Three generation neutrino oscillation parameters after SNO

Abstract

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 Δm²₂₁ and Δm²₃₁ ≈ Δm²₃₂ are taken to be in the solar and atmospheric ranges, respectively. We incorporate the constraints on Δm²₃₁ as obtained by the Super Kamiokande atmospheric neutrino data and determine the allowed values of Δm²₂₁, θ₁₂ and θ₁₃ 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 θ₁₃. Since the allowed values of θ₁₃ are constrained to very small values by the CHOOZ experiment there is no qualitative change over the two generation allowed regions in the Δm²₂₁ −tan²θ₁₂ plane. The best fit comes in the LMA region and no allowed area is obtained in the SMA region at the 3σ level from combined solar and CHOOZ analysis.