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We examine in detail the neutrino masses and mixing patterns in an extensionof the minimal supersymmetric standard model with three gauge-singlet neutrinosand R-parity violation. The Majorana masses for the gauge-singlet neutrinos aswell as the usual $\mu$-term for the Higgs superfields are generated at theelectroweak scale through the vacuum expectation values of the singletsneutrinos. The resulting effective mass matrix for the three light neutrinoshave contributions from the seesaw mechanism involving the singlet neutrinos aswell as due to the mixing with the heavy neutralinos. This model is popularlyknown in the literature as the "$\mu$ from $\nu$ supersymmetric standard model"($\mu\nu$SSM). We show that even with flavour diagonal neutrino Yukawacouplings, the global data on three-flavour neutrinos can be well accounted forin this scenario, at the tree level. We also analyze the mixing in the charginoand the Higgs sector and calculate the decays of the lightest supersymmetricparticle in this model. The decay branching ratios show certain correlationswith the neutrino mixing angles, which can be tested at the LHC. Some otherphenomenological implications of such a model have been discussed.

Neutrino masses and mixing, lightest neutralino decays and a solution to the $\mu$ problem in supersymmetry