Wigner, Husimi and GTMD distributions in the Color Glass Condensate

TL;DR

This paper explores gluon phase space distributions in nucleons and nuclei at small-$x$, incorporating saturation effects, by solving the BK equation with impact parameter dependence to compute Wigner, Husimi, and GTMD distributions, and examines their angular dependence.

Contribution

It introduces a method to compute gluon distributions including impact parameter dependence by solving the BK equation, linking theoretical distributions to measurable angular effects.

Findings

Computed gluon Wigner, Husimi, and GTMD distributions in the saturation regime.

Analyzed the elliptic angular dependence of these distributions.

Provided insights into measurable effects in DIS experiments.

Abstract

We study the phase space distributions of gluons inside a nucleon/nucleus in the small-$x$ regime including the gluon saturation effect. This can be done by using the relation between the gluon Wigner distribution and the dipole S-matrix at small-$x$, the latter satisfies the Balitsky-Kovchegov (BK) equation. By efficiently solving the BK equation with impact parameter dependence, we compute the Wigner, Husimi and generalized TMD (GTMD) distributions in the saturation regime. We also investigate the elliptic angular dependence of these distributions which has been recently shown to be measurable in DIS experiments.