Neutrino masses within the minimal supersymmetric standard model

We investigate the possibility of accommodating neutrino masses compatible with the Mikheyev-Smirnov-Wolfenstein study of the solar neutrino deficit within the minimal supersymmetric standard model. The "gravity-induced" seesaw mechanism based on an interplay of nonrenormalizable and renormalizable terms in the superpotential allows neutrino masses mνmu2M1, with mu the corresponding quark mass and M14×1011 GeV, while at the same time ensuring the grand desert with the gauge coupling unification at MU2×1016 GeV. The proposed scenario may be realized in a class of string vacua, i.e., large radius (R2α′∼20) (0,2) Calabi-Yau spaces. In this case MU2=MC2O(2R2α′) and M1=O(e-R2α′)MC. Here MC=g×5.2×1017 GeV is the scale of the tree-level (genus-zero) gauge coupling (g) unification.