Electron-Neutrino Majorana Mass and Solar Neutrino Oscillations

Abstract

Assuming the Majorana masses of $ν_e$ and the linear combination $c ν_τ- s ν_μ$ to be equal from their couplings to a heavy scalar triplet $ξ$, I show that their radiative splitting is given by $Δm^2/m_ν^2 = (3 c^2/4 π^2) (G_F/\sqrt 2) m_τ^2 \ln (m_ξ^2/m_W^2)$. This is applicable to the small-angle matter-enhanced oscillation solution of the solar neutrino deficit and restricts $m_ν$ to be between 0.20 and 0.36 eV if $c^2 = 0.7$ and $m_ξ= 10^{14}$ GeV.