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Nuclear modification of forward Drell-Yan production at the LHC B. Ducloué University of Jyväskyla¨, Department of Physics, P.O. Box 35, FI-40014 University of Jyva¨skylä, Finland and Helsinki Institute of Physics, P.O. Box 64, FI-00014 University of Helsinki, Finland ForwardDrell-Yanproductionathighenergycanprovideimportantconstraintsongluondensities at small x, in the saturation regime. In this work we focus on the nuclear modification of this process, which could be measured at the LHC in the near future. For this we employ the color dipole approach, using the optical Glauber model to relate the dipole cross section of a nucleus to the one of a proton. Combining these results with our earlier results for forward J/ψ production, wecomputetheratioofthenuclearmodificationfactorsofthesetwoprocesses. Thisobservablewas recently suggested as a way to distinguish between initial and final state effects in forward particle production. 7 1 I. INTRODUCTION parisonoftheseresultswithfuturemeasurementsofthis 0 observablewouldprovideanadditionaltestforthesecor- 2 relators which have been shown to lead to a rather good n Particle production at forward rapidity in high energy agreementwithexperimentaldataonthenuclearmodifi- a proton-protonandproton-nucleuscollisionshasbeenthe cationofsingleinclusiveforwardhadron[1]andJ/ψ[2,4] J subject of numerous studies aiming at improving our production. Such a measurement could be performed at 0 understanding of saturation dynamics. Indeed, these theALICEorLHCbexperimentsattheLHCinthenear 3 processes probe the target proton or nucleus at very future. small x which is where saturation effects should be en- ] h hanced. Two important examples of such processes are p light hadron and quarkonium production, for which it II. FORMALISM - p was shown that saturation could provide an explanation e for the nuclear suppression observed at the LHC [1–4]. The study of the Drell-Yan process in the color dipole h However, these processes are also sensitive to fragmen- approach has been the subject of many theoretical and [ tation and final state effects. In this respect, Drell-Yan phenomenologicalworks,seeforexampleRefs.[6–19]. In 1 production appears as a much cleaner probe of initial this formalism, the physical picture is the following: a v state effects in hadronic collisions. In particular, it was collinear quark emitted by the projectile proton can ra- 0 recently suggested that the ratio of the nuclear modifi- diate a virtual photon either before or after interacting 3 cation factors of J/ψ and Drell-Yan production could be withthedensecolorfieldofthetarget. Thisvirtualpho- 7 usedasawaytodistinguishbetweenvariousapproaches, tonthendecaysintoadileptonpair. Thesetwocontribu- 8 based on either initial or final state effects, that can de- tions are shown in Fig. 1. In collinear factorization, con- 0 scribe the rapidity dependence of the nuclear modifica- tributionswherethegluondensityofthetargetisprobed . 1 tion of forward J/ψ production at the LHC [5]. There- starttoappearonlyatnext-to-leadingorder(seeFig.2). 0 fore, one of the main motivations of the present work is However, in the kinematics considered here these contri- 7 to make predictions for this observable in the saturation butionsareenhancedbythestrongriseofgluondensities 1 : approach. Forthis,wewillfirststudythenuclearmodifi- at small x. Using similar notations as in Ref. [13], the v cationofforwardDrell-YanproductionattheLHCusing dilepton pair production cross section can be written, in i X the dipole correlators introduced in Ref. [1]. The com- the limit of massless quarks, as r a dσ = αe2m (cid:90) 1dα(cid:88)e2(cid:104)q (cid:16)x1,Q2(cid:17)+q¯ (cid:16)x1,Q2(cid:17)(cid:105)(cid:20)2M2(1−α)2(cid:18) I1 − I2(cid:19) (1) dYdM2d2P d2b 3π3M2 α f f α f α P2 +ε2 4ε ⊥ ⊥ x1 f ⊥ (cid:18) (cid:19)(cid:21) εP I I εI +[1+(1−α)2] ⊥ 3 − 1 + 2 , P2 +ε2 2 4 ⊥ where Y, M and P are respectively the rapidity, in- parameter and ε2 =(1−α)M2. I , I and I read 1 2 3 variant mass and tra⊥nsverse momentum of the dilepton (cid:112) √ (cid:90) pair, x1 = P⊥2 +M2eY/ s, b⊥ is the target’s impact I1 = 0∞drrJ0(P⊥r)K0(εr)Nx2(αr,b⊥), (cid:90) I = ∞drr2J (P r)K (εr)N (αr,b ), 2 0 0 ⊥ 1 x2 ⊥ (cid:90) ∞ I = drrJ (P r)K (εr)N (αr,b ). (2) 3 0 1 ⊥ 1 x2 ⊥ 2 Figure 2. Lowest order contributions probing the gluon density of the target in collinear factorization. Figure 1. Diagrams contributing to Drell-Yan production in the color dipole approach. with running coupling corrections [20–22]. In the case of a proton target, the initial condition at x = 0.01 is 0 The description of the projectile proton in terms of parametrized as collinear quark distributions q is justified by the fact f tithaistptrhoebleodngisitnuodtinvaelrymsommaelnltautmfofrrwaacrtdionraxp1id/iαtya.tOwnhtihche Sxp0(r⊥)=exp(cid:20)−r⊥24Q2s0 ln(cid:18)|r |Λ1QCD+ec·e(cid:19)(cid:21), other hand, the target is probed at very small x2 and it ⊥ (7) can thus be described in terms of classical color fields. and it is assumed that there is no impact parameter de- The information about its gluon density is contained in pendence in S, therefore when computing proton-proton thedipolescatteringamplitudeN,whichisrelatedtoS, cross sections we make the replacement the fundamental representation dipole correlator in the (cid:90) color field of the target: σ d2b → 0 , (8) ⊥ 2 N(r =x −y )=1−S(x −y ) (3) ⊥ ⊥ ⊥ 1 (cid:10)⊥ ⊥ (cid:11) where σ0/2 is the effective proton transverse area. The =1− TrU (x )U(y ) , † running coupling in coordinate space is taken as Nc ⊥ ⊥ 12π iwnhtehreeUco(lxo⊥r)fiiesldafoufntdhaemteanrtgaelt.reIpnreRseenf.ta[t1i3o]n, xW2ilissotnalkinene αs(r)= (33−2Nf)log(cid:16)r24ΛC22 (cid:17). (9) as QCD (cid:112) AfitofthefreeparametersintheseexpressionstoHERA P2 +M2 x = √ e Y ≡xmin . (4) DIS data [23] leads to Q2 = 0.060 GeV2, C2 = 7.2, 2 ⊥ s − 2 s0 e = 18.9 and σ /2 = 16.36 mb [1]. Because of the c 0 lack of accurate nuclear DIS data at small x a similar A more detailed treatment of the kinematics taking into fit cannot be performed for a nuclear target. To extrap- account the unobserved outgoing quark leads to olate the proton dipole correlator to a nucleus, we use, (cid:112)P2 +M2 (cid:18) α q2 (cid:19) as in Ref. [1], the optical Glauber model. In this model, x2 = ⊥√s e−Y 1+ 1−α P2 +⊥M2 , (5) the probe coming from the projectile proton is supposed to scatter independently off the target nucleons at the ⊥ initial rapidity and, after averaging over the fluctuating where q is the transverse momentum of the outgoing quark. ⊥Therefore (4) is strictly speaking the minimal positions of the nucleons in the nucleus, we get valueallowedforx . Ontheotherhand,itisnotpossible 2 (cid:20) σ r 2Q2 otoveursteo(a5r)ridviereacttlEyqs.in(c1e).qT⊥oheasstiamlraetaedtyhebeiemnpionrtteagnrcaeteodf SxA0(r⊥,b⊥)=exp −ATA(b⊥) 20 ⊥4 s0 the choice of x2, we will use both (4) and an effective (cid:18) 1 (cid:19)(cid:21) ×ln +e ·e , (10) value |r |Λ c QCD ⊥ (cid:112)P2 +M2 (cid:18) α P2 +Q2 (cid:19) x2 = ⊥√s e−Y 1+ 1−α P2⊥+Ms2 ≡xe2ff , wfuhnecrteionT,A is the standard nuclear transverse thickness ⊥ (6) (cid:90) where Q is the saturation scale of the target (we use n s TA(b )= dz (cid:20)√ (cid:21) , (11) ti.hee. Qsasmies ddeefifinneitdioansothfethseolsuattiuonraotifoNn (srca2le=a2s/iQn2sR)e=f.1[1−], ⊥ 1+exp b⊥2+dz2−RA e 1/2). TheexpressioninEq.