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 $\mathrm{\Delta }{m}_{23}^2=2.2\times {10}^{-3}$ 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, ${10}^{-5}<\mathrm{\Delta }{m}_{12}^2<{10}^{-4}$ eV${}^2$ and/or $10^{-4} < \sin^2(2\theta_{12}) < 0.5$. Assuming that the case (1) is valid, we predict that ${\theta }_{13}\simeq {15}^{\circ }$.