Lepton and Quark Mixing Patterns from Finite Flavor Symmetries

Abstract

We perform a systematical and analytical study of lepton mixing which can be derived from the subgroups of $SU(3)$ under the assumption that neutrinos are Dirac particles. We find that type D groups can predict lepton mixing patterns compatible with the experimental data at $3\sigma$ level. The lepton mixing matrix turns out to be of the trimaximal form, and the Dirac CP violating phase is trivial. Moreover, we extend the flavor symmetry to the quark sector. The Cabibbo mixing between the first two generations of quarks can be generated by type D groups. Since all the finite subgroups of $U(3)$ which are not the subgroups of $SU(3)$ have not been classified, an exhaustive scan over all finite discrete groups up to order 2000 is performed with the help of the computer algebra system \texttt{GAP}. We find that only 90 (10) groups for Dirac (Majorana) neutrinos can generate the lepton mixing angles in the experimentally preferred ranges. The lepton mixing matrix is still the trimaximal pattern and the Dirac CP phase remains trivial. The smallest groups which lead to viable mixing angles are $[162,10]$, $[162,12]$ and $[162,14]$. For quark flavor mixing, the correct order of magnitude of the CKM matrix elements can not be generated. Only the Cabibbo mixing is allowed even if we impose very loose constraints $0.1\le |{\left(V_{CKM}\right)}_{12}|\le 0.3$ and $|{\left(V_{CKM}\right)}_{13}|\le |{\left(V_{CKM}\right)}_{23}|<|{\left(V_{CKM}\right)}_{12}|$. The group $\Delta (6\cdot 7^2)$ can predict a Cabibbo angle ${\theta }_q=\pi /14$ in good agreement with the best fit value. The groups which can give rise to both phenomenologically viable lepton mixing angles and acceptable Cabibbo angle are discussed, and the groups $\Delta (6\cdot 9^2)$, $[648,259]$, $[648,260]$, $[648,266]$ and $\Delta (6\cdot 14^2)$ are especially promising.

52 pages, 9 figures

References in corpus (23)

• Observation of electron-antineutrino disappearance at Daya Bay
• Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Neutrino oscillations refitted
• Improved Measurement of Electron Antineutrino Disappearance at Daya Bay
• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• Improved measurements of the neutrino mixing angle ${\theta }_{13}$ with the Double Chooz detector
• Symmetry of Lepton Mixing
• Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups
• The Flavor Group Delta(6n^2)
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• An A4 flavor model for quarks and leptons in warped geometry
• Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
• Lepton Mixing Predictions including Majorana Phases from $\Delta (6n^2)$ Flavour Symmetry and Generalised CP
• Classification of lepton mixing matrices from finite residual symmetries
• Generalised CP and $\Delta (96)$ Family Symmetry
• On the finite subgroups of U(3) of order smaller than 512
• LBNO-DEMO: Large-scale neutrino detector demonstrators for phased performance assessment in view of a long-baseline oscillation experiment
• Group space scan of flavor symmetries for nearly tribimaximal lepton mixing
• [Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
• A bottom-up analysis of horizontal symmetry

Cited by in corpus (38)

• Unified Models of Neutrinos, Flavour and CP Violation
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• Eclectic Flavor Groups
• Lessons from eclectic flavor symmetries
• Eclectic flavor scheme from ten-dimensional string theory -- I. Basic results
• Leptogenesis and residual CP symmetry
• Neutrino Mixing from CP Symmetry
• Simplified Models of Flavourful Leptoquarks
• $A_4$ and CP symmetry and a model with maximal CP violation
• 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
• Generalized CP and $\Delta (3n^2)$ Family Symmetry for Semi-Direct Predictions of the PMNS Matrix
• Quark and Lepton Mixing Patterns from a Common Discrete Flavor Symmetry with Generalized CP
• The symmetry approach to quark and lepton masses and mixing
• Lepton Mixing Predictions from Infinite Group Series $D_{9n,3n}^{(1)}$ with Generalized CP
• Bottom-Up Discrete Symmetries for Cabibbo Mixing
• Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• Lepton mixing patterns from the group $\Sigma (36\times 3)$ with a generalized CP transformation
• Finite Family Groups for Fermionic and Leptoquark Mixing Patterns
• Perspectives for tests of neutrino mass generation at the GeV scale: Experimental reach versus theoretical predictions
• Informationally complete characters for quark and lepton mixings
• Lepton and Quark Mixing from Stepwise Breaking of Flavor and CP
• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• GAP listing of the finite subgroups of U(3) of order smaller than 2000
• FCNC-free multi-Higgs-doublet models from broken family symmetries
• Discrete symmetries and Efficient Counting of Operators
• Leptogenesis in $\Delta (27)$ with a Universal Texture Zero
• Pocket Formulae for Non-Abelian Discrete Anomaly Freedom
• Reconstructing Effective Lagrangians Embedding Residual Family Symmetries
• Testing the minimal $S_4$ model of neutrinos with the Dirac and Majorana phases
• Dihedral flavor group as the key to understand quark and lepton flavor mixing
• Lepton and Quark Masses and Mixing in a SUSY Model with Delta(384) and CP
• Group-theoretical search for rows or columns of the lepton mixing matrix
• Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models
• Lepton mixing patterns from $PS{L}_2(7)$ with a generalised CP symmetry
• Implications of equalities among the elements of CKM and PMNS matrices
• New partial symmetries from group algebras for lepton mixing