Charged-Lepton-Flavour Violation in the light of the Super-Kamiokande data

Abstract. Motivated by the data from Super-Kamiokande and elsewhere indicating oscillations of atmospheric and solar neutrinos, we study charged-lepton-flavour violation, in particular the radiative decays $\mu \rightarrow e \gamma$ and $\tau \rightarrow \mu \gamma$, but also commenting on $\mu \to 3e$ and $\tau \to 3 \mu/e$ decays, as well as $\mu \to e$ conversion on nuclei. We first show how the renormalization group may be used to calculate flavour-violating soft supersymmetry-breaking masses for charged sleptons and sneutrinos in models with universal input parameters. Subsequently, we classify possible patterns of lepton-flavour violation in the context of phenomenological neutrino mass textures that accommodate the Super-Kamiokande data, giving examples based on Abelian flavour symmetries. Then we calculate in these examples rates for $\mu \rightarrow e \gamma$ and $\tau \rightarrow \mu \gamma$, which may be close to the present experimental upper limits, and show how they may distinguish between the different generic mixing patterns. The rates are promisingly large when the soft supersymmetry-breaking mass parameters are chosen to be consistent with the cosmological relic-density constraints. In addition, we discuss $\mu \rightarrow e$ conversion on Titanium, which may also be accessible to future experiments.