On the gauge independence of the fermion pole mass

TL;DR

This paper proves that the fermion pole mass remains completely gauge independent across a broad class of gauges, provided infrared divergences and singularities are absent, using Nielsen identities and two-point functions.

Contribution

It provides a general proof of gauge independence of the fermion pole mass in all gauges, extending previous results and clarifying the conditions required.

Findings

Fermion pole mass is gauge independent when no infrared divergences are present.

Nielsen identities relate gauge parameter variations to the fermion two-point function.

The proof applies to covariant, axial, and Coulomb gauges.

Abstract

We study the question of complete gauge independence of the fermion pole mass by choosing a general class of gauge fixing which interpolates between the covariant, the axial and the Coulomb gauges for different values of the gauge fixing parameters. We derive the Nielsen identity describing the gauge parameter variation of the fermion two point function in this general class of gauges. Furthermore, we relate the denominator of the fermion propagator to the two point function. This then allows us to study directly the gauge parameter dependence of the denominator of the propa- gator using the Nielsen identity for the two point function. This leads to a simple proof that, when infrared divergences and mass shell singularities are not present at the pole, the fermion pole mass is gauge independent, in the complete sense, to all orders in perturbation theory. Namely, the pole is not only independent of the gauge fixing parameters, but has also the same value in both covariant and non-covariant gauges.