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

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 $\overline{\mathrm{MS}}$ scheme and the regularization-invariant symmetric momentum subtraction (RI/SMOM, RI${}^{\prime }$/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.

Comments: 14 pages, 1 figure, minor changes, references added, matches journal version