Flavour and CP violation in the lepton sector and new physics

We give a pedagogical review of flavour and CP violation in the lepton sector, with a particular emphasis on new physics - and in particular supersymmetric - contributions to flavour and CP violating observables involving leptons. We can see that flavour and CP violation have a very different status in the lepton and in the quark sectors. Indeed, if the PMNS matrix (the Pontecorvo-Maki-Nakagawa-Sakata matrix U) is the only source of flavour and CP violation in the lepton sector, neutrino oscillations are likely to be the only manifestation of lepton flavour violation that can be accessed experimentally, as well as the only place (together with neutrinoless double beta decay if neutrinos are Majorana particles) where one can possibly test leptonic CP violation. Lepton flavour violating processes involving charged leptons and charged lepton electric dipole moments, are therefore a unique probe of new physics. The observation of e.g. μ → eγ, or the measurement of a nonzero muon EDM would definitely testify for physics beyond the Standard Model. A significant improvement of the experimental upper limits on BR(μ → eγ) and BR(τ → μγ) would already provide strong constraints on supersymmetry breaking and on supersymmetric seesaw models