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 $\Delta m_{21}^2$ and $\Delta m_{31}^2\approx \Delta m_{32}^2$ are taken to be in the solar and atmospheric ranges, respectively. We incorporate the constraints on $\Delta m_{31}^2$ as obtained by the SuperKamiokande atmospheric neutrino data and determine the allowed values of $\Delta m_{21}^2,$ ${\theta }_{12}$ 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 $\mathrm{solar}+\mathrm{CHOOZ}$ 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 $\Delta m_{21}^2-{\tan }^2{\theta }_{12}$ plane. The best fit comes in the LMA region and no allowed area is obtained in the SMA region at the $3\sigma$ level from combined solar and CHOOZ analysis.