R-Parity Violation in a SUSY GUT Model and Radiative Neutrino Masses

Within the framework of an SU(5) SUSY GUT model, a mechanism which effectively induces R-parity-violating terms below the unification energy scale M_X is proposed. The model has matter fields \bar{5}_{L(+)}+10_{L(-)} and Higgs fields H_{(-)} and \bar{H}_{(+)} in addition to the ordinary Higgs fields H_{(+)} and \bar{H}_{(-)} which contribute to the Yukawa interactions, where (\pm) denote the transformation properties under a discrete symmetry Z_2. The Z_2 symmetry is only broken by the \mu-term \bar{H}_{(+)}H_{(-)} softly, so that the \bar{5}_{(+)}\leftrightarrow \bar{H}_{(+)} \leftrightarrow \bar{H}_{(-)} mixing appears at \mu < m_{SB}, i.e. R-parity violating terms \bar{5}_L\bar{5}_L 10_L are effectively induced from the Yukawa interactions \bar{H}_{(-)}\bar{5}_{L(+)}10_{L(-)}, so that the effective coupling constants \lambda_{ijk} of \nu_{Li} e_{Lj} e_{Rk}^c and \nu_{Li} d_{Rj}^c d_{Lk} are proportional to the mass matrices (M_e^*)_{jk} and (M_d^\dagger)_{jk}, respectively. The parameter regions which are harmless for the proton decay are investigated. Possible forms of the radiatively induced neutrino mass matrix are also investigated.