(6)ismoti⊥vatedbythefact − thatonaveragethetotaltransversemomentumprovided with d = 0.54fm and R = (1.12A1/3 −0.86A 1/3)fm. A − bythetargetshouldbeoftheorderofitssaturationscale. Here n is fixed so that the distribution is normalized to In this work we use the dipole correlators introduced unity. The other parameters in Eq. (10) take the same inRef.[1]. Therapidity(orx)evolutionofS isobtained values as in the case of a proton target. Because S now by solving numerically the Balitsky-Kovchegov equation depends on b we integrate explicitly Eq. (1) over the ⊥ 3 dσDY wasshowntobeaccessibleexperimentallyatLHCb[24]. [pb] dY The effect of using either the definition (4) or (6) for x as well as varying the factorization scale Q between 2 1000 M/2 and 2M is shown as an uncertainty band. We use theleadingorderMSTW2008parametrization[25]tode- scribethequarkdensitiesintheprojectileproton,taking into account the three light flavors. 500 In Fig. 3 we show the proton-proton cross section as a functionofrapidityintegratedoverP upto15GeV.We observearatherlargeuncertaintydu⊥ebothtothechoice of x and Q. In particular, different choices for Q can 2 P <15GeV lead to different trends: while the choice Q=M/2 leads 0 ⊥ Y 2 3 4 5 toagenerallyincreasingcrosssectionasafunctionofY, the other extreme choice Q = 2M leads to a generally Figure3. Proton-protoncro√sssectionasafunctionofrapidity decreasing cross section. This is due to the behavior of at a center of mass energy s=8 TeV. quark densities in the projectile. In Fig. 4 we also show the P spectrum in proton-proton collisions integrated dσDY over r⊥apidity in the range 2<Y <4.5. dP [pb.GeV−1] While the absolute cross section can be quite sensitive 1000 ⊥ to scale variations, the nuclear modification factor is in 2<Y <4.5 general a more robust observable. Indeed, normalization uncertainties will cancel to some extent in this ratio de- 100 fined as 1 dσ/dP dY| R = ⊥ pA . (12) pA A dσ/dP dY| 10 pp ⊥ This is indeed the case here, as can be seen from Figs. 5 and 6 where we show the nuclear modification factor for 1 P [GeV] Drell-Yanproductionasafunctionofrapidityandtrans- 0 2 4 6 8 10 12 14 ⊥ versemomentumrespectively. Therefore,thisobservable Figure 4. Proton-proton cross section as a function of trans- could provide an interesting test of the formalism used √ verse momentum at a center of mass energy s=8 TeV. here and it could for example be measured at LHCb in the near future [26]. Beyond the interest for Drell-Yan production itself, impact parameter when computing proton-nucleus cross the values of the nuclear modification factor presented sections. At the edge of the nucleus, which is too dilute herecanbecomparedwiththeresultsobtainedforother forourformalismtobereliable,weusetheproton-proton processes in the same formalism, such as forward J/ψ result scaled such that the nuclear modification factor is production. Indeed, it was recently suggested [5] that unity. Weemphasizethatinthismodel,besidesthestan- the ratio RJ/ψ/RDY could be used to disentangle be- pA pA dard Woods-Saxon transverse thickness function TA, no tween several approaches which are compatible with the new parameters are introduced when going from proton- rapidity dependence of the nuclear modification of J/ψ proton to proton-nucleus collisions. Using, in contrast production at the LHC. Computing this ratio, using the to e.g. [17], these proton and nucleus dipole correlators samedipolecorrelatorsasinRefs.[2,4]forconsistency,is already used for light hadron [1] and J/ψ [2, 4] produc- therefore one of the main objectives of the present work. tion leads to a rather precise prediction for the nuclear The variation of this ratio as a function of the rapidity modification factor of forward Drell-Yan production at of the lepton pair is shown in Fig. 7. One can observe the LHC as will be shown in the next section. that this ratio is rather flat and close to unity. This was to be expected since in this formalism the description of thetarget interms ofanunintegrated gluondistribution III. RESULTS isthesameforthesetwoprocessesandthisunintegrated gluon distribution is probed at similar values of x . 