Toward a first-principles description of transverse momentum dependent Drell-Yan production in proton-nucleus collisions

TL;DR

This paper develops a first-principles theoretical framework for understanding the transverse momentum dependent Drell-Yan process in proton-nucleus collisions, emphasizing perturbative dynamics and medium effects.

Contribution

It derives the perturbative contributions to nuclear TMD Drell-Yan cross sections up to next-to-leading order and first order in medium opacity, introducing in-medium evolution equations.

Findings

Derived in-medium renormalization group equation for parton energy loss.

Established BFKL evolution equation for forward scattering cross section.

Applied formalism to small transverse momentum Drell-Yan in p+A collisions.

Abstract

In this paper, we study the parton dynamics in Drell-Yan collisions involving proton-nuclei interactions in the limit of small transverse momentum, emphasizing the role of the cold nuclear matter effects. The distribution of transverse momentum that enter into these collisions differs from that in Drell-Yan collisions with free nucleons in two distinct ways: the intrinsic parton structure of the TMDs are altered, the perturbative dynamics undergo additional modification due to interactions with the nuclear medium. In this paper, we focus on the perturbative dynamics, which we demonstrate enter from forward scattering between the parton constituents of the proton and the nuclear medium. We then derive these partonic contributions to the TMD Drell-Yan cross section up to next-to-leading order in the strong coupling constant and to the first order in the medium opacity. We demonstrate that the collinear and rapidity divergences related to parton showers in matter lead to i) an in-medium renormalization group equation that encodes the transverse momentum dependence of parton energy loss, and ii) a Balitsky-Fadin-Kuraev-Lipatov evolution equation for the forward scattering cross section. We discuss the relation of our results to the phenomenological extraction of nuclear TMDs and apply the new formalism to Drell-Yan production at small transverse momenta in $p$+$A$ reactions.