Confronting color dipole and intrinsic kT approaches in D-Y dilepton production

Abstract

We study the Drell-Yan dilepton production in proton-nucleus collisions at RHIC energies. We use two different approaches: the usual intrinsic transverse momentum approach at NLO in the infinitum momentum frame; and the color dipole in the target rest frame. We compare both formalisms at backward rapidities (proton as a target). At forward rapidities, we use earlier results considering the nucleus in a Color Glass Condensate phase. We show qualitative agreement between the two formalisms through the nuclear modification ratio as a function of both rapidity and transverse momentum and that low-mass dileptons are relevant observables to probe nuclear effects.Keywords: Drell-Yan process; Dilepton production; Nuclear effects; Dipole frame; Infinite momentum frameIn a recent work[1], Drell-Yan dilepton production at backward rapidities in hadrons collisions was studied in the rest frame of the target, i. e., in the color dipole approach. In this work, we compare these previous results with results obtained used well know intrinsic k T approach in the infinitum momentum frame [2,3]. In this frame, the process is understood as the combination of two partons to create a virtual boson that subsequently splits in the dilepton. For dilepton mass M much smaller than the Z mass, the dominant process includes only the photon as the virtual boson. The dilepton production is of particular interest since dileptons do not interact strongly and therefore carry information about initial state effects.The kinematics used here are described now. Partons and hadrons are taken as massless, the momenta of hadrons A and B are P A and P B , and the momenta of partons are p A = x A P A and p B = x B P B (for now, partons are collinear to hadrons). The virtual photon momentum is q and q 2 = M 2 is the squared dilepton mass. The Mandelstam variables are given by: s = 2P A · P B , t = (q − P A ) 2 , and u = (q − P B ) 2 . We also define x 1 = 2P B · q/s, x 2 = 2P A · q/s, and the photon rapidity y = 1 2 ln(x 1 /x 2 ). It can be showed that:in which p T is the photon (also dilepton) transverse momentum. In IMF collinear approximation, partons are considered collinear to hadrons, without intrinsic transverse momentum. Using this framework at leading order, experimental results of transverse momentum distribution cannot be reproduced: although valid for large p T , collinear NLO p T distribution diverges at p T = 0 and is not in agreement with experiments for small p T . We consider then partonic intrinsic transverse momentum, i. e., partons are not collinear to hadrons [2,3]. The partonic distributions are change as the following prescription:In this paper, we consider h( k T ) = 1 2πb 2 exp k 2 T 2b 2 . Therefore, the cross section is given by [4,5]:In the above expression, it is included the NLO collinear double differential cross section:Using the modified minimal subtraction scheme (MS), D q (z) and D g (z) are given e.g. in Ref.[6] (C F = 4/3, T R = 1/2). The second term in the right hand side of equation 3 is calculated only from annihila...