Flavour problems and new physics at TeV scale

There is no explanation in the Standard Model for the replication of fermion families, neither for the mass hierarchy between them nor for the structure of the Yukawa coupling matrices, which remain arbitrary. The key towards under- standing the fermion masses and mixing pattern can be in symmetry principles. Masses of fermions can actually have a dynamical origin, following the spon- taneous symmetry breaking of gauge “horizontal" symmetries unifying families, differently acting on left and right species. U(3) or SU(3) “horizontal" family symmetries seem an intuitive hypothesis to be considered. Fermion masses should be induced by higher order operators containing flavon scalars emerging from renormalizable interactions via ‘universal seesaw’ mechanism after integrat- ing out some heavy fields, scalars or verctor-like fermions. Then in this case the fermion mass hierarchy and mixing among families can be related to the pat- tern of spontaneous breaking of the gauge SU(3) symmetry. The corresponding gauge bosons have flavor-nondiagonal couplings to fermions which in principle can induce flavour changing phenomena. In this case strong lower limits on the flavor symmetry breaking scales are expected. However, for special choices of horizontal symmetries there is a natural suppression of flavour changing effects due to a custodial symmetry. So gauge bosons can have mass in the TeV range, without contradicting the existing experimental limits. However an unexpected anomaly shows up in quark mixing. After the recent high precision determinations of Vus and Vud, the first row of the CKM matrix is about 4σ deviated from unitarity. The existence of the gauge symmetry SU(3)l acting between lepton families can recover unitarity if the symmetry is broken at a scale of about 6 TeV. In fact the gauge bosons of this symmetry contribute to muon decay in interference with the Standard Model, so that the Fermi constant is slightly smaller than the muon decay constant and unitarity is restored. Alternatively, extra vector-like quarks can be thought as a solution to the CKM unitarity problem. The extra species should exhibit a large mixing with the first family in order to recover unitarity, then their mass should be no more than 6 TeV or so. The implications of the existence of so large mixing must be examined, in order to understand if it can actually exist without contradiction with experimental results on flavour changing neutral current processes and Standard Model observables. In principle an extra weak isodoublet can solve all the discrepancies between independent determinations of the CKM elements in the first row. However not all the discrepancies can be entirely recovered with- out contradicting experimental constraints. Then the existence of two or more vector-like doublets or a vector-like isodoublet with a down-type or up-type isos- inglet can be considered. In these scenarios unitarity can be resettled and flavour changing can be avoided by setting to zero some couplings of extra species with Standard Model families. If the anomalies in the determination of CKM mixing angles are confirmed by future experiments with greater precision, there might be strong indication towards the existence of physics beyond the Standard Model at the TeV scale, such as flavour changing gauge bosons and vector-like fermions with masses of few TeV. This new physics can be testable at next runs of high luminosity LHC or, more effectively, in future accelerators.