parton recombinations.2.

Predicted gluon distributions in the nuclei (a) C and (b) Sn. The dashed curvesindicate parton recombination effects (Eq.

(2)) and the solid curves are combinedresults (Eq. (3)) of the recombination and the Q2 rescaling.

ξA=1.60 for C and 2.24for Sn.3. Comparisons of our theoretical results with NMC data [1].

The dashed curveindicate parton recombination effects with z0=0 and the solid (dash-dot) curve showscombined results of the recombination and the Q2 rescaling with z0=0 (z0=2 fm).10

---

출처: arXiv:9301.262 • 원문 보기