Gluon nonlocal operator mixing in lattice QCD

TL;DR

This paper investigates the renormalization of gauge-invariant gluon nonlocal operators on the lattice, providing one-loop renormalization factors and analyzing operator mixing patterns to aid non-perturbative studies.

Contribution

It offers a comprehensive calculation of renormalization factors and operator mixing patterns for gluon nonlocal operators in lattice QCD, facilitating future non-perturbative renormalization.

Findings

Calculated one-loop renormalization factors in $ m ar{MS}$ scheme.

Identified operator mixing patterns under lattice regularization.

Determined conversion factors from RI' scheme to $ m ar{MS}$.

Abstract

In this study, we explore the renormalization of a comprehensive set of gauge-invariant gluon nonlocal operators on the lattice. We calculate the renormalization factors for these operators in the modified Minimal Subtraction $(\rm \overline{MS})$ scheme up to one-loop, using both dimensional and lattice regularizations in the Wilson gluon action. To facilitate a non-perturbative renormalization approach, we examine an appropriate version of the modified regularization-invariant (${\rm RI}'$) scheme and determine the conversion factors from this scheme to $\rm \overline{MS}$. As an integral part of this procedure, by employing symmetry arguments on the lattice, we identify the mixing pattern of these operators under renormalization.