[Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up

Abstract

We present a novel procedure for identifying discrete, leptonic flavour symmetries, given a class of unitary mixing matrices. By creating explicit 3D representations for generators of residual symmetries in both the charged lepton and neutrino sector, we reconstruct large(r) non-abelian flavour groups using the GAP language for computational finite algebra. We use experimental data to construct only those generators that yield acceptable (or preferable) mixing patterns. Such an approach is advantageous because it 1) can reproduce known groups from other 'top-down' scans while elucidating their origins from residuals, 2) find new previously unconsidered groups, and 3) serve as a powerful model building tool for theorists wishing to explore exotic flavour scenarios. We test our procedure on a generalization of the canonical tri-bimaximal (TBM) form.

arXiv comment18 pages, 3 tables; references updated and minor note added; content and results unchanged; text matches published version in JHEP

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• Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
• Generalized $\mu$-$\tau$ symmetry and discrete subgroups of O(3)
• Implications of $\mu -\tau$ Flavored CP Symmetry of Leptons
• Lepton and Quark Mixing Patterns from Finite Flavor Symmetries
• A Bottom-Up Approach to Lepton Flavor and CP Symmetries
• Simplified Models of Flavourful Leptoquarks
• CP Symmetry and Lepton Mixing from a Scan of Finite Discrete Groups
• Alternative Schemes of Predicting Lepton Mixing Parameters from Discrete Flavor and CP Symmetry
• The symmetry approach to quark and lepton masses and mixing
• A Unified Model of Quarks and Leptons with a Universal Texture Zero
• Bottom-Up Discrete Symmetries for Cabibbo Mixing
• Finite Family Groups for Fermionic and Leptoquark Mixing Patterns
• A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios
• Lepton and Quark Mixing from Stepwise Breaking of Flavor and CP
• Neutrino masses and mixing from flavour antisymmetry
• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• Discrete symmetries and Efficient Counting of Operators
• Deviations to Tri-Bi-Maximal mixing in the limit of $\mu -\tau$ symmetry
• Reconstructing Effective Lagrangians Embedding Residual Family Symmetries
• Lepton and Quark Masses and Mixing in a SUSY Model with Delta(384) and CP
• Restricting Majorana phases in the Tri-Bi-Maximal limit
• Group-theoretical search for rows or columns of the lepton mixing matrix
• Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models
• Theories of Leptonic Flavor