The interplay between grand unified and flavour symmetries in a Pati-Salam × S4 model
Both discrete flavour symmetries and Grand Unified symmetries explain apparent structures in the mass sector of the Standard Model. A model that combines both symmetries is therefore very appealing. We construct a model with the S4 flavour symmetry and the Pati-Salam unification. We show that this model can indeed explain many observable relations between the masses of the quarks and leptons and that it is predictive in the neutrino sector. However, the combination of the two symmetries leads to new complications in the Higgs sector and in the running of the renormalisation group equations.

title: Quark mixing in the discrete dark matter model
abstract: We consider a model in which dark matter is stable as it is charged under a Z 2 symmetry that is residual after an A 4 flavour symmetry is broken. We consider the possibility to generate the quark masses by charging the quarks appropriately under A 4 . We find that it is possible to generate the CKM mixing matrix by an interplay of renormalisable and dimension-six operators. In this set-up, we predict the third neutrino mixing angle to be large and the dark matter relic density to be in the correct range. Low energy observables – in particular meson–antimeson oscillations – are hard to facilitate. We find that only in a situation where there is a strong cancellation between the Standard Model contribution and the contribution of the new Higgs fields, B meson oscillations are under control.

title: Constraining flavour symmetries at the EW scale II: the fermion processes
abstract: We study the set of models in which the Standard Model symmetry is extended with the flavour group A4 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 A4 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.

title: Constraining flavour symmetries at the EW scale I: the A4 Higgs potential
abstract: We consider an extension of the Standard Model in which the symmetry is enlarged by a global flavour factor A4 and the scalar sector accounts for three copies of the Standard Model Higgs, transforming as a triplet of A4. 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 A4. We find that this model independent approach discriminates the different minima allowed by the scalar potential.

title: Discrete flavour symmetries in light of T2K
abstract: We show that a non-vanishing angle θ 13 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 G f which is broken in such a way that neutrino and charged lepton sectors remain invariant under the subgroups G ν and G e of G f , respectively. In this limit mixing angles and the Dirac CP violating phase δ CP are determined. By choosing G f = Δ ( 6 n 2 ) ( n = 4 , 8 ), G ν = Z 2 × Z 2 and G e = Z 3 we find sin 2 θ 13 = 0.045 ( 0.011 ) for n = 4 ( 8 ) . At the same time θ 23 and θ 12 remain close to their experimental best fit values, particularly in the case n = 8 , where sin 2 θ 23 ≈ 0.424 and sin 2 θ 12 ≈ 0.337 . δ CP is predicted to be 0 or π so that CP is conserved in our examples.