Right Unitarity Triangles, Stable CP-violating Phases and Approximate Quark-Lepton Complementarity

Abstract

Current experimental data indicate that two unitarity triangles of the CKM quark flavor mixing matrix V are almost the right triangles with α\approx 90^\circ. We find that α= 90^\circ actually points to {\rm Re}(V_{tb}V_{ud}V^*_{td}V^*_{ub}) = 0. Considering a very suggestive parametrization of V, we show that its CP-violating phase ϕis nearly equal to α(i.e., ϕ- α\approx 1.1^\circ). Both ϕand αare stable against the renormalizaton-group evolution from the electroweak scale M_Z to a superhigh energy scale M_X or vice versa, and thus it is impossible to obtain α= 90^\circ at M_Z from ϕ= 90^\circ at M_X. We conjecture that there might also exist a maximal CP-violating phase ϕ\approx 90^\circ in the MNS lepton flavor mixing matrix U. The approximate quark-lepton complementarity relations, which hold in the standard parametrizations of V and U, can also hold in our particular parametrizations of V and U simply due to the smallness of |V_{ub}| and |V_{e3}|.

RevTex 12 pages, 1 PS figure. Accepted for publication in PLB

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• The Matrix of Unitarity Triangle Angles for Quarks
• Quark Mass Hierarchy and Flavor Mixing Puzzles
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• Flavor Mixing Democracy and Minimal CP Violation
• Radiative Corrections to the CKM Unitarity Triangles
• The Kobayashi-Maskawa Parametrization of Lepton Flavor Mixing and Its Application to Neutrino Oscillations in Matter
• Model-independent access to the structure of quark flavor mixing
• Dependence of the Quark-Lepton Complementarity on Parametrizations of the CKM and PMNS Matrices
• Comment on Reparametrization Invariance of Quark-Lepton Complementarity
• Distinguishing between the twin $b$-flavored unitarity triangles on a circular arc
• Fermion Masses and Mixing in General Warped Extra Dimensional Models
• New Aspects of Flavour Model Building in Supersymmetric Grand Unification
• Non-maximal θ_{23}, large θ_{13} and tri-bimaximal θ_{12} via quark-lepton complementarity at next-to-leading order
• Investigation of a kind of neutrino mass matrix
• Nearly right unitarity triangle and CP phase in quark and lepton flavor mixings
• Minimal structure for neutrino mass matrix