A See-Saw $S_4$ model for fermion masses and mixings

Abstract

We present a supersymmetric see-saw $S_4$ model giving rise to the most general neutrino mass matrix compatible with Tri-Bimaximal mixing. We adopt the $S_4\times Z_5$ flavour symmetry, broken by suitable vacuum expectation values of a small number of flavon fields. We show that the vacuum alignment is a natural solution of the most general superpotential allowed by the flavour symmetry, without introducing any soft breaking terms. In the charged lepton sector, mass hierarchies are controlled by the spontaneous breaking of the flavour symmetry caused by the vevs of one doublet and one triplet flavon fields instead of using the Froggatt-Nielsen U(1) mechanism. The next to leading order corrections to both charged lepton mass matrix and flavon vevs generate corrections to the mixing angles as large as $\mathcal{O}({\lambda }_C^2)$. Applied to the quark sector, the symmetry group $S_4\times Z_5$ can give a leading order $V_{CKM}$ proportional to the identity as well as a matrix with $\mathcal{O}(1)$ coefficients in the Cabibbo $2\times 2$ submatrix. Higher order corrections produce non vanishing entries in the other $V_{CKM}$ entries which are generically of $\mathcal{O}({\lambda }_C^2)$.

30 pages, 3 figures, minor changes to match the published version

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• Neutrino Mixings and the S4 Discrete Flavour Symmetry
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• SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry
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• Flavored Orbifold GUT - an SO(10) x S4 model
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• An S4 model for quarks and leptons with maximal atmospheric angle
• Minimal seesaw model with S_4 flavor symmetry
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• Neutrino Mixing Angles in Sequential Dominance to NLO and NNLO
• Admixture of quasi-Dirac and Majorana neutrinos with tri-bimaximal mixing
• Perturbing exactly tri-bimaximal neutrino mixings with charged lepton mass matrices
• S_4 x Z_2 Flavor Symmetry in Supersymmetric Extra U(1) Model
• Towards Minimal S4 Lepton Flavor Model
• Strong coupling, discrete symmetry and flavour
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• Renormalization Group Running of Lepton Mixing Parameters in See-Saw Models with $S_4$ Flavor Symmetry
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• Coxeter groups and the PMNS matrix
• Dark Matter interactions in an $S_4\times Z_5$ flavor symmetry framework
• Resonant leptogenesis and TM${}_1$ mixing in minimal Type-I seesaw model with S${}_4$ symmetry