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Register a new user$B_{s1}(5778)$ as a $B^*bar{K}$ molecule in the Bethe-Salpeter equation approach
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We interpret the $B_{s1}(5778)$ as an $S$-wave $B^astbar{K}$ molecular state in the Bethe-Salpeter equation approach. In the ladder and instantaneous approximations, and with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the vertex, we find the bound state exists. We also study the decay widths of the decay $B_{s1}(5778)rightarrow B_s^astpi$ and the radiative decays $B_{s1}(5778)rightarrow B_sgamma$ and $B_{s1}(5778)rightarrow B_s^{ast}gamma$, which will be instructive for the forthcoming experiments.
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We interpret the $X_1(2900)$ as an $S$-wave $bar{D}_1K$ molecular state in the Bethe-Salpeter equation approach with the ladder and instantaneous approximations for the kernel. By solving the Bethe-Salpeter equation numerically with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the verties, we find the bound state exists. We also study the decay width of the decay $X_1(2900)$ to $D^-K^+$.
We study the possible bound states of the $D_1D$ system in the Bethe-Salpeter (BS) formalism in the ladder and instantaneous approximations. By solving the BS equation numerically with the kernel containing one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we investigate whether the isoscalar and isovector $D_1D$ bound states may exist, respectively. We find that $Y(4260)$ could be accommodated as a $D_1D$ molecule, whereas the interpretation of $Z_2^+(4250)$ as a $D_1D$ molecule is disfavored. The bottom analog of $Y(4260)$ may exist but that of $Z_2^+(4250)$ does not.
In this work, we assume that the observed state $Xi(1620)$ is a $s$-wave $Lambdabar{K}$ or $Sigmabar{K}$ bound state. Based on this molecule picture, we establish the Bethe-Salpeter equations for $Xi(1620)$ in the ladder and instantaneous approximations. We solve the Bethe-Salpeter equations for the $Lambdabar{K}$ and $Sigmabar{K}$ systems numerically and find that the $Xi(1620)$ can be explained as $Lambdabar{K}$ and $Sigmabar{K}$ bound states with $J^P=1/2^-$, respectively. Then we calculate the decay widths of $Xi(1620)rightarrowXipi$ in these two different molecule pictures systems, respectively.
We discuss the possibility that the X(3872) can be a $Dbar{D}^*$ molecular bound state in the Bethe-Salpeter equation approach in the ladder and instantaneous approximations. We show that the $Dbar{D}^*$ bound state with quantum numbers $J^{PC}=1^{++}$ exists. We also calculate the decay width of $X(3872) rightarrow gamma J/psi$ channel and compare our result with those from previous calculations.
Using a well-established effective interaction in a rainbow-ladder truncation model of QCD, we fix the remaining model parameter to the bottomonium ground-state spectrum in a covariant Bethe-Salpeter equation approach and find surprisingly good agreement with the available experimental data including the 2^{--} Upsilon(1D) state. Furthermore, we investigate the consequences of such a fit for charmonium and light-quark ground states.
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