Electron-Neutrino Majorana Mass and Solar Neutrino Oscillations

Assuming the Majorana masses of $\nu_e$ and the linear combination $c \nu_\tau - s \nu_\mu$ to be equal from their couplings to a heavy scalar triplet $\xi$, I show that their radiative splitting is given by $\Delta m^2/m_\nu^2 = c^2 G_F m_\tau^2 \ln (m_\xi^2/m_W^2)/\pi^2 \sqrt 2$. This is applicable to the small-angle matter-enhanced oscillation solution of the solar neutrino deficit and restricts $m_\nu$ to be between 0.17 and 0.31 eV if $c^2 = 0.7$ and $m_\xi = 10^{14}$ GeV.