Majorana Physics Through the Cabibbo Haze

Abstract

We present a model in which the Supersymmetric Standard Model is augmented by the family symmetry $\bs{\m Z_7 \rtimes \m Z_3}$. Motivated by $SO(10)$, where the charge two-thirds and neutral Dirac Yukawa matrices are related, we propose, using family symmetry, a special form for the seesaw Majorana matrix; it contains a squared correlated hierarchy, allowing it to mitigate the severe hierarchy of the quark sector. It is reproduced naturally by the invariant operators of $\bs{\m Z_7 \rtimes \m Z_3}$, with the hierarchy carried by familon fields. In addition to relating the hierarchy of the $\Delta I_{\mathrm{w}}=1/2$ to the $\Delta I_{\mathrm{w}}=0$ sector, it contains a Gatto-Sartori-Tonin like relation, predicts a normal hierarchy for Tri-bimaximal and Golden Ratio mixings, and gives specific values for the light neutrino masses.

33 pages, 1 figure. This revised version omits a section where a particular linear combination of dimension-five operators was mistakenly claimed to produce the special form of the Majorana matrix. The main changes are to the Introduction, Sec. 5.1 of the previous version, and Summary and Conclusions. In addition to minor changes throughout, we have corrected an erroneous sign in Eq. 19

References in corpus (5)

• Observation of electron-antineutrino disappearance at Daya Bay
• Leptogenesis
• Neutrino Mass and Mixing with Discrete Symmetry
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• Unification and Fermion Mass Structure

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• Leptogenesis from the Asymmetric Texture
• Tribimaximal Mixing in the $SU(5)\times {\mathcal{T}}_{13}$ Texture
• Neutrino masses, the $\mu$-term and ${\mathcal{P}\mathcal{SL}}_2(7)$
• Effective Theories of Flavor and the Non-Universal MSSM
• Low-scale Resonant Leptogenesis in $SU(5)$ GUT with ${\mathcal{T}}_{13}$ Family Symmetry
• Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine Equations
• $\mathcal{C}\mathcal{P}$ violation with an unbroken $\mathcal{C}\mathcal{P}$ transformation
• Modulated bimaximal neutrino mixing
• Asymmetric tri-bi-maximal mixing and residual symmetries
• Clebsch-Gordan coefficients of discrete groups in subgroup bases