Three loop MSbar operator correlation functions for deep inelastic scattering in the chiral limit

TL;DR

This paper calculates third-order operator-operator correlation functions in the MSbar scheme for deep inelastic scattering, aiding non-perturbative lattice matching and renormalization constant determination.

Contribution

It provides explicit third-order correlation functions and the mixing matrix of renormalization constants for non-singlet currents in the MSbar scheme, including the tensor current R-ratio.

Findings

Explicit third-order correlation functions computed.

Renormalization mixing matrix determined.

Tensor current R-ratio deduced to third order.

Abstract

We compute a variety of operator-operator correlation functions to third order in the MSbar scheme in the chiral limit. These include combinations of quark bilinear currents with gauge invariant operators such as moments n = 2 and 3 of the flavour non-singlet Wilson operators of deep inelastic scattering and moment n = 2 of the transversity operator, as well as the correlation functions of the latter operators with themselves. The explicit values of these gauge independent correlation functions are required to assist with non-perturbative matching to lattice regularized calculations of the same quantities. As part of the computation we determine the mixing matrix of renormalization constants of these non-singlet currents with their associated total derivative operators at the same twist to three loops in MSbar. Such operators are crucial in extracting renormalization constants for the operator-operator correlation functions which are consistent with the corresponding renormalization group equation. As a by-product we deduce the R-ratio for the tensor current to third order in the MSbar scheme.