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

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 $\mathcal{O}$, whose evolution is also known in the literature. We show that the effect of non-zero skewness $\xi \ne 0$ is to modify the value of the evolution parameter (rapidity) in the arguments for the dipole amplitudes $N$ and $\mathcal{O}$ from $Y=\ln (1/x)$ to $Y=\ln \min \left\{1/|x|,1/|\xi |\right\}$.

Comments: 12 pages, 2 figures; typos corrected