Seesaw Options for Three Neutrinos

TL;DR

This paper clarifies the seesaw mechanism for three neutrinos, emphasizing the role of inverse or linear seesaw models and the necessity of lepton number symmetry breaking to explain neutrino masses and mixing.

Contribution

It demonstrates that the true underlying mechanism is inverse or linear seesaw and discusses how lepton number symmetry breaking influences neutrino mass textures.

Findings

Inverse/linear seesaw explains large mixing.

Zero mass eigenvalues require lepton number symmetry.

Heavy neutrinos can have specific lepton number assignments.

Abstract

The seesaw mechanism for three neutrinos is discussed, clarifying the situation where the seesaw texture results in three approximately zero mass eigenvalues. The true underlying mechanism is shown to be just the $inverse$ (or $linear$) seesaw, which explains why there could be large mixing. However, these zeroes cannot occur naturally, unless there is a conserved symmetry, i.e. lepton number $L$, either global or gauged, which is softly or spontaneously broken at the TeV scale. We discuss in particular the case where the three heavy singlet neutrinos have $L=3,-2,-1$.