Unified Parametrization for Quark and Lepton Mixing Angles

Abstract

We propose a new parametrization for the quark and lepton mixing matrices: the two 12-mixing angles (the Cabibbo angle and the angle responsible for solar neutrino oscillations) are at zeroth order pi/12 and pi/5, respectively. The resulting 12-elements in the CKM and PMNS matrices, V_{us} and U_{e2}, are in this order irrational but simple algebraic numbers. We note that the cosine of pi/5 is the golden ratio divided by two. The difference between pi/5 and the observed best-fit value of solar neutrino mixing is of the same order as the difference between the observed value and the one for tri-bimaximal mixing. In order to reproduce the central values of current fits, corrections to the zeroth order expressions are necessary. They are small and of the same order and sign for quarks and leptons. We parametrize the perturbations to the CKM and PMNS matrices in a 'triminimal' way, i.e., with three small rotations in an order corresponding to the order of the rotations in the PDG-description of mixing matrices.

10 pages. Comments and references added, to appear in PLB

References in corpus (13)

• Phenomenology with Massive Neutrinos
• Three-flavour neutrino oscillation update
• Hints of theta_13>0 from global neutrino data analysis
• The golden ratio prediction for the solar neutrino mixing
• Parametrizing the lepton mixing matrix in terms of deviations from tri-bimaximal mixing
• Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups
• TriMinimal Parametrization of the Neutrino Mixing Matrix
• Contrasting solar and reactor neutrinos with a non-zero value of theta13
• CP violation and the CKM matrix
• What we (would like to) know about the neutrino mass
• theta_C from the Dihedral Flavor Symmetries D_7 and D_14
• Triminimal Parametrization of Quark Mixing Matrix
• Unified parametrization of quark and lepton mixing matrices in tri-bimaximal pattern

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