ar X iv : h ep - p h / 01 09 16 1 v 1 1 8 Se p 20 01 MASSIVE NEUTRINOS AND LEPTON - FLAVOUR - VIOLATING PROCESSES

If neutrino masses and mixings are suitable to explain the atmospheric and solar neutrino fluxes, this amounts to contributions to FCNC processes, in particular µ → e, γ. If the theory is supersymmetric and the origin of the masses is a seesaw mechanism, we show that the prediction for BR(µ → e, γ) is in general larger than the experimental upper bound, especially if the solar data are explained by a large angle MSW effect, which recent analyses suggest as the preferred scenario. In the pure Standard Model, flavour is exactly conserved in the leptonic sector since one can always choose a basis in which the (charged) lepton Yukawa matrix, Y e , and gauge interactions are flavour-diagonal. If neutrinos are massive and mixed, as suggested by the observation of atmospheric and solar fluxes 1 , this is no longer true and there exists a source of lepton flavour violation (LFV), in analogy with the Kobayashi–Maskawa mechanism in the quark sector. Unfortunately, due to the smallness of the neutrinos masses, the predicted branching ratios for these processes are so tiny that they are completely unobservable, namely BR(µ → eγ) < 10 −50 2. In a supersymmetric (SUSY) framework the situation is completely different. Besides the previous mechanism, supersymmetry provides new direct sources of flavour violation in the leptonic sector, namely the possible presence of off-diagonal soft terms 3. In a self-explanatory notation, they have the form