We discuss the possibility that the X(3872) can be a DD * molecular bound state in the Bethe-Salpeter equation approach in the ladder and instantaneous approximations. We show that the DD * bound state with quantum numbers J P C = 1 ++ exists. We also calculate the decay width of X(3872) → γJ/ψ channel and compare our result with those from previous calculations.

In this work, we study the localized CP violation in B − → K − π + π − and B − → K − σ(600) decays by employing the quasi two-body QCD factorization approach. Both the resonance and the nonresonance contributions are studied for the B − → K − π + π − decay. The resonance contributions include those not only from [ππ] channels including σ(600), ρ 0 (770) and ω(782) but also from [Kπ] channels including K * (892), K * 0 (1430), K * (1410), K * (1680) and K * 2 (1430). By fitting the experimental data A CP (K − π + π − ) = 0.678 ± 0.078 ± 0.0323 ± 0.007 for m 2 K − π + < 15 GeV 2 and 0.08 < m 2 π + π − < 0.66 GeV 2 , we get the end-point divergence parameters in our model, φ S ∈ [4.75, 5.95] and ρ S ∈ [4.2, 8]. Using these results for ρ S and φ S , we predict that the CP asymmetry parameter A CP ∈ [−0.094, −0.034] and the branching fraction B ∈ [1.82, 20.0] × 10 −5 for the B − → K − σ(600) decay. In addition, we also analyse contributions to the localized CP asymmetry A CP (B − → K − π + π − ) from [ππ], [Kπ] channel resonances and nonresonance individually, which are found to beComparing these results, we can see that the localized CP asymmetry in the B − → K − π + π − decay is mainly induced by the [ππ] channel resonances while contributions from the [Kπ] channel resonances and nonresonance are both very small. Nonleptonic decays of hadrons containing a heavy quark play an important role in testing the Standard Model (SM) picture of the Charge-Parity (CP ) violation mechanism in flavor physics, improving our understanding of nonperturbative and perturbative QCD and exploring new physics beyond the SM. CP violation is related to the weak complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix, whichdescribes the mixing of different generations of quarks [1,2]. Besides the weak phase, a large strong phase is also needed for a large CP asymmetry. Generally, this strong phase is provided by QCD loop corrections and some phenomenological models.Three-body decays of heavy mesons are more complicated than the two-body case as they receive resonant and nonresonant contributions and involve three-body matrix elements. The direct nonresonant three-body decay of mesons generally receives two separate contributions: one from the point like weak transition and the other from the pole diagrams that involve three-point or four-point strong vertices.The nonresonant background in charmless three-body B decays due to the transition B → M 1 M 2 M 3 has been studied extensively based on Heavy Meson Chiral Perturbation Theory (HMChPT) [3][4][5]. However, the predicted decay rates are, in general, unexpectedly large and not recovered in the soft meson region.

In this work, we assume that the observed state Ξ(1620) is a s-wave ΛK or ΣK bound state. Based on this molecule picture, we establish the Bethe-Salpeter equations for Ξ(1620) in the ladder and instantaneous approximations. We solve the Bethe-Salpeter equations for the ΛK and ΣK systems numerically and find that the Ξ (1620) can be explained as ΛK and ΣK bound states with J P = 1/2 − , respectively. Then we calculate the decay widths of Ξ(1620) → Ξπ in these two different molecule pictures systems, respectively.

Up to now, the excited charmed and bottom baryon states have still not been well studied experimentally or theoretically. In this paper, we predict the mass of Ω * b , the only L = 0 baryon state which has not been observed, to be 6069.2 MeV. The spectra of charmed and bottom baryons with the orbital angular momentum L = 1 are studied in two popular constituent quark models, the Goldstone boson exchange (GBE) model and the one gluon exchange (OGE) hyperfine interaction model. Inserting the latest experimental data from the "Review of Particle Physics", we find that in the GBE model, there exist some multiplets (Σ c(b) , Ξ ′ c(b) and Ω c(b) ) in which the total spin of the three quarks in their lowest energy states is 3/2, but in the OGE model there is no such phenomenon. This is the most important difference between the GBE and OGE models. These results can be tested in the near future. We suggest more efforts to study the excited charmed and bottom baryons both theoretically and experimentally, not only for the abundance of baryon spectra, but also for determining which hyperfine interaction model best describes nature.

In this work, we study the localized violation and the branching fraction of the four-body decay by employing a quasi-two-body QCD factorization approach. Considering the interference of and channels, we predict and , respectively, which shows that the interference mechanism of these two channels can induce the localized violation to this four-body decay. Meanwhile, within the two quark model framework for the scalar mesons and , we calculate the direct CP violations and branching fractions of the and decays, respectively. The corresponding results are , , and , indicating that the violations of these two-body decays are both positive and the branching fractions quite different. These studies provide a new way to investigate the aforementioned four-body decay and can be helpful in clarifying the configuration of the structure of the light scalar meson.