Full two-loop electroweak corrections to the pole masses of gauge bosons

TL;DR

The authors perform a complete two-loop SM calculation of the pole positions of W and Z propagators, including gamma-Z mixing and tadpole effects to ensure gauge invariance. They automate the diagram generation, reduce multi-mass integrals to a compact master-set via Tarasov recurrence, and compute many integrals analytically or numerically using novel variable substitutions and expansions. They derive RG-invariant expressions for the pole masses, relate MS and on-shell parameters, and analyze scheme dependence, highlighting that MS can be self-consistent for unstable particles while exposing large Higgs- and top-mass contributions at two loops. The results yield precise two-loop mass renormalization constants applicable to precision electroweak predictions and to assessments of higher-order uncertainties in observables such as muon lifetime.

Abstract

We discuss progress in SM two-loop calculations of the pole position of the massive gauge-boson propagators.