Minimal flavour violation extensions of the seesaw

We analyze the most natural formulations of the minimal lepton flavour violation hypothesis compatible with a type-I seesaw structure with three heavy singlet neutrinos N , and satisfying the requirement of being predictive, in the sense that all LFV effects can be expressed in terms of low energy observables. We find a new interesting realization based on the flavour group SU(3) e × SU(3) ℓ + N (being e and ℓ respectively the SU(2) singlet and doublet leptons). An intriguing feature of this realization is that, in the normal hierarchy scenario for neutrino masses, it allows for sizeable enhancements of μ → e transitions with respect to LFV processes involving the τ lepton. We also discuss how the symmetries of the type-I seesaw allow for a strong suppression of the N mass scale with respect to the scale of lepton number breaking, without implying a similar suppression for possible mechanisms of N production.