On the process dependent nuclear $k_\perp$ broadening effect

TL;DR

This work develops a quantitative framework for process-dependent nuclear $k_ot$ broadening within TMD (and GTMD) factorization using the McLerran–Venugopalan model. By systematically incorporating process-dependent gauge links, the authors connect nuclear TMDs to nucleon TMDs via convolutions with small-$x$ gluon distributions, obtaining explicit results for SIDIS, DY, photon-jet, and heavy-quark-pair production, including polarized distributions such as the quark Boer–Mulders function and the linearly polarized gluon distribution. In the semi-hard region, unpolarized nuclear TMDs are governed by the relevant small-$x$ gluon distributions, while Boer–Mulders nuclear TMDs factorize into $T_F^{( ext{ } ext{)}}(x,x)$ times derivatives of these gluon distributions, yielding measurable azimuthal asymmetries like $ obreak ig< ext{cos}2\phiig>$. The paper provides phenomenological estimates of $k_ot$ broadening (e.g., $ riangleig<k_ot^2ig> o Q_s^2/2$ with nucleus-dependent corrections) and demonstrates consistency with higher-twist collinear approaches, offering testable predictions for RHIC and the future EIC.

Abstract

We study the process dependent nuclear $k_\perp$ broadening effect by employing the transverse momentum dependent(TMD) factorization approach in combination with the Mclerran-Venugopalan(MV) model. More specifically, we investigate how the parton transverse momentum distributions are affected by the process dependent gauge links in cold nuclear matter. In particular, our analysis also applies to the polarized cases including the nuclear quark Boer-Mulders function and the linearly polarized gluon distribution. Our main focus is on the nuclear TMDs at intermediate or large x.

Figures (3)

• Figure 1: The ordinary future pointing gauge link is reduced to a short one by evaluating part of the gauge link stretching from $R^-$ to $\infty$ in the MV model, where $R^-$ is the radius of a nucleon.
• Figure 2: The gauge link $U^{[+]}U^{[+]\dag}$ is reduced to two short ones with different color structures by evaluating part of the gauge link stretching from $R^-$ to $\infty$ in the MV model, where $R^-$ is the radius of a nucleon.
• Figure 3: Feynman diagrams contributing to quark antiquark pair production.