Radiative neutrino mass matrix for three active plus one sterile species

Abstract

A simple unifying mass matrix is presented for the three active and one sterile neutrinos ${\nu }_e$, ${\nu }_{\mu }$, ${\nu }_{\tau }$ and ${\nu }_s$, using an extension of the radiative mechanism proposed some time ago by Zee. The total neutrino-oscillation data are explained by the scheme ${\nu }_e\leftrightarrow {\nu }_s$ (solar), ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ (atmospheric) and ${\nu }_e\leftrightarrow {\nu }_{\mu }$ (LSND). We obtain the interesting approximate relationship $(\Delta m^2{)}_{atm}\simeq 2[(\Delta m^2{)}_{solar}(\Delta m^2{)}_{LSND}{]}^{1/2}$ which is well satisfied by the data.

Comments: Latex, 12 pages including two figures.