A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing

We present a see-saw $A_4$ model for Tri-Bimaximal mixing which is based on a very economical flavour symmetry and field content and still possesses all the good features of $A_4$ models. In particular the charged lepton mass hierarchies are determined by the $A_4\times Z_4$ flavour symmetry itself without invoking a Froggatt-Nielsen U(1) symmetry. Tri-Bimaximal mixing is exact in leading order while all the mixing angles receive corrections of the same order in next-to-the-leading approximation. As a consequence the predicted value of $\theta_{13}$ is within the sensitivity of the experiments which will take data in the near future. The light neutrino spectrum, typical of $A_4$ see-saw models, with its phenomenological implications, also including leptoproduction, is studied in detail.Comment: 20 pages, 2 figure

Towards Minimal S4 Lepton Flavor Model

We study lepton flavor models with the $S_4$ flavor symmetry. We construct simple models with smaller numbers of flavon fields and free parameters, such that we have predictions among lepton masses and mixing angles. The model with a $S_4$ triplet flavon is not realistic, but we can construct realistic models with two triplet flavons, or one triplet and one doublet flavons.Comment: 18 pages, 4 figures, references are adde

Tri-Bimaximal Lepton Mixing and Leptogenesis

In models with flavour symmetries added to the gauge group of the Standard Model the CP-violating asymmetry necessary for leptogenesis may be related with low-energy parameters. A particular case of interest is when the flavour symmetry produces exact Tri-Bimaximal lepton mixing leading to a vanishing CP-violating asymmetry. In this paper we present a model-independent discussion that confirms this always occurs for unflavoured leptogenesis in type I see-saw scenarios, noting however that Tri-Bimaximal mixing does not imply a vanishing asymmetry in general scenarios where there is interplay between type I and other see-saws. We also consider a specific model where the exact Tri-Bimaximal mixing is lifted by corrections that can be parametrised by a small number of degrees of freedom and analyse in detail the existing link between low and high-energy parameters - focusing on how the deviations from Tri-Bimaximal are connected to the parameters governing leptogenesis.Comment: 29 pages, 6 figures; version 2: references added, minor correction

A See-Saw S4S_4 model for fermion masses and mixings

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 ${\cal O}(\lambda_C^2)$. 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 ${\cal O}(1)$ 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 ${\cal O}(\lambda_C^2)$.Comment: 30 pages, 3 figures, minor changes to match the published versio

The Interplay Between GUT and Flavour Symmetries in a Pati-Salam x S4 Model

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 $\lambda^{-2}$ and $\lambda^2$, with $\lambda\simeq0.2$. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.Comment: 62 pages, 4 figures; references added, version accepted for publication in JHE