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 Z2​ is assumed: although, at the unification scale, we have
two types of superfields ΨL(±)​=5ˉL(±)​+10L(±)​, which
are transformed as ΨL(±)​→±ΨL(±)​ under the discrete
symmetry Z2​, the particles ΨL(+)​ 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.Comment: 6 pages, Revtex, no figur