Stable lepton mass matrices

TL;DR

This paper investigates stable lepton mass matrices, identifying specific neutrino textures consistent with stability, and explores their implications for neutrino mixing, phases, and grand unification, with potential experimental tests in neutrinoless double-beta decay.

Contribution

It classifies all stable neutrino mass textures and analyzes their phenomenological implications within the context of naturalness and grand unification.

Findings

Four stable neutrino textures identified

Preference for Majorana phase around π/2 for neutrinoless double-beta decay

Constraints on lepton mixing matrices from stability considerations

Abstract

We study natural lepton mass matrices, obtained assuming the stability of physical flavour observables with respect to the variations of individual matrix elements. We identify all four possible stable neutrino textures from algebraic conditions on their entries. Two of them turn out to be uniquely associated to specific neutrino mass patterns. We then concentrate on the semi-degenerate pattern, corresponding to an overall neutrino mass scale within the reach of future experiments. In this context we show that i) the neutrino and charged lepton mixings and mass matrices are largely constrained by the requirement of stability, ii) naturalness considerations give a mild preference for the Majorana phase most relevant for neutrinoless double-beta decay, $\alpha \sim \pi/2$, and iii) SU(5) unification allows to extend the implications of stability to the down quark sector. The above considerations would benefit from an experimental determination of the PMNS ratio $|U_{32}/U_{31}|$, i.e. of the Dirac phase $\delta$.