Complex-mass definition and the structure of unstable particle's propagator

TL;DR

This paper derives modified Breit-Wigner propagators for unstable particles using the convolution representation, providing analytical expressions for scalar, vector, and spinor fields that incorporate the complex-mass concept.

Contribution

It introduces a spectral function approach to derive propagators in the complex-mass framework for various unstable particles.

Findings

Derived spectral function for scalar unstable particles with Breit-Wigner form

Obtained analytical expressions for vector and spinor propagators in the complex-mass scheme

Presented modified Breit-Wigner forms for unstable particle propagators

Abstract

The propagators of unstable particles are considered in the framework of the convolution representation. Spectral function was found for a special case when the propagator of scalar unstable particle has Breight-Wigner form. The expressions for the dressed propagators of unstable vector and spinor fields are derived in an analytical way for this case. We got the propagators in modified Breit-Wigner forms which correspond to the complex-mass definition.