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Constraints on a general 3-generation neutrino mass matrix from neutrino data: application to the MSSM with R-parity violation

We consider a general symmetric $(3\times 3)$ mass matrix for three generations of neutrinos. Imposing the constraints, from the atmospheric neutrino and solar neutrino anomalies as well as from the CHOOZ experiment, on the mass squared differences and on the mixing angles, we identify the ranges of allowed inputs for the 6 matrix elements. We apply our results to Majorana left-handed neutrino masses generated at tree level and through fermion--sfermion loop diagrams in the MSSM with R-parity violation. The present experimental results on neutrinos from laboratories, cosmology and astrophysics are implemented to either put bounds on trilinear ($λ_{ijk}, λ'_{ijk}$) and bilinear ($μ_{e,μ,τ}$) R-parity-violating couplings or constrain combinations of products of these couplings.