A Non-Perturbative Operator Product Expansion

TL;DR

This paper presents a non-perturbative lattice QCD calculation of Wilson coefficients in the operator product expansion for nucleon structure functions, enabling better comparison with experimental deep inelastic scattering data.

Contribution

It provides the first precision non-perturbative computation of Wilson coefficients using lattice QCD with chiral fermions, reducing operator mixing issues.

Findings

Wilson coefficients computed non-perturbatively from lattice propagators

Use of chiral fermions suppresses operator mixing

Reliable extraction of coefficients via Singular Value Decomposition

Abstract

Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photon momenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This over-determines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition.