Zee model and Neutrinoless double beta decay

The original Zee model can easily accommodate a bi-maximal mixing solution for the atmospheric and solar neutrino problems. From the most recent fit to the data we obtain a set of parameters for the Zee model. However, the recent claim on a positive signal observed in a neutrinoless double beta decay, which requires a nonzero $m_{ee}$, cannot be accounted for by the Zee model. Based on the observed neutrino mass-square differences and mixings, we derive a few general patterns for the neutrino mass matrix in the flavor basis, which can correctly describe the atmospheric, solar, and $0\nu\beta\beta$ data. Finally, we investigate a few possible extensions to the Zee model, which can give the required mass patterns.