---
author:
- |
    J.A. Gracey,\
    Theoretical Physics Division,\
    Department of Mathematical Sciences,\
    University of Liverpool,\
    P.O. Box 147,\
    Liverpool,\
    L69 3BX,\
    United Kingdom.
title: 'RI${}^\prime$/SMOM scheme amplitudes for deep inelastic scattering operators at one loop in QCD'
---

[**Abstract.**]{} We compute the amplitudes for the insertion of various operators in a quark $2$-point function at one loop in the RI${}^\prime$ symmetric momentum scheme, RI${}^\prime$/SMOM. Specifically we focus on the moments $n$ $=$ $2$ and $3$ of the flavour non-singlet twist-$2$ operators used in deep inelastic scattering as these are required for lattice computations.

Introduction.
=============

Lattice gauge theories are the main theoretical tool for exploring the non-perturbative régime of the strong nuclear force by simulating the underlying quantum field theory which is the non-abelian gauge theory of quarks and gluons, (QCD). The numerical techniques allows one to explore the infrared region where perturbation theory becomes impractical because the value of the parameter controlling the expansion, which is the coupling constant, becomes large. Briefly, one uses the path integral formalism but with the space-time continuum replaced by a discrete Euclidean grid. Then one can construct Green’s functions numerically, representing, for example, bound state particle spectra, and make measurements of the 