Patterns in the Fermion Mixing Matrix, a bottom-up approach

Abstract

We first obtain the most general and compact parametrization of the unitary transformation diagonalizing any 3 by 3 hermitian matrix H, as a function of its elements and eigenvalues. We then study a special class of fermion mass matrices, defined by the requirement that all of the diagonalizing unitary matrices (in the up, down, charged lepton and neutrino sectors) contain at least one mixing angle much smaller than the other two. Our new parametrization allows us to quickly extract information on the patterns and predictions emerging from this scheme. In particular we find that the phase difference between two elements of the two mass matrices (of the sector in question) controls the generic size of one of the observable fermion mixing angles: i.e. just fixing that particular phase difference will "predict" the generic value of one of the mixing angles, irrespective of the value of anything else.

29 pages, 3 figures, references added, to appear in PRD

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• A model for trimaximal lepton mixing
• Predictive flavour symmetries of the neutrino mass matrix
• Grand unification of $\mu -\tau$ Symmetry
• 'Mu-Tau' symmetry, tribimaximal mixing and four zero neutrino Yukawa textures
• An approach to permutation symmetry for the electroweak theory
• Perturbed S3 neutrinos
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• Soft breaking of $L_{\mu }-L_{\tau }$ symmetry: Light neutrino spectrum and Leptogenesis
• A Supersymmetric Contribution to the Neutrino Mass Matrix and Breaking of mu-tau Symmetry
• Softly broken $\mu \leftrightarrow \tau$ symmetry in the minimal see-saw model
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Cited by in corpus (10)

• Nearest-Neighbour Interaction from an Abelian Symmetry and Deviations from Hermiticity
• Non-Hermitian Perturbations to the Fritzsch Textures of Lepton and Quark Mass Matrices
• Minimal Weak Basis Textures and Quark Mixing Data
• Flavor Mixing Democracy and Minimal CP Violation
• Lower bound on neutrino mass and possible CP violation in neutrino oscillations
• Perturbative Bottom-up Approach for Neutrino Mass Matrix in Light of Large θ_{13} and Role of Lightest Neutrino Mass
• Generic lepton mass matrices and neutrino oscillations
• Texture zeros and hierarchical masses from flavour (mis)alignment
• Coherent mixing in three and four quark generations
• On dynamics of fermion generations