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We show that a non-vanishing angle θ13 of order 0.1 can be predicted in the framework of discrete flavour symmetries. We assume that left-handed leptons transform as triplets under a group Gf which is broken in such a way that neutrino and charged lepton sectors remain invariant under the subgroups Gν and Ge of Gf, respectively. In this limit mixing angles and the Dirac CP violating phase δCP are determined. By choosing Gf=Δ(6n2) (n=4,8), Gν=Z2×Z2 and Ge=Z3 we find for n=4(8). At the same time θ23 and θ12 remain close to their experimental best fit values, particularly in the case n=8, where and . δCP is predicted to be 0 or π so that CP is conserved in our examples

Abstract:We study the set of models in which the Standard Model symmetry is extended with the flavour group A 4 and there are three copies of the Standard Model Higgs that transform as a triplet under this group. In this setup, new channels for flavour violating processes can be studied once the A 4 representations of the fermions in the theory are given. We show that it is of great importance to take these constraints into account as they can put severe constraints on the viability of flavour models.

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry S 4 that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between λ −2 and λ 2 , with λ ≃ 0.2. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.

We consider an extension of the Standard Model in which the symmetry is enlarged by a global flavour factor A 4 and the scalar sector accounts for three copies of the Standard Model Higgs, transforming as a triplet of A 4. In this context, we study the most general scalar potential and its minima, performing for each of them a model independent analysis on the related phenomenology. We study the scalar spectrum, the new contributions to the oblique corrections, the decays of the Z and W ± , the new sources of CP and flavour violation, which all are affected by the introduction of multiple Higgses transforming under A 4. We find that this model independent approach discriminates the different minima allowed by the scalar potential.