Quark mixing sum rules and the right unitarity triangle

Abstract

In analogy with the recently proposed lepton mixing sum rules, we derive quark mixing sum rules for the case of hierarchical quark mass matrices with 1-3 texture zeros, in which the separate up and down type 1-3 mixing angles are approximately zero, and $V_{ub}$ is generated from $V_{cb}$ as a result of 1-2 up type quark mixing. Using the sum rules, we discuss the phenomenological viability of such textures, including up to four texture zeros, and show how the right-angled unitarity triangle, i.e., $\alpha \approx 90^{\circ }$, can be accounted for by a remarkably simple scheme involving real mass matrices apart from a single element being purely imaginary. In the framework of grand unified theories we show how the quark and lepton mixing sum rules may combine to yield an accurate prediction for the reactor angle.

8 pages, 1 figure; version published in PRD

References in corpus (29)

• Updated Values of Running Quark and Lepton Masses
• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• Parametrizing the lepton mixing matrix in terms of deviations from tri-bimaximal mixing
• A SUSY A4 model for fermion masses and mixings
• Mass Independent Textures and Symmetry
• New GUT predictions for quark and lepton mass ratios confronted with phenomenology
• On the origin of neutrino flavour symmetry
• Towards a Complete Theory of Fermion Masses and Mixings with SO(3) Family Symmetry and 5d SO(10) Unification
• A new family symmetry for SO(10) GUTs
• Deviations from Tri-bimaximal Mixing: Charged Lepton Corrections and Renormalization Group Running
• Third Family Corrections to Quark and Lepton Mixing in SUSY Models with non-Abelian Family Symmetry
• 'Mu-Tau' symmetry, tribimaximal mixing and four zero neutrino Yukawa textures
• Phenomenological consequences of four zero neutrino Yukawa textures
• Four Zero Neutrino Yukawa Textures in the Minimal Seesaw Framework
• Third Family Corrections to Tri-bimaximal Lepton Mixing and a New Sum Rule
• Flavor Violation in Supersymmetric Q_6 Model
• Flavor Symmetry and Vacuum Aligned Mass Textures
• Right Unitarity Triangles, Stable CP-violating Phases and Approximate Quark-Lepton Complementarity
• Two Categories of Approximately mu-tau Symmetric Neutrino Mass Textures
• Minimal Textures in Seesaw Mass Matrices and their low and high Energy Phenomenology
• Invariant see-saw models and sequential dominance
• Improved Determination of the CKM Angle alpha from B to pi pi decays
• Textures with two traceless submatrices of the neutrino mass matrix
• Yukawa Textures, New Physics and Nondecoupling
• The Matrix of Unitarity Triangle Angles for Quarks
• Plaquette Invariants and the Flavour Symmetric Description of Quark and Neutrino Mixings
• S4 Flavor Model of Quarks and Leptons
• Up Quark Masses from Down Quark Masses
• D-brane Inspired Fermion Mass Textures

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• Flavor structures of charged fermions and massive neutrinos
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• Family symmetries in F-theory GUTs
• θ^PMNS_13 = θ_C / \sqrt2 from GUTs
• A SUSY SU(5)xT' Unified Model of Flavour with large θ_{13}
• A flavour GUT model with theta_13^PMNS = theta_C / sqrt(2)
• Spontaneous CP violation in A4xSU(5) with Constrained Sequential Dominance 2
• Solving the Strong CP Problem with Discrete Symmetries and the Right Unitarity Triangle
• Towards predictive flavour models in SUSY SU(5) GUTs with doublet-triplet splitting
• Measurable Neutrino Mass Scale in A4 x SU(5)
• Quark mass and mixing in the 3-3-1 model with neutral leptons based on $D_4$ flavor symmetry
• Inverse neutrino mass hierarchy in a flavour GUT model
• Relating the neutrino mixing angles to a lepton mass hierarchy
• Model of flavor with quaternion symmetry
• Nucleon decay in a minimal non-SUSY GUT with predicted quark-lepton Yukawa ratios
• Flavor Mixing Democracy and Minimal CP Violation
• Predictions from a flavour GUT model combined with a SUSY breaking sector
• Distinguishing between the twin $b$-flavored unitarity triangles on a circular arc
• Employing nucleon decay as a fingerprint of SUSY GUT models using \texttt{SusyTCProton}
• A bottom-up approach to the strong CP problem
• Implications of the Zero 1-3 Flavour Mixing Hypothesis: Predictions for ${\theta }_{23}^{\mathrm{PMNS}}$ and ${\delta }^{\mathrm{PMNS}}$
• The mass ratios parametrization
• The Strong CP Problem and Discrete Symmetries