Neutrino masses and lepton flavour violating phenomena in the MSSM

Abstract

The most general supersymmetric model with minimal particle content and an additional discrete Ƶ(_3) symmetry, which allows lepton number violating terms, is considered. In this model, we calculate at the level of one-loop the resulting Majorana neutrino masses and the flavour violating radiative decays of charged leptons, ﺎ→ﺎ’γ. We first study the neutral scalar sector of the model, performing a calculable rotation of the scalar fields to a basis in which the sneutrino vacuum expectation values are zero. Lagrangian parameters are initialised without recourse to assumptions concerning trilinear or bilinear terms, CP-conservation or intergenerational mixing and one-loop corrections to the neutrino masses are analysed. We present scenarios in which the experimental data are reproduced. We find that with bilinear lepton number violating couplings in the superpotential of the order 1MeV the atmospheric mass scale can be reproduced. Certain trilinear superpotential couplings, usually of the order of the electron Yukawa coupling can give rise to either atmospheric or solar mass scales and bilinear supersymmetry breaking terms of the order 0.1 GeV(^2) can set the solar mass scale. Taking parameters which correctly describe the neutrino sector, we consider their repercussions in flavour violating radiative lepton decays. Such decays have not been observed and upper bounds on their branching ratios exist. We note that certain parameter sets, which correctly describe the neutrino sector, will also generate observable branching ratios and suggest four such sets as Benchmarks scenarios. We present as Appendices the full set of Feynman Rules for the general super- symmetric standard model with minimal particle content and details of the loop calculations in the Weyl spinor notation.