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Register a new userA light pseudoscalar in a model with lepton family symmetry O(2)
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We discuss a realization of the non-abelian group O(2) as a family symmetry for the lepton sector. The reflection contained in O(2) acts as a mu-tau interchange symmetry, enforcing--at tree level--maximal atmospheric neutrino mixing and a vanishing mixing angle theta_13. The small ratio m_mu/m_tau (muon over tau mass) gives rise to a suppression factor in the mass of one of the pseudoscalars of the model. We argue that such a light pseudoscalar does not violate any experimental constraint.
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Motivated by the neutrino data, an extension of the Standard Model with three Higgs-boson doublets has been proposed. Imposing an O(2) x Z2 family symmetry, a neutrino mixing matrix with theta23 = pi/4 and theta13 = 0 appears in a natural way. Even though these values for the mixing matrix do not follow the recent experimental constraints, they are nevertheless a good approximation. We study the Higgs potential of this model in detail. We apply recent methods which allow for the study of any three-Higgs-boson doublet model. It turns out that for a variety of parameters the potential is stable, has the correct electroweak symmetry breaking, and gives the correct vacuum expectation value.
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