Charged-lepton-flavour violation in the light of the Super-Kamiokande data

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 --> e gamma and tau --> mu gamma, but also commenting on mu --> 3e and tau --> 3 mu/e decays, as well as mu --> 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 phenomenalogical 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 --> e gamma and tau --> 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 --> e conversion on Titanium, which may also be accessible to future experiments.