Mass Spectrum and Number of Light Neutrinos: An Attempt of the Gauge Explanation

TL;DR

This paper explores how symplectic flavor symmetry constraints lead to a specific neutrino mass spectrum with three light and three heavy neutrinos, explaining observed neutrino properties within a gauge symmetry framework.

Contribution

It demonstrates that a symplectic flavor symmetry group constrains neutrino mass matrices, resulting in a natural explanation for the light neutrino spectrum and mass hierarchy.

Findings

Neutrino spectrum with two states far from the third is explained by properties of Sp(3) mass matrices.

Normal mass hierarchy is consistent with the model's predictions.

Mass differences are comparable to masses, not significantly less, within this framework.

Abstract

Symplectic flavour symmetry group Sp(n/2) (n is even) of n Majorana states does not allow for invariant Majorana masses. Only specific mass matrices with diagonal and nondiagonal elements are possible here. As a result of the spontaneous violation of flavour and chiral symmetries, a mass matrix could appear only for the number of flavours n = 6 and only together with R,L-symmetry violation (i.e., parity violation). The see-saw mechanism produces here three light and three heavy Dirac particles (neutrinos). The peculiarity of the observed light neutrino spectrum: two states located far from the third one, can be explained by certain simple properties of mass matrices appearing in Sp(3). The ordering of the states corresponds to normal mass hierarchy. Situation, when neutrino mass differences are significantly less than masses themselves, appears to be unrealizable here. Mixing angles for neutrinos can not be determined without understanding formation mechanisms for charged lepton spectrum and Majorana state weak currents.