Calculating TMDs of a Large Nucleus: Quasi-Classical Approximation and Quantum Evolution

TL;DR

This paper develops a formalism within saturation physics to calculate TMDs of large nuclei, incorporating spin-orbit effects, and explores their evolution across different x regimes, providing new insights into TMD mixing and evolution.

Contribution

It generalizes the quasi-classical approximation to include spin-orbit coupling, enabling calculation of any TMD in the saturation framework, and applies this to large-x and small-x regimes.

Findings

Spin-orbit coupling causes mixing between TMDs.

Calculated unpolarized and Boer-Mulders quark TMDs for large nuclei.

Identified different evolution mechanisms for TMDs at large-x and small-x.

Abstract

We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) using the tools of saturation physics. By generalizing the quasi-classical Glauber-Gribov-Mueller/McLerran-Venugopalan approximation to allow for the possibility of spin-orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large "nucleus." To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer-Mulders distribution. We observe that spin-orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dominated by the QCD Reggeon.