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 $\xi$ to obtain nonzero Majorana neutrino masses, I derive the following simple realistic connection between atmospheric and solar neutrino vacuum oscillations: $(\Delta m^2{)}_{sol}(\Delta m^2{)}_{atm}/m_{\nu }^4({\sin }^{2}2\theta {)}_{atm}=2I^2$, 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.

Comments: Version to appear in Phys. Rev. Lett