Stringy Origin of Neutrino Masses within the Minimal Supersymmetric Standard Model

Abstract

We present a ``gravity-induced'' seesaw mechanism, which accommodates neutrino masses ($m_\nu\propto m_u^2/M_I$, with $m_u$ the corresponding quark mass and $M_I\simeq 4\times10^{11}$ GeV) compatible with the MSW study of the Solar neutrino deficit within the minimal supersymmetric Standard Model (the grand desert with the gauge coupling unification at $M_U\simeq 2\times10^{16}$ GeV). We show that for large radius ($R^2/\alpha '={\cal O}(20)$) Calabi-Yau spaces, threshold corrections ensure $M_U^2=M_C^2/{\cal O} (2R^2/\alpha')$ and the magnitude of the non-renormalizable terms in the superpotential yields $M_I= {\cal O}(e^{-R^2/\alpha'})M_C$. Here $M_C=g\times 5.2\times 10^{17}$GeV is the scale of the tree level (genus zero) gauge coupling ($g$) unification.