Muon conversion to electron in nuclei in type-I seesaw models

TL;DR

This paper calculates muon to electron conversion rates in nuclei within type-I seesaw models, analyzing how these rates depend on right-handed neutrino parameters and comparing them with other mu-e transition processes.

Contribution

It provides detailed predictions for muon to electron conversion ratios in nuclei based on right-handed neutrino masses and mixings, extending analysis to very light and heavy sterile neutrinos.

Findings

Conversion ratios depend only on the seesaw scale for quasi-degenerate neutrinos.

Ratios vanish for sterile neutrinos heavier than a few TeV.

Future experiments can probe sterile neutrinos from 2 MeV to 1000 TeV.

Abstract

We compute the muon to electron conversion in the type-I seesaw model, as a function of the right-handed neutrino mixings and masses. The results are compared with previous computations in the literature. We determine the definite predictions resulting for the ratios between the muon to electron conversion rate for a given nucleus and the rate of two other processes which also involve a mu-e flavour transition: mu -> e gamma and mu -> eee. For a quasi-degenerate mass spectrum of right-handed neutrino masses -which is the most natural scenario leading to observable rates- those ratios depend only on the seesaw mass scale, offering a quite interesting testing ground. In the case of sterile neutrinos heavier than the electroweak scale, these ratios vanish typically for a mass scale of order a few TeV. Furthermore, the analysis performed here is also valid down to very light masses. It turns out that planned mu -> e conversion experiments would be sensitive to masses as low as 2 MeV. Taking into account other experimental constraints, we show that future mu -> e conversion experiments will be fully relevant to detect or constrain sterile neutrino scenarios in the 2 GeV-1000 TeV mass range.