The Complex-Mass Scheme and Unitarity in perturbative Quantum Field Theory
Ansgar Denner, Jean-Nicolas Lang
TL;DR
This paper examines unitarity in the Complex-Mass Scheme for perturbative Quantum Field Theory, deriving new cutting rules to ensure unitarity when using complex masses and couplings for unstable particles.
Contribution
It introduces modified unitarity cutting rules based on Veltman's Largest-Time Equation for theories with unstable particles in the Complex-Mass Scheme.
Findings
Derived unitarity rules for scalar theories with unstable particles.
Proved unitarity within the Complex-Mass Scheme.
Ensured gauge invariance in perturbative calculations.
Abstract
We investigate unitarity within the Complex-Mass Scheme, a convenient universal scheme for perturbative calculations involving unstable particles in Quantum Field Theory which guarantees exact gauge invariance. Since this scheme requires to introduce complex masses and complex couplings, the Cutkosky cutting rules, which express perturbative unitarity in theories of stable particles, are no longer valid. We derive corresponding rules for scalar theories with unstable particles based on Veltman's Largest-Time Equation and prove unitarity in this framework.
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