Radiative four neutrino masses and mixings

The radiative model, proposed by Zee, is extended from the three neutrino $(\nu_{e,\mu,\tau})$ sector to include a fourth sterile neutrino $\nu_s$. The oscillations $\nu_e \leftrightarrow \nu_s$ (solar), $\nu_\mu \leftrightarrow \nu_\tau$ (atmospheric) and $\nu_e \leftrightarrow \nu_\mu$ (LSND) are invoked to explain all oscillation data with the successful relation $(\Delta m^2)_{atm} \simeq 2[(\Delta m^2)_{solar} (\Delta m^2)_{LSND}]^{1/2}$ as an added bonus.