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Register a new userThe flavour problem and family symmetry
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We show how two different family symmetries can be used to address the flavour problem in SO(10)-like models. The first is based on a gauged $U(1)_F$, whose problems dissappear in the context of a type I string model embedding. The second is based on $SU(3)_F$, the maximal family group consistent with SO(10); in this case the family symmetry is more constaining, so we merely look at it in the context of a supersymmetric field theory
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We show how the SUSY flavour and CP problems can be solved using gauged SU(3) family symmetry previously introduced to describe quark and lepton masses and mixings, in particular neutrino tri-bimaximal mixing via constrained sequential dominance. The Yukawa and soft trilinear and scalar mass squared matrices and kinetic terms are expanded in powers of the flavons used to spontaneously break the SU(3) family symmetry, and the canonically normaliz
Can a theory of flavour capable of describing the spectrum of fermion (including neutrino) masses and mixings also contain within it the seeds for a solution of the SUSY flavour and CP problems? We argue that supergravity together with a non-Abelian family symmetry can completely resolve the SUSY flavour and CP problems in a broad class of theories in which family symmetry and CP is spontaneously broken in the flavon sector. We show that a simple superpotential structure can suppresses the F-terms of the flavons and GUT scale Higgs fields and that, if this mechanism is implemented, the resulting flavour and CP violation is suppressed and comfortably within the experimental limits. For illustration, we study a specific model based on SU(3) family symmetry, but similar models based on non-Abelian (continuous or discrete) family symmetry will lead to similar results.
We consider the problem of trying to understand the recently measured neutrino data simultaneously with understanding the heirarchical form of quark and charged lepton Yukawa matrices. We summarise the data that a sucessful model of neutrino mass must predict, and then move on to attempting to do so in the context of spontaneously broken `family symmetries. We consider first an abelian U(1) family symmetry, which appears in the context of a type I string model. Then we consider a model based on a non-abelian SU(3)_F, which is the maximal family group consitent with an SO(10) GUT. In this case the symmetry is more constraining, and is examined in the context of SUSY field theory.
We discuss our recently proposed S3(down)xS3(up) flavour-permutation-symmetric mixing observables, giving expressions for them in terms of (moduli-squared) of the mixing matrix elements. We outline their successful use in providing flavour-symmetric descriptions of (non-flavour-symmetric) lepton mixing schemes. We develop our partially unified flavour-symmetric description of both quark and lepton mixings, providing testable predictions for CP-violating phases in both B decays and neutrino oscillations.
We present a supersymmetric extension of the Standard Model with a gauged SU(2) family symmetry for the leptons. It is shown that this family symmetry can be consistently broken at the TeV scale along with supersymmetry. If supersymmetry breaking is driven by anomaly mediation, this model can provide positive squared masses for the sleptons and thus cure the tachyon problem. We analyze the constraints and consequences of this scenario. A characteristic feature of this model is the non-degeneracy of the first two family sleptons. The model predicts large value of tan(beta) and observable tau to e gamma and B to mu^+ mu^- decay rates.
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