Complex mass definition and the concept of continuous mass

TL;DR

This paper explores the spectral representation of propagators for unstable particles, deriving dressed propagators for various fields within a continuous mass framework, aligning with the complex mass scheme.

Contribution

It introduces a general formalism for propagators of unstable particles based on continuous mass and derives analytical expressions for different field types.

Findings

Spectral functions derived from general assumptions

Analytical dressed propagators for scalar, vector, and spinor fields

Consistency with the complex mass scheme

Abstract

Propagators of unstable particles are considered in the spectral representation which naturally follows from the concept of continuous mass. The spectral functions are found with the help of the most general formal and physical assumptions. Dressed propagators of unstable scalar, vector, and spinor fields are derived in an analytical way for a variant of parameter space. The structure of the propagators is in a correspondence with the complex mass scheme.