Radiative origin of solar scale and $U_{e3}$

We make a general study of possibility of generating the solar scale $\Delta_{\odot}$ and the CHOOZ angle $U_{e3}$ radiatively by assuming that they are zero at some high scale. The most general neutrino mass matrix leading to this result is determined in a CP conserving theory. This matrix contains four independent parameters which can be fixed in terms of physical observables. The standard weak radiative corrections then lead to non-zero $\Delta_{\odot}$ and $U_{e3}$ without drastically altering the other tree level results. As a consequence, both $\Delta_{\odot}$ and $U_{e3}$ are predicted in terms of other physically observable parameters. These predictions are insensitive to specific form of the neutrino mass matrix. The solar scale and $U_{e3}$ are strongly correlated with the effective neutrino mass $m_{ee}$ probed in neutrinoless double beta decay. In particular, the LMA solution to the solar neutrino problem arise for $m_{ee}$ close to the present experimental limit. An example of specific texture is presented which predicts maximal atmospheric mixing and $\tan^2 \theta_{\odot}\approx 0.5$ for the solar mixing angle $\theta_{\odot}$. LMA solution is obtained in this case for values of $m_{ee}$ around 0.4 eV.