2 In this section we present our results for the cross sec- WhiletheresultsshownhereforRJ/ψ/RDY cannotbe pA pA tion and nuclear modification factor of forward Drell- directlycomparedwiththoseshowninRef.[5]becauseof Yan production at the LHC at a center of mass energy the different center of mass energies and dilepton invari- √ s=8TeV.Sincesaturationeffectsshouldbestrongest ant mass ranges considered, it is interesting to note that at low x values, we consider small invariant masses in the behaviour of this ratio as a function of rapidity can 2 the range 5GeV<M <9.25GeV. This low mass region beverydifferentdependingontheapproachfollowed. In 4 RpDPYb RpJP/ψb/RpDPYb 0.9 1.2 1 0.8 0.8 0.7 0.6 0.4 0.6 0.2 P <15GeV P <15GeV 0.5 ⊥ Y 0 ⊥ Y 2 3 4 5 2 3 4 5 Figure5. Nuclearmodificat√ionfactorasafunctionofrapidity Figure7. RatioofthenuclearmodificationfactorsofJ/ψand at a center of mass energy s=8 TeV. Drell-Yan production as a function of rapidity at a center of √ mass energy s=8 TeV. RDY pPb 1 IV. CONCLUSIONS 0.8 In this work we have studied forward Drell-Yan production in high energy proton-nucleus collisions at the 0.6 LHCinthecolordipoleformalism, usingforthedescrip- tion of the dense target the same dipole correlators as in 0.4 Refs.[1,2,4]. Inparticular, weusedtheopticalGlauber model to obtain the dipole correlator of a nucleus from 0.2 the one of a proton. This avoids the need to introduce 2<Y <4.5 new free parameters to describe a nuclear target. This 0 P [GeV] 0 2 4 6 8 10 12 14 ⊥ approach was shown in Refs. [1, 2, 4] to lead to a rather good agreement with experimental measurements of the Figure 6. Nuclear modification factor as a fu√nction of trans- nuclear modification of forward light hadron and J/ψ verse momentum at a center of mass energy s=8 TeV. production. The comparison of the nuclear modification factors presented here with future measurements would provideanadditionaltestforthesecorrelators,whichare collinear factorization, at leading order J/ψ production assumed to be process-independent. In addition, using probes the gluon density of the target while Drell-Yan the same dipole correlators as in Refs. [2, 4] allowed us productioninvolvesthequarkdistributions. Becausethe to compute consistently the ratio RJ/ψ/RDY, which was pA pA nuclear PDFs are still not yet strongly constrained by recentlyproposedasawaytodistinguishbetweenseveral data, the predictions for the ratio RJ/ψ/RDY in this ap- approaches that can describe the nuclear modification of pA pA proach show a relatively wide spread compatible with J/ψ production at the LHC [5]. An experimental de- values close to unity [5], as are the results presented termination of this ratio would therefore be extremely here. The contrast is much more drastic when com- valuable to better understand J/ψ suppression in high paring with the results obtained in the coherent energy energy proton-nucleus collisions. loss model [27, 28], in which this ratio decreases quickly as the rapidity increases [5]. Therefore, this observable could help to discriminate between approaches based on ACKNOWLEDGEMENTS the modification of parton densities on one hand and on medium-inducedradiationontheotherhand. Moregen- We thank F. Arleo for discussions, T. Lappi for com- erally, an accurate measurement of the nuclear modifica- ments on this manuscript and H. Mäntysaari for pro- tion of forward Drell-Yan production at the LHC would viding the dipole cross sections used here. 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