Drell-Yan production and Lam-Tung relation in the Color Glass Condensate formalism

TL;DR

This work probes Drell-Yan production in proton-nucleus collisions within the Color Glass Condensate framework, treating the nucleus with CGC dynamics (including multiple scatterings and small-$x$ evolution) while describing the proton with conventional PDFs. By decomposing the hadronic tensor into Collins-Soper structure functions and examining the Lam-Tung relation, the authors isolate higher-twist effects arising from dense nuclear matter. They implement both BK evolution and dipole-model parameterizations (DHJ) to model the dipole cross-section and compute the angular coefficients $A_0,A_1,A_2$ across kinematics relevant to RHIC and LHC. The results show Lam-Tung violations that grow at low transverse momentum and small $x_2$, with notable differences between BK and DHJ especially in rapidity dependence, providing a concrete testbed for saturation physics in high-density QCD.

Abstract

We study the Drell-Yan production cross section and structure functions in proton (deuteron)-nucleus collisions using the Color Glass Condensate formalism. The nucleus is treated in the Color Glass Condensate framework which includes both higher twist effects due to the inclusion of multiple scatterings and leading twist pQCD shadowing due to the small x resummation, while the proton (or deuteron) is treated within the DGLAP improved parton model. In particular, the Drell-Yan structure functions are used in order to investigate the Lam-Tung relation at small x, which is known to be identically zero at leading twist up to Next-to-Leading order, and is thus a good playground for studying higher twist effects. In agreement with this, we find that violations of this relation are more important for low momentum and invariant mass of the Drell-Yan pair, and also in the region of rapidity that corresponds to smaller values of x in the nucleus.

Figures (10)

• Figure 1: The two diagrams contributing to the emission of a photon in pA collisions. The black dot denotes the Wilson line that resums all the multiple scatterings of the quark off the color field of the nucleus.
• Figure 2: Definition of the angle $\delta$.
• Figure 3: $x_1$ dependence of the integrand for the $W$'s. The kinematical parameters of the virtual photons are $k_\perp=3$ GeV, $M=3$ GeV and $y=-3$, and the center of mass energy is $\sqrt{s}=8.8$ TeV. Lines: BK evolution. Points: DHJ model.
• Figure 4: $x_2$ dependence of the integrand for the $W$'s, with the BK evolution. The kinematical parameters of the virtual photons are $k_\perp=3$ GeV, $M=3$ GeV and we consider the rapidities $y=-6,-3$ and 0. The center of mass energy is $\sqrt{s}=8.8$ TeV.
• Figure 5: Drell-Yan structure functions as a function of $k_\perp$, for RHIC (right) and LHC (left). Lines: BK evolution. Points: DHJ model.