Modifying the Dyson Series for Unstable Particles and Resonances

TL;DR

This paper proposes a modified Dyson series that systematically handles unstable particles and resonances, avoiding singularities and double-counting without relying on specific renormalization schemes.

Contribution

It introduces a new formulation of the Dyson series based on perturbative unitarity to better treat unstable particles and resonances.

Findings

Systematic avoidance of singularities in unstable particle calculations

Elimination of double-counting issues in resonance states

Scheme-independent approach to Dyson series modifications

Abstract

In this work, we introduce a modification of the Dyson series based on the perturbative unitarity as a starting point. The presented approach systematically avoids singularities and double-counting related to the presence of unstable particles as intermediate states and, at the same time, it does not rely on a specific choice of the renormalization scheme.