Two-Loop Fermionic Integrals in Perturbation Theory on a Lattice

TL;DR

This paper computes one-loop fermionic integrals on a lattice with Wilson fermions, enabling the extension of two-loop integral techniques to fermionic cases, and provides explicit results for the fermionic propagator.

Contribution

It introduces a method to evaluate two-loop fermionic integrals on the lattice, extending existing procedures to include fermionic contributions.

Findings

Computed a comprehensive set of one-loop integrals for Wilson fermions.

Extended the Luscher-Weisz procedure to fermionic two-loop integrals.

Provided explicit fermionic propagator expressions in coordinate space.

Abstract

A comprehensive number of one-loop integrals in a theory with Wilson fermions at $r=1$ is computed using the Burgio-Caracciolo-Pelissetto algorithm. With the use of these results, the fermionic propagator in the coordinate representation is evaluated, thus making it possible to extend the Luscher-Weisz procedure for two-loop integrals to the fermionic case. Computations are performed with FORM and REDUCE packages.