Full Numerical Estimation of Neutrino Mixing Parameters from Solar Neutrino Data

We have numerically computed survival probabilities of solar neutrinos interacting with matter via MSW mechanism in the full three generation formalism with $\Delta m^2_{23}=2.2\times 10^{-3}$ eV$^2$. For $\theta_{13} \lesssim 30^{\circ}$, we confirm the two regions found in the two generation case, (1) with the most likelyhood, small $\sin^2(2\theta_{12}) \sim 0.006$, (2) with less likelyhood, large $\sin^2(2\theta_{12}) \gtrsim 0.5$. For $\theta_{13}\gtrsim 30^{\circ}$, we find an additional region, (3) with even less likelyhood, $10^{-5} < \Delta m^2_{12}< 10^{-4}$ eV$^2$ and/or $10^{-4} < \sin^2(2\theta_{12}) < 0.5$. Assuming that the case (1) is valid, we predict that $\theta_{13} \simeq 15^\circ$.