Muon decay across scales: from LEFT to SMEFT

Abstract

We revisit precision muon decay in the framework of the LEFT by considering how the LEFT perturbs the total rate as well as the standard and polarization-dependent Michel parameters. We derive the dependence of these observables on the dimension-five and -six LEFT operators, including lepton number violating operators, allowing for arbitrary neutrino flavor assignments. We consider fits of the LEFT to the muon decay data, in particular an approach to neutrino flavor general fits that does not respect the LEFT power counting and assuming new physics couples to all flavors equally and therefore allows for a consistent fit. We then consider how new physics imprints on the SMEFT and subsequently the LEFT in order to constrain specific scenarios of single-field extensions as well as two motivated two-field extensions. While we infer associated mass scales for these scenarios in the hundreds of GeV to multi-TeV range we also find that for the specific cases of lepton number violation, neutrino mass constraints from operator mixing are more restrictive than muon decay.