$B_s\pi$--$B\bar{K}$ interactions in finite volume and the $X(5568)$

Understand

The recent observation of $X(5568)$ by the D0 Collaboration has aroused a lot of interest both theoretically and experimentally.

• In the present work, we first point out that $X(5568)$ and $D_{s0}^*(2317)$ cannot simultaneously be of molecular nature, from the perspective of heavy-quark symmetry and chiral symmetry, based on a previous study of the lattice QCD scattering lengths of $DK$ and its coupled channels.
• Then we compute the discrete energy levels of the $B_s\pi$ and $B\bar{K}$ system in finite volume using unitary chiral perturbation theory.
• The comparison with the latest lattice QCD simulation, which disfavors the existence of $X(5568)$, supports our picture where the $B_s\pi$ and $B\bar{K}$ interactions are weak and $X(5568)$ cannot be a $B_s\pi$ and $B\bar{K}$ molecular state.