Unified Parametrization for Quark and Lepton Mixing Angles

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 π/12 and π/5, respectively. The resulting 12-elements in the CKM and PMNS matrices, Vus and Ue2, are in this order irrational but simple algebraic numbers. The difference between π/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. email: [email protected] Quark and lepton mixing can successfully be described in the Standard Model of elementary particle physics. For each sector a unitary mixing matrix connects mass and flavor states, and can be parametrized as [1] V, U = R23(θ q,l 23 )R q,l 13 (θ q,l 13 ; δ )R12(θ q,l 12 ) =   c 12 c q,l 13 s q,l 12 c q,l 13 s q,l 13 e −iδ −s 12 c 23 − c 12 s 23 s 13 e q,l c 12 c q,l 23 − s 12 s 23 s 13 e q,l s 23 c q,l 13 s 12 s q,l 23 − c 12 c 23 s 13 e q,l −c 12 s 23 − s 12 c 23 s 13 e q,l c 23 c q,l 13 