Electron-Neutrino Majorana Mass and Solar Neutrino Oscillations

Abstract

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 $\Delta m^2/m_{\nu }^2=(3c^2/4{\pi }^2)(G_F/\sqrt{2})m_{\tau }^2\ln (m_{\xi }^2/m_W^2)$. This is applicable to the small-angle matter-enhanced oscillation solution of the solar neutrino deficit and restricts $m_{\nu }$ to be between 0.20 and 0.36 eV if $c^2=0.7$ and $m_{\xi }=10^{14}$ GeV.

Comments: 7 pages including 1 figure, slightly revised version to appear in Physics Letters B