The semileptonic decay of heavy flavor mesons offers a clean environment for extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, which describes the CP-violating and flavor changing process in the Standard Model. The involved form factors where the dynamical information is encoded play an essential role in achieving any conclusive statement. That is, the knowledge of the form factors should be under good control, requiring one to examine more observables in addition to the branching fraction. In this paper, we provide the mean value and the q²-dependent shape for further observables [differential decay distribution (dΓ/dq²), forward-backward asymmetry $$ \left({\mathcal{A}}_{FB}^{ls}\right) $$A FB ls , longitudinal $$ \left({P}_L^l\right) $$P L l and transverse $$ \left({P}_T^l\right) $$P T l polarization of a charged lepton, longitudinal polarization of a vector meson in the final state $$ \left({F}_L^l(V)\right) $$F L l V , leptonic convexity parameter $$ \left({C}_F^l\right) $$C F l , and trigonometric moments $$ \left({W}_i^l\right) $$W i l in the decay of D_(s) and B_(s) to P/Vl⁺ν_l (l = e, μ or τ)], based on the predictions of the relevant form factors from the covariant light-front quark model. P and V denote the pseudoscalar and vector meson, respectively. As a comparison, we find a good agreement with the results from the covariant confining quark model and the relativistic quark model in the literature. As it has been observed that the $$ {P}_L^l $$P L l and $$ {F}_L^l(V) $$F L l V are crucial quantities to discriminate various New Physics models, the reexamination of these observables from a different method is also essential and necessary.

In this work, we systematically study the $D{\overline{D}}^{*}/B{\overline{B}}^{*}$ and $D{D}^{*}/\overline{B}{\overline{B}}^{*}$ systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations for the kernel. By solving the Bethe-Salpeter equation numerically with the kernel containing the direct and crossed one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we find only the isoscalar $D{\overline{D}}^{*}/B{\overline{B}}^{*}$ and $D{D}^{*}/\overline{B}{\overline{B}}^{*}$ systems can exist as bound states. This indicate that the $X(3872)$ and $T_{cc}^{+}$ could be accommodated as $I^G(J^{PC})=0^{+}(1^{++})$ $D{\overline{D}}^{*}$ and $(I)J^P=(0)1^{+}D{D}^{*}$ bound states while the bound-state explanations for $Z_b(10610)$ and $Z_c(3900)$ are excluded.

We study the localized direct CP violation in the hadronic decays $$B^\pm \rightarrow \rho ^0 (\omega )\pi ^\pm \rightarrow \pi ^+ \pi ^-\pi ^\pm $$ , incl

We study the S-wave [equation]bound state in the Bethe–Salpeter formalism in the ladder and instantaneous approximations. With the kernel generated by the hadronic effective Lagrangian, two...

