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.

26 pages, no figures

References in corpus (4)

• Observation of electron-antineutrino disappearance at Daya Bay
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• Unification and Fermion Mass Structure
• Simple Finite Non-Abelian Flavor Groups

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• Leptogenesis from the Asymmetric Texture
• Spontaneous Breaking of Gauge Groups to Discrete Symmetries
• Effective Theories of Flavor and the Non-Universal MSSM
• Low-scale Resonant Leptogenesis in $SU(5)$ GUT with ${\mathcal{T}}_{13}$ Family Symmetry
• Anomaly-free ALP from non-Abelian flavor symmetry
• Clebsch-Gordan coefficients of discrete groups in subgroup bases
• PSL(2,7) Representations and their relevance to Neutrino Physics