The Weizs\"acker-Williams distribution of linearly polarized gluons (and its fluctuations) at small x

TL;DR

This paper investigates the small-x behavior of the Weizs"acker-Williams gluon distributions, including their fluctuations, using solutions of the JIMWLK equations, revealing approximate geometric scaling and significant configuration-dependent variations.

Contribution

It provides the first analysis of the functional distributions and fluctuations of linearly polarized gluon distributions at small x from the JIMWLK evolution.

Findings

Distributions exhibit approximate geometric scaling.

Large fluctuations and negative values occur in the polarized gluon distribution.

Variations can be several times the average at the saturation scale.

Abstract

The conventional and linearly polarized Weizs\"acker-Williams gluon distributions at small x are defined from the two-point function of the gluon field in light-cone gauge. They appear in the cross section for dijet production in deep inelastic scattering at high energy. We determine these functions in the small-x limit from solutions of the JIMWLK evolution equations and show that they exhibit approximate geometric scaling. Also, we discuss the functional distributions of these WW gluon distributions over the JIMWLK ensemble at rapidity $Y\sim 1/\alpha_s$. These are determined by a 2d Liouville action for the logarithm of the covariant gauge function $g^2 \mathrm{tr}\,A^+(q)A^+(-q)$. For transverse momenta on the order of the saturation scale we observe large variations across configurations (evolution trajectories) of the linearly polarized distribution up to several times its average, and even to negative values.