Relation between bare lattice coupling and MSbar coupling at one loop with general lattice fermions

TL;DR

This paper derives a general integral formula linking the bare lattice coupling to the MSbar coupling at one loop, improving numerical accuracy for various lattice fermion formulations.

Contribution

A new integral formula is introduced that accurately computes the fermionic contribution to the one-loop MSbar coupling for general lattice fermions.

Findings

Reproduces known results for naive, staggered, and Wilson fermions.

Facilitates evaluation for improved lattice fermion formulations.

Provides more accurate numerical coefficients for Wilson clover fermions.

Abstract

A compact general integral formula is derived from which the fermionic contribution to the one-loop coefficient in the perturbative expansion of the MSbar coupling in powers of the bare lattice coupling can be extracted. It is seen to reproduce the known results for unimproved naive, staggered and Wilson fermions, and has advantageous features which facilitate the evaluation in the case of improved lattice fermion formulations. This is illustrated in the case of Wilson clover fermions, and an expression in terms of known lattice integrals is obtained in this case which gives the coefficient to much greater numerical accuracy than in the previous literature.