Non-perturbative renormalization of quark and gluon operators using a gauge-invariant scheme

TL;DR

This paper introduces a gauge-invariant scheme for non-perturbative renormalization of quark and gluon operators in lattice QCD, demonstrating its effectiveness through calculations of renormalization functions and operator mixing coefficients.

Contribution

It presents a novel gauge-invariant coordinate-space renormalization scheme (GIRS) and applies it to compute renormalization functions and mixing coefficients in lattice QCD.

Findings

GIRS reduces statistical noise in lattice calculations.

RFs for vector quark operators are successfully computed.

First results on gluon-quark operator mixing are obtained.

Abstract

We present preliminary results for the renormalization functions (RFs) of a number of quark and gluon operators studied in lattice QCD using a gauge-invariant renormalization scheme (GIRS). GIRS is a variant of the coordinate-space renormalization prescription, in which Green's functions of gauge-invariant operators are calculated in position space. A novel aspect is that summations over different time slices of the positions of the operators are employed in order to reduce the statistical noise in lattice simulations. We test the reliability of this scheme by calculating RFs for the vector one-derivative quark bilinear operator, which enters the average momentum fraction of the nucleon. We use $N_f=4$ degenerate twisted mass clover-improved fermion ensembles of different volumes and lattice spacings. We also present first results of applying GIRS when operator mixing occurs: the mixing coefficients of the gluon and quark singlet energy-momentum tensor operators are evaluated by imposing appropriate renormalization conditions on the lattice.