On the power divergence in quasi gluon distribution function

TL;DR

This paper investigates the renormalization of quasi gluon distribution functions, demonstrating that operator mixing can eliminate linear divergences, enabling more accurate extraction of gluon distributions in large momentum effective theory.

Contribution

It introduces an auxiliary field approach to study operator mixing, showing how to remove linear divergences from quasi gluon distributions.

Findings

Linear divergences can be absorbed into operator mixing.

Renormalized quasi gluon distributions contain only logarithmic divergences.

Method improves the extraction of gluon distributions in large momentum effective theory.

Abstract

Recent perturbative calculation of quasi gluon distribution function at one-loop level shows the existence of extra linear ultraviolet divergences in the cut-off scheme. We employ the auxiliary field approach, and study the renormalization of gluon operators. The non-local gluon operator can mix with new operators under renormalization, and the linear divergences in quasi distribution function can be into the newly introduced operators. After including the mixing, we find the improved quasi gluon distribution functions contain only logarithmic divergences, and thus can be used to extract the gluon distribution in large momentum effective theory.