Authentic Majorana versus singlet Dirac neutrino contributions to $\mu^{+}\mu^{+}\to \ell^{+}\ell^{+}$ $(\ell=e,\tau)$ transitions

TL;DR

This paper analyzes the impact of heavy Majorana neutrinos on lepton number violating muon-muon to lepton-lepton transitions, highlighting differences between Majorana and Dirac neutrino contributions in low-scale seesaw models.

Contribution

It provides a detailed calculation of the cross section for $ u$-induced transitions considering nondegenerate heavy Majorana neutrinos, emphasizing the distinction from degenerate Dirac cases.

Findings

Heavy Majorana neutrinos significantly affect $ u$-induced transitions.

Degenerate heavy neutrinos mimic Dirac neutrino behavior.

Results constrain heavy-light mixing parameters.

Abstract

We revisited the computation of the cross section for the $\mu^+\mu^+\to \ell^+\ell^{+}$ $(\ell^+=\tau^+,\, e^+)$ transitions in the presence of new heavy Majorana neutrinos. We focus on scenarios where the masses of the new states are around some few TeV, the so-called low-scale seesaw models. Our analysis is set in a simple model with only two new heavy Majorana neutrinos considering the current limits on the heavy-light mixings. Our results illustrate the difference between the genuine effects of two nondegenerate heavy Majorana states and the degenerate case where they form a Dirac singlet field.