Complex-mass scheme and perturbative unitarity

TL;DR

This paper develops cutting rules for loop integrals with complex masses and demonstrates that the complex-mass scheme maintains perturbative unitarity in a specific quantum field theory model, given real renormalized couplings.

Contribution

It introduces a method to derive cutting rules for complex-mass propagators and proves unitarity preservation in the complex-mass scheme within a field-theoretical context.

Findings

Cutting rules for complex-mass propagators derived.

Unitarity preserved order by order with real couplings.

Applicable to models with heavy vector bosons and light fermions.

Abstract

We derive cutting rules for loop integrals containing propagators with complex masses. Using a field-theoretical model of a heavy vector boson interacting with a light fermion, we demonstrate that the complex-mass scheme respects unitarity order by order in a perturbative expansion provided that the renormalized coupling constant remains real.