An approach to permutation symmetry for the electroweak theory

Abstract

The form of the leptonic mixing matrix emerging from experiment has, in the last few years, generated a lot of interest in the so-called tribimaximal type. This form may be naturally associated with the possibility of a discrete permutation symmetry ($S_3$) among the three generations. However, trying to implement this attractive symmetry has resulted in some problems and it seems to have fallen out of favor. We suggest an approach in which the $S_3$ holds to first approximation, somewhat in the manner of the old SU(3) flavor symmetry of the three flavor quark model. It is shown that in the case of the neutrino sector, a presently large experimentally allowed region can be fairly well described in this first approximation. We briefly discuss the nature of the perturbations which are the analogs of the Gell-Mann Okubo perturbations but confine our attention for the most part to the $S_3$ invariant model. We postulate that the $S_3$ invariant mass spectrum consists of non zero masses for the $(\tau ,b,t)$ and zero masses for the other charged fermions but approximately degenerate masses for the three neutrinos. The mixing matrices are assumed to be trivial for the charged fermions but of tribimaximal type for the neutrinos in the first approximation. It is shown that this can be implemented by allowing complex entries for the mass matrix and spontaneous breakdown of the $S_3$ invariance of the Lagrangian.

24 pages, 1 figure, minor corrections and acknowledgment added. To appear in IJMP

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Cited by in corpus (38)

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• The Flavor Group Delta(3n^2)
• The Flavor Group Delta(6n^2)
• Relatively large theta13 and nearly maximal theta23 from the approximate S3 symmetry of lepton mass matrices
• The S_3 flavor symmetry in 3-3-1 models
• Simple Finite Non-Abelian Flavor Groups
• Broken S_3 Flavor Symmetry of Leptons and Quarks: Mass Spectra and Flavor Mixing Patterns
• Getting at large theta_13 with almost maximal theta_23 from tri-bimaximal mixing
• Consequences of Approximate $S_3$ Symmetry of the Neutrino Mass Matrix
• The D_4 flavor symmery in 3-3-1 model with neutral leptons
• Broken S3 Symmetry in the Neutrino Mass Matrix and Non-Zero theta_{13}
• The T7 flavor symmetry in 3-3-1 model with neutral leptons
• Perturbed S3 neutrinos
• Neutrino Mixing with Non-Zero ${\theta }_{13}$ and CP Violation in the 3-3-1 Model Based on $S_4$ Flavor Symmetry
• The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Neutrino mixing with broken $S_3$ symmetry
• Gauge boson families in grand unified theories of fermion masses: E_6^4 x S_4
• Broken $S_3$ Symmetry in the Neutrino Mass Matrix
• Discrete flavour symmetries for degenerate solar neutrino pair and their predictions
• Doubly perturbed $S_3$ neutrinos and the $s_{13}$ mixing parameter
• Radiative and Seesaw Threshold Corrections to the $S_3$ Symmetric Neutrino Mass Matrix
• Phase broken $\mu -\tau$ symmetry and the neutrino mass hierarchy
• Lepton mass and mixing in a Neutrino Mass Model based on $S_4$ flavor symmetry
• Neutrino Mass Textures and Partial $\mu$-$\tau$ Symmetry
• Patterns in the Fermion Mixing Matrix, a bottom-up approach
• Naturally perturbed S${}_3$ neutrinos
• Broken $S_3$ Neutrinos
• Diagonal reflection symmetries, four-zero texture, and trimaximal mixing with predicted ${\theta }_{13}$ in an $A_4$ symmeric model
• Form Invariance and Symmetry in the Neutrino Mass Matrix
• (Z_2)^3 Symmetry of the Tripartite Model
• Diagonal reflection symmetries and universal four-zero texture
• Partial $\mu -\tau$ Textures and Leptogenesis
• Phenomenology of Trimaximal mixing with one texture equality
• Note about the implementation of finite symmetries in the lepton sector
• An analytical treatment of the neutrino masses and mixings
• Note about lepton masses and mixings in two Ansatze
• Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3-symmetry