Michel parameters in the presence of massive Dirac and Majorana neutrinos

TL;DR

This paper investigates how massive Dirac and Majorana neutrinos influence leptonic decays of muons and taus, introducing generalized Michel parameters and highlighting potential experimental signatures of heavy sterile neutrinos.

Contribution

It provides a comprehensive analysis of the effects of heavy neutrino masses on decay distributions and Michel parameters, including the impact of neutrino nature and mixing.

Findings

Heavy neutrino masses can significantly alter decay distributions.

Tau decays with heavy neutrinos could produce measurable effects.

Linear term suppression in tau decay could be around 10^{-4}.

Abstract

We analyse the effects of Dirac and Majorana neutrinos on leptonic decays of muon and tau leptons using the most general four-lepton effective interaction Hamiltonian of dimension six. We calculate the specific energy and angular distribution of the final charged lepton, including the polarizations of the initial and final charged leptons. We discuss the new generalized Michel parameters and focus on the effects of the heavy neutrino masses that would lead to sizable contributions on scenarios where the new sterile neutrinos have non-negligible mixing. Specifically, the most promising scenario is found for the case of $\tau$ decay with one heavy final-state neutrino with a mass around $10^2 - 10^3$ MeV, where the linear term suppression could be of order $10^{-4}$, low enough to be measured in current and forthcoming experiments.