RI'/SMOM scheme amplitudes for quark currents at two loops

TL;DR

This paper computes two-loop corrections to quark current Green's functions at the symmetric point in different renormalization schemes, ensuring consistency with identities and exploring alternative definitions.

Contribution

It provides two-loop amplitudes for scalar, vector, and tensor quark currents in MSbar and RI'/SMOM schemes, including a novel treatment for the vector current.

Findings

Two-loop amplitudes for scalar, vector, tensor currents calculated.

RI'/SMOM scheme results agree with previous work for scalar and tensor.

A special treatment for the vector current renormalization is demonstrated.

Abstract

We determine the two loop corrections to the Green's function of a quark current inserted in a quark 2-point function at the symmetric subtraction point. The amplitudes for the scalar, vector and tensor currents are presented in both the MSbar and RI'/SMOM renormalization schemes. The RI'/SMOM scheme two loop renormalization for the scalar and tensor cases agree with previous work. The vector current renormalization requires special treatment as it must be consistent with the Slavnov-Taylor identity which we demonstrate. We also discuss the possibility of an alternative definition of the RI'/SMOM scheme in the case of the tensor current.