Regularization Prescription for the Mixing Between Nonlocal Gluon and Quark Operators

TL;DR

This paper addresses the ambiguity in mixing nonlocal gluon and quark operators by proposing a dimensional regularization method that ensures consistent results across coordinate and momentum space analyses.

Contribution

It introduces a regularization prescription using dimensional regularization to resolve singularity ambiguities in operator mixing studies.

Findings

Dimensional regularization resolves the mixing ambiguity.

The method is compatible with lattice QCD extractions.

Consistent results achieved in both coordinate and momentum space.

Abstract

It is well-known that in the study of mixing between nonlocal gluon and quark bilinear operators there exists an ambiguity when relating coordinate space and momentum space results, which can be conveniently resolved through Mellin moments matching in both spaces. In this work, we show that this ambiguity is due to the lack of a proper regularization prescription of the singularity that arises when the separation between the gluon/quark fields approaches zero. We then demonstrate that dimensional regularization resolves this issue and yields consistent results in both coordinate and momentum space. This prescription is also compatible with lattice extractions of parton distributions from nonlocal operators.