Three Generation Neutrino Oscillation Parameters after SNO

We examine the solar neutrino problem in the context of the realistic three neutrino mixing scenario including the SNO charged current (CC) rate. The two independent mass squared differences $\mathrm{\Delta }{m}_{21}^2$ and $\Delta m^2_{31} \approx \Delta m^2_{32}$ are taken to be in the solar and atmospheric ranges respectively. We incorporate the constraints on $\mathrm{\Delta }$m${}_{31}^2$ as obtained by the SuperKamiokande atmospheric neutrino data and determine the allowed values of $\mathrm{\Delta }{m}_{21}^2$, ${\theta }_{12}$ and ${\theta }_{13}$ from a combined analysis of solar and CHOOZ data. Our aim is to probe the changes in the values of the mass and mixing parameters with the inclusion of the SNO data as well as the changes in the two-generation parameter region obtained from the solar neutrino analysis with the inclusion of the third generation. We find that the inclusion of the SNO CC rate in the combined solar + CHOOZ analysis puts a more restrictive bound on ${\theta }_{13}$. Since the allowed values of ${\theta }_{13}$ are constrained to very small values by the CHOOZ experiment there is no qualitative change over the two generation allowed regions in the $\Delta m^2_{21} - \tan^2 \theta_{12}$ plane. The best-fit comes in the LMA region and no allowed area is obtained in the SMA region at 3$\sigma$ level from combined solar and CHOOZ analysis.