Moments $n=2$ and $n=3$ of the Wilson twist-two operators at three loops in the RI${}'$/SMOM scheme

TL;DR

This paper computes three-loop renormalization factors for twist-two operators in QCD, enabling more accurate lattice QCD calculations of structure function moments by connecting RI/SMOM and MSbar schemes.

Contribution

It provides the first three-loop conversion factors for twist-two operators in the RI/SMOM scheme, improving the precision of lattice QCD determinations.

Findings

Three-loop conversion factors between RI/SMOM and MSbar schemes.

Results applicable to lattice QCD calculations of structure functions.

Enhanced accuracy in moments of structure functions from lattice data.

Abstract

We study the renormalization of the matrix elements of the twist-two non-singlet bilinear quark operators, contributing to the $n=2$ and $n=3$ moments of the structure functions, at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $\overline{\rm MS}$ scheme and the regularization-invariant symmetric momentum subtraction (RI/SMOM, RI${}'$/SMOM) schemes. The obtained results can be used to reduce errors in determinations of moments of structure functions from lattice QCD simulations. The results are given in Landau gauge.