Topics in Broken Supersymmetry.

Studies on two topics in the framework of broken supersymmetry are presented. Chapter I is a brief introduction in which the motivation and the background of this work are discussed. In Chapter II, we study the decay K('+)( --->)(pi)('+)(gamma)(gamma) in models with spontaneous supersymmetry breaking and find that it is generally suppressed relative to the decay K('+) (--->) (pi)('+)(nu)(nu) of the conventional model, except possibly for a class of models where the scalar quark masses are generated by radiative corrections from a much larger supersymmetry breaking scale. For a small range of scalar quark and photino mass parameters, the cascade decay process K('+) (--->) (pi)('+)(pi)('0) (--->) (pi)('+)(gamma)(gamma) will become dominant over the (nu)(nu) mode. We also comment on the possibility of probing the neutrino mass through the K('+) (--->) (pi)('+)(pi)('0) (--->) (pi)('+)(nu)(nu) cascade decay. Chapter III is concerned with the implications of explicit lepton number violating soft operators in a general low energy effective theory with softly broken supersymmetry. We find that nonvanishing but relatively small vacuum expectation values of scalar neutrinos could exist. In the case where the vacuum expectation values of scalar neutrinos vanish, appreciable coefficients of the dimension two lepton number violating soft operators are allowed.