An SU(5) SUSY Model with R-Parity Violation and Radiatively Induced Neutrino Masses

The radiatively induced neutrino mass matrix is investigated on the basis of an SU(5) SUSY model. In order to evade the proton decay, an ansatz based on a discrete symmetry $Z_2$ is assumed: although, at the unification scale, we have two types of superfields ${\mathrm{\Psi }}_{L(\pm )}={\bar{5}}_{L(\pm )}+{10}_{L(\pm )}$, which are transformed as ${\mathrm{\Psi }}_{L(\pm )}\to \pm {\mathrm{\Psi }}_{L(\pm )}$ under the discrete symmetry Z${}_2$, the particles ${\mathrm{\Psi }}_{L(+)}$ are decoupled after the SU(5) symmetry is broken, so that our quarks and leptons belong to \Psi_{L(-)}. The R-parity-violating terms for our quarks and leptons \Psi_{L(-)} are basically forbidden under the symmetry Z_2. However, we assume that mixings between members of \Psi_{L(+)} and those of \Psi_{L(-)} are in part caused after SU(5) is broken. As a result, the R-parity-violating interactions are in part allowed, so that the neutrino masses are radiatively generated, while the proton decay due to the R-parity violating terms is still forbidden because the term d_R^c d_R^c u_R^c has z=-1.