Narrow Results

We propose a universal mixing hypothesis between quark and lepton sectors at high energy scale (probably GUT scale) where quark–lepton universality holds. Namely in the charged lepton diagonal base, all the other mass matrices for up and down quarks and neutrinos are diagonalized by the same unitary matrix except for the phase elements. Thanks to this hypothesis, the observed values of the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix and the mixing angles θ₁₂ and θ₂₃ in the Maki–Nakagawa–Sakata (MNS) lepton mixing matrix can predict the unknown magnitudes of the mixing angle θ₁₃ and of the CP violating Dirac phase δ in the MNS matrix. Their allowed regions are rather narrow, 0.036 < sin θ₁₃ < 0.048 and 6° < δ < 12°.

The recently observed lepton mixing angle θ₁₃ of the MNS mixing matrix is well incorporated in a universal mixing hypothesis between quark and lepton sectors. This hypothesis asserts that, in the charged lepton diagonal base, all other mass matrices for up- and down-type quarks and light neutrinos are diagonalized by the same unitary matrix except for the phase elements. It is expressed as V_CKM = U_MNS(δ′)^†PU_MNS(δ) for quark mixing matrix V_CKM and lepton mixing matrix U_MNS(δ) in the phenomenological level. Here P is a diagonal phase mass matrix. δ′ is a slightly different phase parameter from the Dirac CP-violating phase δ = 1.1π (best fit) in the MNS lepton mixing matrix.

The universality hypothesis for quark and lepton mixing matrices (CKM and MNS) is further developed. This hypothesis explains why the CKM is almost diagonal whereas the MNS is almost maximally mixed. If this hypothesis is true, the Dirac CP violating phase of the MNS mixing matrix is bounded around π or 0. Quark–lepton mass matrices which realize this hypothesis are constructed, showing simple power law relations among mass matrices for up-type, down-type quarks and neutrinos.

We consider a universal mass matrix model which has a seesaw-invariant structure with the most general texture based on flavor 2 ↔ 3 symmetry common to all quarks and leptons. The CKM quark mixing matrix of the model is analyzed. It is shown that the model is consistent with all the experimental data of quark mixings by tuning free parameters of the model. We also show that the values of parameters of the present model consistent with the experimental data are not far from the ones of the mass matrix model with a vanishing (1, 1) element.