One-Loop Diagrams in Lattice QCD with Wilson Fermions

TL;DR

This paper computes numerous one-loop integrals in lattice QCD with Wilson fermions using advanced algorithms and provides explicit recursion relations, aiding future perturbative calculations.

Contribution

It introduces explicit analytical recursion relations and applies the Burgio--Caracciolo--Pelissetto algorithm to compute integrals in lattice QCD with Wilson fermions.

Findings

Computed a comprehensive set of one-loop integrals.

Provided explicit analytical recursion relations.

Enhanced computational methods for lattice QCD perturbation theory.

Abstract

A comprehensive number of integrals emerging in one-loop computations in a gauge perturbation theory on the lattice with Wilson fermions at $r=1$ is computed using the Burgio--Caracciolo--Pelissetto algorithm and the FORM package. An explicit analytical form of the recursion relations needed for such computations is presented.