# How to compute one-loop Feynman diagrams in lattice QCD with Wilson fermions

## TL;DR

This paper introduces an algebraic algorithm for efficiently computing one-loop lattice integrals in QCD with Wilson fermions, enabling high-precision calculations and potential generalization to higher dimensions.

## Contribution

The authors present a novel algebraic method to express one-loop lattice integrals with Wilson fermions in terms of basic constants, facilitating precise and scalable computations.

## Key findings

- Algorithm expresses integrals in terms of a small set of constants.
- Method generalizes to any space dimension.
- Provides a way to represent the Wilson fermion propagator in coordinate space.

## Abstract

We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of L\" uscher and Weisz to higher-loop integrals with fermions.