Abstract
We discuss the breaking of SO(3) down to finite family symmetries such as A4, S4 and A5 using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric A4 and its finite subgroups Z3 and Z2. We then propose a supersymmetric A4 model of leptons along these lines, originating from SO(3) × U(1), which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged SO(3), leading to massive gauge bosons, and show that all domain wall problems are resolved in this model.
Highlights
The discovery of neutrino mass and lepton mixing [1] represents the first laboratory particle physics beyond the Standard Model (BSM) and raises additional flavour puzzles such as why the neutrino masses are so small, and why lepton mixing is so large [2]
We propose a supersymmetric A4 model of leptons along these lines, originating from SO(3) × U(1), which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account
We discuss the phenomenological consequences of having a gauged SO(3), leading to massive gauge bosons, and show that all domain wall problems are resolved in this model
Summary
The discovery of neutrino mass and lepton mixing [1] represents the first laboratory particle physics beyond the Standard Model (BSM) and raises additional flavour puzzles such as why the neutrino masses are so small, and why lepton mixing is so large [2]. To avoid the domain wall problem of SUSY flavour models, since the non-Abelian discrete flavour symmetry is just an approximate effective residual symmetry arising from the breaking of the continuous symmetry. In the present paper, motivated by the above considerations, we discuss the breaking of a continuous SUSY gauge theory to a non-Abelian discrete symmetry using a potential which preserves SUSY. As stated above, this is the first time that such a symmetry breaking has been discussed in the literature, and the formalism developed here may be applied to the numerous SUSY flavour models in the literature [17,18,19].
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