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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 (ω^{+1},ω^0,ω^{-1}) (ω^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 μ< M_X. Of the R-parity violating terms \bar{5}_{L(+)} \bar{5}_{L(+)} 10_{L(+)}, only the terms (e_Lν_-ν_Le_)e_R^c sizably appear at μ< M_X.