Group-theoretical search for rows or columns of the lepton mixing matrix

Abstract

We have used the SmallGroups library of groups, together with the computer algebra systems GAP and Mathematica, to search for groups with a three-dimensional irreducible representation in which one of the group generators has a twice-degenerate eigenvalue while another generator has non-degenerate eigenvalues. By assuming one of these group generators to commute with the charged-lepton mass matrix and the other one to commute with the neutrino (Dirac) mass matrix, one derives group-theoretical predictions for the moduli of the matrix elements of either a row or a column of the lepton mixing matrix. Our search has produced several realistic predictions for either the second row, or the third row, or for any of the columns of that matrix.

arXiv comment23 pages, 1 figure, added references, new appendices concerning the nilpotent groups and groups with a normal Sylow 3-subgroups, conclusions unchanged; some minor changes, matches published version

References in corpus (30)

• Neutrino oscillations refitted
• Status of three-neutrino oscillation parameters, circa 2013
• Finite Modular Groups and Lepton Mixing
• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• Global Analyses of Neutrino Oscillation Experiments
• Comparing Trimaximal Mixing and Its Variants with Deviations from Tri-bimaximal Mixing
• Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
• The golden ratio prediction for the solar neutrino mixing
• A model for trimaximal lepton mixing
• The Flavor Group Delta(6n^2)
• Unified Parametrization for Quark and Lepton Mixing Angles
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Golden Ratio Prediction for Solar Neutrino Mixing
• Classification of lepton mixing matrices from finite residual symmetries
• Finite Symmetry of Leptonic Mass Matrices
• Mixing Patterns from the Groups Sigma (n phi)
• Lepton and Quark Mixing Patterns from Finite Flavor Symmetries
• Realistic $\mathrm{SU}(3{)}_{\mathrm{c}}\otimes \mathrm{SU}(3{)}_{\mathrm{L}}\otimes \mathrm{U}(1{)}_{\mathrm{X}}$ model with a type II Dirac neutrino seesaw mechanism
• Type II seesaw mechanism for Higgs doublets and the scale of new physics
• On the finite subgroups of U(3) of order smaller than 512
• [Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
• Residual Z2 x Z2 symmetries and lepton mixing
• Golden ratio lepton mixing and nonzero reactor angle with $A_5$
• Triangular mass matrices of quarks and Cabibbo-Kobayashi-Maskawa mixing
• Direct and Semi-Direct Approaches to Lepton Mixing with a Massless Neutrino
• On the characterization of the SU(3)-subgroups of type C and D
• Leptonic Generation Mixing, Noncommutative Geometry and Solar Neutrino Fluxes
• Double seesaw mechanism and lepton mixing
• Sweeping the Space of Admissible Quark Mass Matrices

Cited by in corpus (3)

• Informationally complete characters for quark and lepton mixings
• GAP listing of the finite subgroups of U(3) of order smaller than 2000
• Coxeter groups and the PMNS matrix