The discrete flavor symmetry $A_4$ explains very well neutrino data at low energy, but it seems difficult to extend it to grand unified models since, in general, left-handed and right-handed fields belong to different $A_4$ representations. Recently a model has been proposed where all the fermions equally transform under $A_4$. We study here a concrete $SO(10)$ realization of such a model providing small neutrino masses through the see-saw mechanism. We fit the charged fermion masses run up to the unification scale. Some fermion masses properties come from the $SO(10)$ symmetry while lepton mixing angles are a consequence of the $A_4$ properties. Moreover, our model predicts the absolute value of the neutrino masses; these are in the range $m_{\nu }\simeq 0.005–0.052\mathrm{eV}$.

We address two fundamental aspects of flavor physics: the mass hierarchy and the large lepton mixing angles. On one side, left–right flavor symmetry realizes the democratic mass matrix patterns and explains why one family is much heavier than the others. On the other side, discrete flavor symmetry such as A₄ $A_4$ <!--mathContainer--> <!--Loading Mathjax--> leads to the observed tribimaximal mixing for the leptons. We show that, by explicitly breaking the left–right flavor symmetry into the diagonal A₄ $A_4$ <!--mathContainer--> <!--Loading Mathjax--> , it is possible to explain both the observed charged fermion mass hierarchies and quark and lepton mixing angles. In particular we predict a heavy 3rd family, the tribimaximal mixing for the leptons, and we suggest a possible origin of the Cabibbo and other mixing angles for the quarks.

We analyze all possible extensions of the recently proposed minimal renormalizable SUSY SU(5) grand unified model with the inclusion of an additional A4 flavor symmetry. We find that there are five possible cases but only one of them is phenomenologically interesting. We develop in detail such case and we show how the fermion masses and mixing angles come out. As a prediction we obtain the neutrino masses of order of 0.1 eV with an inverted hierarchy.Comment: V1: 22 pages, V2: 16 pages, published version, results unchange

We address the problem of rationalizing the pattern of fermion masses and mixings by adding a non-Abelian flavor symmetry in a grand unified framework. With this purpose, we include an A4 flavor symmetry into a unified renormalizable supersymmetric grand unified theory SU(5) model. With the help of the ``type~II seesaw'' mechanism we are able to obtain the pattern of observed neutrino mixings in a natural way, through the so-called tribimaximal matrix.

We generalize to three active flavors a previous two-flavor model for the resonant spin flavor conversion of solar neutrinos to sterile ones, a mechanism which is added to the well-known large mixing angle (LMA) one. The transition magnetic moments from the muon and tau neutrinos to the sterile play the dominant role in fixing the amount of active flavor suppression. We also show, through numerical integration of the evolution equations, that the data from all solar neutrino experiments except Borexino exhibit a clear preference for a sizable magnetic field either in the convection zone or in the core and radiation zone. This is possibly related to the fact that the data from the first set are average ones taken during a period of mostly intense solar activity, whereas in contrast Borexino data were taken during a period of quiet Sun. We argue that the solar neutrino experiments are capable of tracing the possible modulation of the solar magnetic field. Those monitoring the high-energy neutrinos, namely, the ${}^8\mathrm{B}$ flux, appear to be sensitive to a field modulation either in the convection zone or in the core and radiation zone. Those monitoring the low-energy fluxes will be sensitive to the second type of solar field profiles only. In this way Borexino alone may play an essential role, since it examines both energy sectors, although experimental redundancy from other experiments will be most important.