Simple Connection Between Atmospheric and Solar Neutrino Vacuum Oscillations

Abstract

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