A Model of Fermion Masses and Flavor Mixings with Family Symmetry SU(3)U(1)

The family symmetry SU（3） U（1） is proposed to solve flavor problems about fermion masses and flavor mixings. It is breaking is implemented by some flavon fields at the high-energy scale. In addition a discrete group Z2 is introduced to generate tiny neutrino masses, which is broken by a real singlet scalar field at the middle-energy scale. The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling. All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters. The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation quark masses and the values of θ13and JCp in neutrino physics. All of the results are promising to be tested in the future experiments.

Possible hadronic molecular states composed of S-wave heavy-light mesons

We perform a systematical study of possible molecular states composed of the S wave heavy light mesons,where the S–D mixing and η-η＇ mixing are explicitly included.Our calculation indicates that the observed X（3872） could be a loosely shallow molecular state composed of D＊＋ h.c,while neither Z_c（3900）/Z_c（4020） nor Z_b（10610）/Z_b（10650） is supported to be a molecule.Some observed possible molecular states are predicted,which could be searched for by further experimental measurements.

The breaking of flavor democracy in the quark sector

The democracy of quark flavors is a well-motivated flavor symmetry, but it must be properly broken in order to explain the observed quark mass spectrum and flavor mixing pattern. We reconstruct the texture of flavor democracy breaking and evaluate its strength in a novel way, by assuming a parallelism between the Q=＋2/3 and Q=-1/3 quark sectors and using a nontrivial parametrization of the flavor mixing matrix. Some phenomenological implications of such democratic quark mass matrices, including their variations in the hierarchy basis and their evolution from the electroweak scale to a super-high energy scale, are also discussed.

Implications of the Daya Bay observation of θ_(13) on the leptonic flavor mixing structure and CP violation

The Daya Bay collaboration has recently reported its first νe → νe oscillation result which points to θ13 8.8 ± 0.8 （best-fit ±1σ range） or θ13 = 0 at the 5.2σ level. The fact that this smallest neutrino mixing angle is not strongly suppressed motivates us to look into the underlying structure of lepton flavor mixing and CP violation. Two phenomenological strategies are outlined： （1） the lepton flavor mixing matrix U consists of a constant leading term U0 and a small perturbation term U ; and （2） the mixing angles of U are associated with the lepton mass ratios. Some typical patterns of U0 are reexamined by constraining their respective perturbations with current experimental data. We illustrate a few possible ways to minimally correct U0 in order to fit the observed values of three mixing angles. We point out that the structure of U may exhibit an approximate μ-τ permutation symmetry in modulus, and reiterate the geometrical description of CP violation in terms of the leptonic unitarity triangles. The salient features of nine distinct parametrizations of U are summarized, and its Wolfenstein-like expansion is presented by taking U0 to be the democratic mixing pattern.

Naumov- and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos

In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the 3×3 flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalizationgroup （RG） equations in the tau-dominance approximation, and for the running behaviors of up- and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.

Correlation of normal neutrino mass ordering with upper octant of θ_(23) and third quadrant of δ via RGE-induced μ-τ symmetry breaking

The recent global analysis of three-flavor neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the 3σ level, and the best-fit values of the largest neutrino mixing angle 023 and the Dirac CP-violating phase δ are located in the higher octant and third quadrant, respectively. We show that all these important issues can be naturally explained by the μ-τ reflection symmetry breaking of massive neutrinos from a superhigh energy scale down to the electroweak scale owing to the one-loop renormalization-group equations （RGEs） in the minimal supersymmetric standard model （MSSM）. The complete parameter space is explored for the first time in both the Majorana and Dirac cases, by allowing the smallest neutrino mass m1 and the MSSM parameter tanβ to vary within their reasonable regions.