Abstract
Abstract Discrete flavour groups have been studied in connection with special patterns of neutrino mixing suggested by the data, such as Tri-Bimaximal mixing (groups A 4, S 4…) or Bi-Maximal mixing (group S 4…) etc. We review the predictions for sin θ 13 in a number of these models and confront them with the experimental measurements. We compare the performances of the different classes of models in this respect. We then consider, in a supersymmetric framework, the important implications of these flavour symmetries on lepton flavour violating processes, like μ → eγ and similar processes. We discuss how the existing limits constrain these models, once their parameters are adjusted so as to optimize the agreement with the measured values of the mixing angles. In the simplified CMSSM context, adopted here just for indicative purposes, the small tan β range and heavy SUSY mass scales are favoured by lepton flavour violating processes, which makes it even more difficult to reproduce the reported muon g − 2 discrepancy.
Highlights
In the following we will mainly refer to TB or BM mixing which are the most studied first approximations to the data
The rather large value measured for θ13, close to the old CHOOZ bound, has validated the prediction of models based on anarchy [118, 119], i.e. no symmetry in the leptonic sector, only chance, so that this possibility remains valid, as discussed, for example, in ref
Anarchy can be formulated in a SU(5)⊗U(1) context by taking different FroggattNielsen [121] charges only for the SU(5) tenplets (for example 10 ∼ (3, 2, 0), where 3 is the charge of the first generation, 2 of the second, zero of the third) while no charge differences appear in the5 ( ̄5 ∼ (0, 0, 0))
Summary
At the LO the lepton mixing arises from a mismatch between the residual symmetries Ge and Gν of charged lepton and neutrino sectors, respectively In this approximation charged leptons and neutrinos acquire mass from two independent sets of flavons, Φe and Φν, whose VEVs preserve two Abelian groups: Ge = Zn (n ≥ 3) and Gν = Z2 × Z2. Gei and gνi are the elements of Ge and Gν and ρ denotes an irreducible threedimensional unitary representation of the group G generated by Ge and Gν.2 Both Ge and Gν are Abelian and the matrices ρ(gei) and ρ(gνi) can be diagonalized by two independent unitary transformations Ωe and Ων ρ(gνi)diag = Ω†ν ρ(gνi) Ων , ρ(gei)diag = Ω†e ρ(gei) Ωe ,. Higher order operators contribute to lepton masses without respecting the LO residual symmetries. Depending on the agreement of the LO approximation to the data, Φe /Λ and Φν /Λ will typically range between λ2C and λC
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