Unpolarized GPDs at small $x$ and non-zero skewness

TL;DR

This paper analyzes the small-$x$ behavior of unpolarized GPDs and GTMDs with non-zero skewness, linking their evolution to dipole amplitudes and showing how skewness modifies the evolution parameter.

Contribution

It introduces a novel analysis of small-$x$ GPDs and GTMDs considering non-zero skewness and non-linear evolution, extending previous literature.

Findings

Unpolarized GPDs and GTMDs relate to dipole amplitude $N$ and odderon amplitude $ ext{O}$.

Non-zero skewness modifies the evolution parameter from $Y = ext{ln}(1/x)$ to $Y = ext{ln} ext{min}igrace{1/|x|, 1/|\xi|}igrace$.

Evolution of amplitudes is governed by BK/JIMWLK equations.

Abstract

We study the small-$x$ asymptotics of unpolarized generalized parton distributions (GPDs) and generalized transverse momentum distributions (GTMDs). Unlike the previous works in the literature, we consider the case of non-zero (but small) skewness while allowing for non-linear contributions to the evolution equations. We show that unpolarized GPDs and GTMDs at small $x$ are related to the eikonal dipole amplitude $N$, whose small-$x$ evolution is given by the BK/JIMWLK evolution equations, and to the odderon amplitude $\cal O$, whose evolution is also known in the literature. We show that the effect of non-zero skewness $\xi \neq 0$ is to modify the value of the evolution parameter (rapidity) in the arguments for the dipole amplitudes $N$ and $\cal O$ from $Y = \ln (1/x)$ to $Y = \ln \min \left\{ 1/|x| , 1/|\xi| \right\}$.