QCD Factorization of Quasi Generalized Gluon Distributions

TL;DR

This paper investigates the factorization relations between quasi gluon GPDs and twist-2 GPDs, providing one-loop level perturbative coefficients, addressing operator mixing, and establishing connections to gluon PDFs in the forward limit.

Contribution

It presents the first detailed one-loop factorization relations for quasi gluon GPDs, including gauge invariance, operator mixing patterns, and the connection to gluon PDFs.

Findings

One-loop perturbative coefficient functions are divergence-free.

Ghost contributions are necessary for gauge invariance in quasi gluon GPDs.

Factorization relations hold for all quasi gluon GPDs and connect to gluon PDFs.

Abstract

We study the factorization relations between quasi gluon GPDs and twist-2 GPDs. The perturbative coefficient functions are obtained at one-loop level. They are free from any collinear- or I.R. divergences. Unlike the case of the factorization of quasi quark GPDs at one-loop, we have to add ghost contributions for the factorization of quasi gluon GPDs in order to obtain gauge-invariant results. In general, operators will be mixed beyond tree-level. Our work shows that the mixing pattern of the nonlocal operators in quasi gluon GPDs is the same as local operators, i.e., the nonlocal operators considered are mixed with gauge-invariant operators, BRST-variation operators and operators involving EOM operator. The factorization relations are obtained for all quasi gluon GPDs. Taking the forward limit, we also obtain the relations between quasi gluon PDFs and twist-2 PDFs.