Neutrino masses, the $\mu$-term and ${\mathcal{P}\mathcal{SL}}_2(7)$

Abstract

Using an $SO(10)$-inspired form for the Dirac neutrino mass, we map the neutrino data to right-handed neutrino Majorana mass-matrix, $\mathcal{M}$, and investigate a special form with \emph{seesaw} tribimaximal mixing; it predicts a normal hierarchy, and the values of the light neutrino masses. It may be generated by mapping the top quark hierarchy onto the vacuum values of familon fields transforming under the family group ${\mathcal{P}\mathcal{SL}}_2(7)$. We next investigate the hypothesis that these familons play a dual role, generating a hierarchy in the supersymmetric $\mu$-mass matrix of Higgses carrying family quantum numbers. A special ${\mathcal{P}\mathcal{SL}}_2(7)$ invariant coupling produces a $\mu$-matrix with a hierarchy of thirteen orders of magnitude. Only one Higgs field (per hypercharge sector) is light enough (with a $\mu$-mass $\sim 10-100$ GeV) to be destabilized by SUSY soft breaking at the TeV scale, and upon spontaneous symmetry breaking, gives \emph{tree-level} masses for the heaviest family.

arXiv comment26 pages, no figures

References in corpus (20)

• Planck 2013 results. XVI. Cosmological parameters
• Observation of electron-antineutrino disappearance at Daya Bay
• A Supersymmetry Primer
• Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment
• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• Indication for the disappearance of reactor electron antineutrinos in the Double Chooz experiment
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Neutrino Mass and Mixing with Discrete Symmetry
• Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP violation searches
• Symmetries and Generalisations of Tri-Bimaximal Neutrino Mixing
• Theory of Neutrinos: A White Paper
• A 2-3 Symmetry in Neutrino Oscillations
• Bimaximal Neutrino Mixing and Neutrino Mass Matrix
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• Unification and Fermion Mass Structure
• Cabibbo Haze in Lepton Mixing
• Simple Finite Non-Abelian Flavor Groups
• SO(10) GUT in Four and Five Dimensions: A Review
• Majorana Physics Through the Cabibbo Haze

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