Neutrino-Mass Hierarchies and Non-linear Representation of Lepton-Flavour Symmetry

TL;DR

This paper develops a non-linear effective-theory framework to analyze lepton-flavour symmetry breaking caused by neutrino masses, enabling separation of effects from different neutrino mass hierarchies and exploring minimal lepton-flavour violation.

Contribution

It introduces a novel non-linear representation of lepton-flavour symmetry in effective theory, distinguishing effects of neutrino mass hierarchies and defining minimal lepton-flavour violation.

Findings

Framework separates atmospheric and solar neutrino oscillation effects.

Illustrates minimal lepton-flavour violation in decay processes.

Provides systematic definition of next-to-minimal lepton-flavour violation.

Abstract

Lepton-flavour symmetry in the Standard Model is broken by small masses for charged leptons and neutrinos. Introducing neutrino masses via dimension-5 operators associated to lepton-number violation at a very high scale, the corresponding coupling matrix may still have entries of order 1, resembling the situation in the quark sector with large top Yukawa coupling. As we have shown recently, in such a situation one may introduce the coupling matrices between lepton and Higgs fields as non-linear representations of lepton-flavour symmetry within an effective-theory framework. This allows us to separate the effects related to the large mass difference observed in atmospheric neutrino oscillations from those related to the solar mass difference. We discuss the cases of normal or inverted hierarchical and almost degenerate neutrino spectrum, give some examples to illustrate minimal lepton-flavour violation in radiative and leptonic decays, and also provide a systematic definition of next-to-minimal lepton-flavour violation within the non-linear framework.