Bottom-Up Discrete Symmetries for Cabibbo Mixing

Abstract

We perform a bottom-up search for discrete non-Abelian symmetries capable of quantizing the Cabibbo angle that parameterizes CKM mixing. Given a particular Abelian symmetry structure in the up and down sectors, we construct representations of the associated residual generators which explicitly depend on the degrees of freedom present in our effective mixing matrix. We then discretize those degrees of freedom and utilize the Groups, Algorithms, Programming (GAP) package to close the associated finite groups. This short study is performed in the context of recent results indicating that, without resorting to special model-dependent corrections, no small-order finite group can simultaneously predict all four parameters of the three-generation CKM matrix and that only groups of $\mathcal{O}(10^2)$ can predict the analogous parameters of the leptonic PMNS matrix, regardless of whether neutrinos are Dirac or Majorana particles. Therefore a natural model of flavour might instead incorporate small(er) finite groups whose predictions for fermionic mixing are corrected via other mechanisms.

arXiv comment14 pages, 4 figures. v2: minor changes, references added, accepted by IJMPA

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• Quark and Lepton Mixing Patterns from a Common Discrete Flavor Symmetry with Generalized CP
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• A Unified Model of Quarks and Leptons with a Universal Texture Zero
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• Finite Family Groups for Fermionic and Leptoquark Mixing Patterns
• Quark mixing in an $S_3$ symmetric model with two Higgs doublets
• Lepton and Quark Mixing from Stepwise Breaking of Flavor and CP
• FCNC-free multi-Higgs-doublet models from broken family symmetries
• An $S_3$ flavored left-right symmetric model of quarks
• Leptogenesis in $\Delta (27)$ with a Universal Texture Zero
• Discrete symmetries and Efficient Counting of Operators
• Pocket Formulae for Non-Abelian Discrete Anomaly Freedom
• Reconstructing Effective Lagrangians Embedding Residual Family Symmetries
• Dihedral flavor group as the key to understand quark and lepton flavor mixing
• A Radiative Model of Quark Masses with Binary Tetrahedral Symmetry