Amplitudes for the n = 3 moment of the Wilson operator at two loops in the RI/'SMOM scheme

TL;DR

This paper computes two-loop amplitudes and conversion functions for the third moment of the Wilson operator in the RI'/SMOM scheme, enabling precise renormalization and anomalous dimension calculations in QCD.

Contribution

It provides the first two-loop renormalization constants and conversion functions for the third moment of the Wilson operator in the RI'/SMOM scheme, including mixing with total derivative operators.

Findings

Two-loop amplitudes for the Wilson operator are calculated.

Conversion functions between MSbar and RI'/SMOM schemes are derived.

Three-loop anomalous dimension in Landau gauge is obtained.

Abstract

The renormalization of the third moment of the twist-2 flavour non-singlet Wilson operator is given to two loops in the RI'/SMOM renormalization scheme. This involves renormalizing the operator itself and the two total derivative operators into which it mixes by inserting it into a quark 2-point function and evaluating the amplitudes at the symmetric subtraction point. The corresponding two loop conversion functions are derived from which the three loop Landau gauge anomalous dimension is deduced. The full set of amplitudes for the two loop Green's function for each of the operators are given in both the MSbar and RI'/SMOM schemes.