Radiative Neutrino Masses in a SUSY GUT Model

Radiatively-induced neutrino mass matrix is investigated within the framework of an SU(5) SUSY GUT model. The model has matter fields of three families \bar{5}{L(+)i}+5{L(+)i} in addition to the ordinary matter fields \bar{5}{L(-)i}+10{L(+)i} and Higgs fields H_{(+)}+\bar{H}{(0)}, where (+,0,-) denote the transformation properties (\omega^{+1},\omega^0,\omega^{-1}) (\omega^3=+1) under a discrete symmetry Z_3. R-parity violating terms are given by \bar{5}{L(+)} \bar{5}{L(+)} 10{L(+)}, while the Yukawa interactions are given by \bar{H}{(0)} \bar{5}{L(-)} 10_{L(+)}, i.e. the \bar{5}-fields in both are different from each other. The Z_3 symmetry is only broken by the terms \bar{5}{L(+)i}5{L(+)i} softly, so that the \bar{5}{L(+)i}\leftrightarrow \bar{5}{L(-)i} mixings appear at \mu < M_X. Of the R-parity violating terms \bar{5}{L(+)} \bar{5}{L(+)} 10_{L(+)}, only the terms (e_L\nu_-\nu_Le_)e_R^c sizably appear at \mu < M_X.