Renormalization of three-quark operators at two loops in the RI${}'$/SMOM scheme

TL;DR

This paper calculates two-loop renormalization factors for three-quark operators in QCD within the RI/SMOM scheme, providing essential conversion factors to improve lattice QCD baryon studies.

Contribution

It presents the first two-loop renormalization of three-quark operators in the RI/SMOM scheme, including analytical and numerical results for conversion factors.

Findings

Provides analytical expressions in R_ξ gauge

Offers numerical results in Landau gauge

Enables more accurate lattice QCD baryon calculations

Abstract

We consider the renormalization of the three-quark operators without derivatives at next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $\bar{\rm MS}$ scheme and the regularization invariant symmetric MOM (RI/SMOM, RI${}'$/SMOM) schemes. The results are presented both analytically in $R_\xi$ gauge in terms of a set of master integrals and numerically in Landau gauge. They can be used to reduce the errors in determinations of baryonic distribution amplitudes in lattice QCD simulations.