Simple Connection Between Atmospheric and Solar Neutrino Vacuum Oscillations

TL;DR

This paper presents a simple theoretical link between atmospheric and solar neutrino oscillations within an extended standard model, connecting neutrino mass differences and mixing angles through radiative corrections.

Contribution

It introduces a minimal extension of the standard model with a scalar triplet to relate neutrino oscillation parameters via a straightforward formula.

Findings

Derives a relation between  and  mass-squared differences and mixing angles.

Shows how radiative splitting due to charged leptons influences neutrino degeneracy.

Provides a potential framework for hot dark matter neutrino mass scale.

Abstract

Extending the minimal standard model of particle interactions (without right-handed singlet neutrinos) to include a heavy scalar triplet $\xi$ to obtain nonzero Majorana neutrino masses, I derive the following simple realistic connection between atmospheric and solar neutrino vacuum oscillations: $(\Delta m^2)_{sol} (\Delta m^2)_{atm} / m_\nu^4 ~(\sin^2 2 \theta)_{atm} = 2 I^2$, where $m_\nu$ is the assumed common approximate mass of each neutrino (which may be suitable for hot dark matter) and $I = (3/16 \pi^2)(G_F/\sqrt 2) m_\tau^2 \ln (m_\xi^2/m_W^2)$ comes from the radiative splitting of the degeneracy due to the charged leptons.