The complex-mass scheme for perturbative calculations with unstable particles

TL;DR

This work advocates the complex-mass scheme (CMS) as a universal, gauge-invariant approach to include finite-width effects of unstable particles in perturbative calculations across the full phase space. It presents the tree-level formulation with complex pole masses, and a one-loop extension that introduces complex renormalization, ensuring consistent cancellations and avoiding double counting. The renormalization prescription is adapted to complex masses, with practical expansion techniques to evaluate self-energies, and it is compatible with standard Ward identities and unitarity considerations. The CMS is demonstrated as a practical, rigorous tool for precise electroweak corrections, exemplified by calculations of e+e- → 4f and H → 4f decays.

Abstract

Perturbative calculations with unstable particles require the inclusion of their finite decay widths. A convenient, universal scheme for this purpose is the complex-mass scheme. It fully respects gauge-invariance, is straight-forward to apply, and has been successfully used for the calculation of various tree-level processes and of the electroweak radiative corrections to e+ e- -> 4f and H -> 4f.