Shedding light on flavour symmetries with rare decays of quarks and leptons

In the last few years there has been a great experimental progress in quark and lepton flavour physics. On the quark side, the two B-factories have been very successful, both from the accelerator and the detector point of view. As a result, all the relevant parameters describing quark-flavour mixing within the Standard Model (quark masses and CKM angles) are now know with good accuracy. Despite this great progress, the overall picture of quark flavour physics is a bit frustrating as far as the search for physics beyond the Standard Model (SM) is concerned. The situation is somehow similar to the flavour-conserving electroweak physics after LEP: the SM works very well and genuine one-loop electroweak effects have been tested with relative accuracy in the 10%–30% range. The situation of the lepton sector is more uncertain but also more exciting. The discovery of neutrino oscillations has two very significant implications: i) the SM is not complete; ii) there exists new flavour structures in addition to the three SM Yukawa couplings. We have not yet enough information to unambiguously determine how the SM Lagrangian should be modified in order to describe the phenomenon of neutrino oscillations. However, natural explanations point toward the existence of new degrees of freedom with explicit breaking of lepton number at very high energy scales (ΛLN ∼ 10–10 GeV), in agreement with the expectations of Grand Unified Theories (GUT). As I will discuss in this talk, these insight about non-SM degrees of freedom from neutrino physics are likely to have non-trivial implications in other sectors of the model. In particular, in rare decays of charged leptons and, possibly, in a few rare B and K decays. Interestingly enough, these connections can be derived without specific dynamical assumptions about new physics, but only analysing the flavour-symmetry structure of the theory be means of general Effective Field Theory (EFT) approaches.