In this work, we study the localized $CP$ violation in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}\sigma (600)$ decays by employing the quasi-two-body QCD factorization approach. Both the resonance and the nonresonance contributions are studied for the $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ decay. The resonance contributions include those not only from $[\pi \pi ]$ channels including $\sigma (600)$, ${\rho }^0(770)$ and $\omega (782)$ but also from $[K\pi ]$ channels including $K_0^{*}(700)(\kappa )$, $K^{*}(892)$, $K_0^{*}(1430)$, $K^{*}(1410)$, $K^{*}(1680)$ and $K_2^{*}(1430)$. By fitting the four experimental data ${\mathcal{A}}_{\mathcal{C}\mathcal{P}}(K^{-}{\pi }^{+}{\pi }^{-})=0.678\pm 0.078\pm 0.0323\pm 0.007$ for $m_{K^{-}{\pi }^{+}}^2<15{\mathrm{GeV}}^2$ and $0.08<m_{{\pi }^{+}{\pi }^{-}}^2<0.66{\mathrm{GeV}}^2$, ${\mathcal{A}}_{\mathcal{C}\mathcal{P}}(B^{-}\to K_0^{*}(1430){\pi }^{-})=0.061\pm 0.032$, $\mathcal{B}(B^{-}\to K_0^{*}(1430){\pi }^{-})=({39}_{-5}^{+6})\times {10}^{-6}$ and $\mathcal{B}(B^{-}\to \sigma (600){\pi }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-})<4.1\times {10}^{-6}$, we get the end-point divergence parameters in our model, ${\varphi }_S\in [1.77,2.25]$ and ${\rho }_S\in [2.39,4.02]$. Using these results for ${\rho }_S$ and ${\varphi }_S$, we predict that the $CP$ asymmetry parameter ${\mathcal{A}}_{\mathcal{C}\mathcal{P}}\in [-0.34,-0.11]$ and the branching fraction $\mathcal{B}\in [6.53,17.52]\times {10}^{-6}$ for the $B^{-}\to K^{-}\sigma (600)$ decay. In addition, we also analyze contributions to the localized $CP$ asymmetry ${\mathcal{A}}_{\mathcal{C}\mathcal{P}}(B^{-}\to K^{-}{\pi }^{+}{\pi }^{-})$ from $[\pi \pi ]$, $[K\pi ]$ channel resonances and nonresonance individually, which are found to be ${\mathcal{A}}_{\mathcal{C}\mathcal{P}}(B^{-}\to K^{-}[{\pi }^{+}{\pi }^{-}]\to K^{-}{\pi }^{+}{\pi }^{-})=0.509\pm 0.042$, ${\mathcal{A}}_{\mathcal{C}\mathcal{P}}(B^{-}\to [K^{-}{\pi }^{+}]\pi \to K^{-}{\pi }^{+}{\pi }^{-})=0.174\pm 0.025$ and ${{\mathcal{A}}_{\mathcal{C}\mathcal{P}}}^{\mathrm{NR}}(B^{-}\to K^{-}{\pi }^{+}{\pi }^{-})=0.061\pm 0.0042$, respectively. Comparing these results, we can see that the localized $CP$ asymmetry in the $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ decay is mainly induced by the $[\pi \pi ]$ channel resonances while contributions from the $[K\pi ]$ channel resonances and nonresonance are both very small.

In this work, we study weak transitions of ${\mathrm{\Lambda }}_b$ to light baryons $\mathrm{\Lambda }$ and $p$ in the Bethe-Salpeter equation approach. In the heavy quark limit, based on the picture that ${\mathrm{\Lambda }}_b$ is composed of a heavy $b$-quark and a light diquark, the Bethe-Salpeter equation for ${\mathrm{\Lambda }}_b$ was established in previous works. Although the light baryon $\mathrm{\Lambda }(p)$ is composed of various quark-diquark configurations based on the $SU(6)$ spin-flavor wave functions, only the configuration $s(ud{)}_{0,0}$ [$u(ud{)}_{0,0}$] [$(ud{)}_{0,0}$ is a scalar diquark composed of $u$ and $d$ quarks] contributes to ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }$ (${\mathrm{\Lambda }}_b\to p$) transition. We establish the Bethe-Salpeter equations for the systems $s(ud{)}_{0,0}$ and $u(ud{)}_{0,0}$ and calculate their Bethe-Salpeter wave functions in the covariant instantaneous approximation with the kernel containing both scalar confinement and one-gluon-exchange terms. Then, the form factors for ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }$ and ${\mathrm{\Lambda }}_b\to p$ weak transitions are obtained with Bethe-Salpeter wave functions for ${\mathrm{\Lambda }}_b$, $\mathrm{\Lambda }$, and $p$. Consequently, we calculate the branching ratios of ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }P$, ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }V$, $\mathrm{\Lambda }\to pP$, and ${\mathrm{\Lambda }}_b\to pV$ ($P$ and $V$ denote pseudoscalar and vector mesons, respectively) in the factorization approach.