Generalized unitarity method for unstable particles

TL;DR

This paper extends the generalized unitarity method to handle one-loop amplitudes with unstable particles, demonstrating its reliability under certain conditions despite the exclusion of unstable states in unitarity cuts.

Contribution

It proves the validity of the generalized unitarity method for unstable particles at one-loop level with specific physical assumptions and modifications.

Findings

The method remains reliable for resonances in one-loop amplitudes.

Unitarity cuts should exclude unstable particles for consistency.

Simple examples illustrate the approach's effectiveness.

Abstract

In theories with unstable particles, unitarity is satisfied by the inclusion of only stable states in unitarity sums. Hence unitarity cuts are not to be taken through unstable particles. This raises a challenge to the generalized unitarity method, whose aim is to reconstruct amplitudes by analyzing sets of unitarity cuts. Nevertheless, under some general physical conditions, and perhaps some methodological modifications, we prove that the method is still reliable for one-loop amplitudes containing resonances. We discuss some simple examples which illustrate these features.