Constraints on radiative neutrino mass models from oscillation data

The three neutrino Zee model and its extension, including three active and one sterile species, are studied in the light of new neutrino oscillation data. We obtain analytical relations for the mixing angle in solar oscillations in terms of neutrino mass squared differences. For the four neutrino case, we obtain the result ${\sin }^{2}2{\theta }_{\odot }\approx 1-\left[\right(\Delta {\mathrm{m}}_{\mathrm{Atm}}^2{)}^2/\left(4\mathrm{}\Delta {\mathrm{m}}_{\mathrm{LSND}}^2\Delta {\mathrm{m}}_{\odot }^2\right){]}^2,$ which can accommodate both the large and small mixing scenarios. We show that, within this framework, while both the small mixing angle–Mikheyev-Smirnov-Wolfenstein (MSW) and the large mixing angle–MSW solutions can easily be accommodated, it would be difficult to reconcile the low probability, low mass–quasivacuum oscillation solutions. We also comment on the active-sterile admixture within phenomenologically viable textures.