Parton distribution function for topological charge at one loop

TL;DR

This paper calculates the one-loop corrections to a topological charge generalized parton distribution, providing evolution kernels and confirming gauge invariance without zero mode contributions.

Contribution

It introduces the one-loop correction calculations for the topological charge GPD and derives its evolution kernel with gauge invariance verified.

Findings

Derived the evolution kernel for the topological charge GPD.

Confirmed gauge invariance using on-shell gluon states in different gauges.

Found no zero mode delta function terms in the twist-4 gluon GPD.

Abstract

We present results for the $gg$-part of the one-loop corrections to the recently introduced "topological charge" GPD $\widetilde F(x,q^2)$. In particular, we give expression for its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No "zero mode" $\delta (x)$ terms were found for the twist-4 gluon GPD $\widetilde F(x,q^2)$.