A three-parameter model for the neutrino mass matrix

Abstract

Using the type-II seesaw mechanism with three Higgs doublets phi_alpha (alpha = e, mu, tau) and four Higgs triplets, we build a model for lepton mixing based on a 384-element horizontal symmetry group, generated by the permutation group S_3 and by six Z_2 transformations. The charged-lepton mass matrix is diagonal; the symmetries of the model would require all the three masses m_alpha to be equal, but different vacuum expectation values of the phi_alpha allow the m_alpha to split. The number of parameters in the Majorana neutrino mass matrix m_nu depends on two options: full breaking of the permutation group S_3, or leaving a mu--tau interchange symmetry intact; and hard or spontaneous violation of CP. We discuss in detail the case with the minimal number of three parameters, wherein m_nu is real, symmetric under mu--tau interchange, and has equal diagonal elements. In that case, CP is conserved in lepton mixing, atmospheric neutrino mixing is maximal, and theta_{13} = 0; moreover, the type of neutrino mass spectrum and the absolute neutrino mass scale are sensitive functions of the solar mixing angle.

16 pages, one eps figure; some clarifications added, contains new section 5, version accepted for publication in J. Phys. G

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• Finite flavour groups of fermions
• Maximal CP violation in lepton mixing from a model with Delta(27) flavour symmetry
• An A4 model for lepton masses and mixings
• A Supersymmetric D4 Model for mu-tau Symmetry
• Tri-bimaximal lepton mixing from symmetry only
• Inverted Mass Hierarchy from Scaling in the Neutrino Mass Matrix: Low and High Energy Phenomenology
• Correlation between Leptonic CP Violation and mu-tau Symmetry Breaking
• Cobimaximal lepton mixing from soft symmetry breaking
• Non-Abelian Discrete Flavor Symmetries
• A three-parameter neutrino mass matrix with maximal CP violation
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• Symmetryless Dark Matter
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