Mass Splitting of Three Seesaw Neutrinos

TL;DR

This paper explores how a family symmetry in neutrino masses, broken by charged-lepton interactions, naturally leads to tiny mass differences suitable for explaining solar neutrino oscillations.

Contribution

It demonstrates that a family symmetry with equal Majorana neutrino masses results in naturally small mass splittings compatible with solar neutrino data.

Findings

Mass splitting $ extless 10^{-9}m_0$ due to symmetry breaking

Natural $ riangle m^2 extasciitilde 10^{-10}$ eV$^2$ for hot dark matter neutrinos

Supports vacuum oscillation solution for solar neutrinos

Abstract

If a family symmetry exists so that all three neutrinos have equal Majorana masses (via the seesaw mechanism), then the breaking of this symmetry from charged-lepton masses (via two-loop double $W$ exchange) implies $\Delta m$ less than about $10^{-9}m_0$. With the common mass $m_0 \sim$ eV for hot dark matter, $\Delta m^2 \sim 10^{-10}$ eV$^2$ is natural for vacuum solar neutrino oscillations.