Origin of Symmetric PMNS and CKM Matrices

Abstract

The PMNS and CKM matrices are phenomenologically close to symmetric, and a symmetric form could be used as zeroth-order approximation for both matrices. We study the possible theoretical origin of this feature in flavor symmetry models. We identify necessary geometric properties of discrete flavor symmetry groups that can lead to symmetric mixing matrices. Those properties are actually very common in discrete groups such as $A_4$, $S_4$ or $\Delta (96)$. As an application of our theorem, we generate a symmetric lepton mixing scheme with ${\theta }_{12}={\theta }_{23}=36.21^{\circ };{\theta }_{13}=12.20^{\circ }$ and $\delta =0$, realized with the group $\Delta (96)$.

arXiv comment8 pages. 4 figures. minor corrections to appear in PRD

References in corpus (21)

• Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Status of three-neutrino oscillation parameters, circa 2013
• Finite Modular Groups and Lepton Mixing
• The Unique Horizontal Symmetry of Leptons
• Possible Alternatives to Tri-bimaximal Mixing
• The Horizontal Symmetry for Neutrino Mixing
• Discrete Flavour Symmetries in Light of T2K
• The Flavor Group Delta(6n^2)
• Common Origin of mu-tau and CP Breaking in Neutrino Seesaw, Baryon Asymmetry, and Hidden Flavor Symmetry
• Octahedral Symmetry with Geometrical Breaking: New Prediction for Neutrino Mixing Angle theta_{13} and CP Violation
• TFH Mixing Patterns, Large ${\theta }_{13}$ and $\Delta (96)$ Flavor Symmetry
• Group Theory and Dynamics of Neutrino Mixing
• Can the Lepton Flavor Mixing Matrix Be Symmetric?
• Quark-Lepton universality and large leptonic mixing
• The neutrino mixing matrix could (almost) be diagonal with entries {\pm}1
• Is the Cabibbo-Kobayashi-Maskawa Matrix Symmetric at the GUT Scale?
• On Symmetric Lepton Mixing Matrices
• Quark mixings as a test of a new symmetry of quark Yukawa couplings
• A Possible Hermitian Neutrino Mixing Ansatz
• Is the quark- mixing matrix moduli symmetric?

Cited by in corpus (3)

• Origin of Constrained Maximal CP Violation in Flavor Symmetry
• A left-right symmetric flavor symmetry model
• Neutrino mixing in SO(10) GUTs with non-abelian flavor symmetry in the hidden sector