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 $ν_e$, $ν_μ$, $ν_τ$ and $ν_s$, using an extension of the radiative mechanism proposed some time ago by Zee. The total neutrino-oscillation data are explained by the scheme $ν_e \leftrightarrow ν_s$ (solar), $ν_μ\leftrightarrow ν_τ$ (atmospheric) and $ν_e \leftrightarrow ν_μ$ (LSND). We obtain the interesting approximate relationship $(Δm^2)_{atm} \simeq 2[(Δm^2)_{solar} (Δm^2)_{LSND}]^{1/2}$ which is well satisfied by the data.