Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions

TL;DR

This paper calculates one-loop renormalization factors for operators measuring moments of non-singlet quark distributions in lattice QCD using overlap fermions, maintaining chiral symmetry and enabling physical predictions.

Contribution

It provides the first one-loop renormalization constants for these operators with overlap fermions, ensuring chiral symmetry is preserved in the calculations.

Findings

Renormalization factors for ten operators computed

Chiral symmetry maintained in all results

Consistent renormalization constants for related operators

Abstract

Using the overlap-Dirac operator proposed by Neuberger, we have computed in lattice QCD the one-loop renormalization factors of ten operators which measure the lowest two moments of unpolarized and polarized non-singlet quark distributions. These factors are necessary to extract physical numbers from Monte Carlo simulations made with overlap fermions. An exact chiral symmetry is maintained in all our results, and the renormalization constants of corresponding unpolarized and polarized operators which differ by a $\gamma_5$ matrix have the same value. We have considered two lattice representations for each continuum operator. The computations have been carried out using the symbolic language FORM, in a general covariant gauge. In some simple cases they have also been checked by hand.