Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

TL;DR

This paper develops a three-loop Wilson operator product expansion for QCD propagators, including dimension two and three operators, to improve the accuracy of lattice QCD operator extraction.

Contribution

It provides the first three-loop analytical calculation of coefficient functions for dimension two and three operators in QCD propagators in covariant gauges.

Findings

Analytical three-loop coefficient functions for gluon, quark, and ghost propagators.

Results in Landau gauge aid lattice QCD operator extraction.

Enhances precision in determining vacuum expectation values.

Abstract

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.