Pole Mass, Width, and Propagators of Unstable Fermions

TL;DR

This paper extends the concepts of pole mass and width to unstable fermions within gauge theories, providing gauge-independent definitions and expressions for their propagators, addressing issues of unphysical singularities.

Contribution

It introduces gauge-independent definitions of pole mass and width for unstable fermions and derives general expressions for their propagators and renormalization constants.

Findings

Pole mass and width are gauge independent for unstable fermions.

Provides explicit formulas for dressed propagators of unstable fermions.

Addresses unphysical singularities in fermion propagators.

Abstract

The concepts of pole mass and width are extended to unstable fermions in the general framework of parity-nonconserving gauge theories, such as the Standard Model. In contrast with the conventional on-shell definitions, these concepts are gauge independent and avoid severe unphysical singularities, properties of great importance since most fundamental fermions in nature are unstable particles. General expressions for the unrenormalized and renormalized dressed propagators of unstable fermions and their field-renormalization constants are presented.