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In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic density, from the formal solution of the distribution function, which is then discretized by following characteristics for the transport part with a backward finite difference semi-Lagrangian approach, while the diffusive part is discretized implicitly. After the macroscopic density is available, the distribution function can be efficiently solved even with a fully implicit time discretization, since all discrete velocities are decoupled, resulting in a low-dimensional linear system from spatial discretizations at each discrete velocity. Both first and second order discretizations in space and in time are considered. The resulting schemes can be shown to be asymptotic preserving (AP) in the diffusive limit. Uniformly unconditional stabilities are verified from a Fourier analysis based on eigenvalues of corresponding amplification matrices. Numerical experiments, including high dimensional problems, have demonstrated the corresponding orders of accuracy both in space and in time, uniform stability, AP property, and good performances of our proposed approach.

Last year, the $\Xi(1620)$ state that is cataloged in the Particle Data Group (PDG) with only one star is reported again in the $\Xi^{-}\pi^{+}$ final state by the Belle Collaboration. Its properties not only the spectroscopy but also the decay width cannot be simply explained in the context of conventional constituent quark models. This intrigues an active discussion on the structure of this resonance. In this work, we study the radiative decays of the newly observed $\Xi(1620)$ assuming that it is a meson-baryon molecular state of $\Lambda\bar{K}$ and $\Sigma\bar{K}$ with spin-parity $J^P=1/2^{-}$ in our previous work. The partial decay widths of the $\Lambda\bar{K}-\Sigma\bar{K}$ molecular state into $\Xi\gamma$ and $\Xi\pi\gamma$ final states through hadronic loops are evaluated with the help of the effective Lagrangians. The partial widths for the $\Xi(1620)^0\to\gamma\Xi$ and $\Xi(1620)^0\to\gamma\Xi\pi$ are evaluated to be about $118.76-174.21$ KeV and $58.19-68.75$ eV, respectively, which may be accessible for the LHCb. If the $\Xi(1620)$ is $\Lambda\bar{K}-\Sigma\bar{K}$ molecule, the radiative transition strength $\Xi(1620)^0\to\gamma\bar{K}\Lambda$ is quite small and the decay width is of the order of 0.01 eV. Future experimental measurements of these processes can be useful to test the molecule interpretations of the $\Xi(1620)$.

Very recently, three new structures $\Xi_c(2923)^0$, $\Xi(2938)^0$, and $\Xi(2964)^0$ at the invariant mass spectrum of $\Lambda_c^{+}K^{-}$ observed by the LHCb Collaboration triggers a hot discussion about their inner structure. In this work, we study the strong decay mode of the newly observed $\Xi_c$ assuming that the $\Xi_c$ is a $\bar{D}\Lambda-\bar{D}\Sigma$ molecular state. With the possible quantum numbers $J^p=1/2^{\pm}$ and $3/2^{\pm}$, the partial decay widths of the $\bar{D}\Lambda-\bar{D}\Sigma$ molecular state into the $\Lambda_c^{+}K^{-}$, $\Sigma_c^{+}K^{-}$,and $\Xi_c^{+}\pi^{-}$ final states through hadronic loop are calculated with the help of the effective Lagrangians. By comparison with the LHCb observation, the current results of total decay width support the $\Xi(2923)^0$ as $\bar{D}\Lambda-\bar{D}\Sigma$ molecule while the decay width of the $\Xi_c(2938)^0$ and $\Xi(2964)^0$ can not be well reproduced in the molecular state picture. In addition, the calculated partial decay widths with $S$ wave $\bar{D}\Lambda-\bar{D}\Sigma$ molecular state picture indicate that allowed decay modes, $\Xi_c^{+}\pi^{-}$, may have the biggest branching ratios for the $\Xi_c(2923)$. The experimental measurements for this strong decay process could be a crucial test for the molecule interpretation of the $\Xi_c(2923)$., Comment: arXiv admin note: text overlap with arXiv:1002.0218 by other authors

The $\Xi_b(6227)$ baryon with the quantum number $J^P=1/2^{-}$ is considered as a molecular state composed of a $\Sigma_b$ baryon and $\bar{K}$ meson. The partial decay widths of the $\Sigma_b\bar{K}$ molecular state into $\Xi_b\gamma$ and $\Xi_b^{'}\gamma$ final states through hadronic loops are evaluated with the help of the effective Lagrangians. The partial widths for the $\Xi_b(6227)\to\gamma\Xi_b$ and $\Xi_b(6227)\to\gamma\Xi^{'}_b$ are evaluated to be about 1.50-1.02 KeV and 17.56-24.91 KeV, respectively, which may be accessible for the LHCb. Based on our results we argue that an experimental determination of the radiative decay width of $\Xi_b(6227)$ is important for the understanding of its intrinsic properties.

We investigate the possibility to study the charmed-strange mesons $D_{s0}(2317)$ and $D_{s1}(2460)$ by kaon-induced reactions on a proton target in an effective Lagrangian approach. The production process is described by the $t$-channel $D^{0}$ and $D^{*0}$ exchanges, respectively. Our theoretical approach is based on the chiral unitary theory where the $D_{s0}(2317)$ and $D_{s1}(2460)$ resonances are dynamically generated. Within the coupling constants of the $D_{s0}(2317)$ to $KD$ and $D_{s1}(2460)$ to $KD^{*}$ channels obtained from the chiral unitary theory, the total and differential cross sections of the $K^{-}p\to{}\Lambda_cD_{s0}(2317)$ and $K^{-}p\to{}\Lambda_cD_{s1}(2460)$ are evaluated. The $\bar{K}p$ initial state interaction mediated by Pomeron and Reggeon exchanges is also included, which reduces the production cross sections of the $D_{s0}(2317)$ and $D_{s1}(2460)$. If measured in future experiments, the predicted total cross sections and specific features of the angular distributions can be used to test the (molecular) nature of the $D_{s0}(2317)$ and $D_{s1}(2460)$.