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

TL;DR

This paper investigates the nature of the $X(5568)$ particle, concluding it is unlikely to be a molecular state formed by $B_s o ext{pi}$ and $Bar{K}$ interactions, based on lattice QCD and theoretical analysis.

Contribution

The study combines finite volume energy level calculations and the Weinberg compositeness condition to argue against the molecular interpretation of $X(5568)$.

Findings

Lattice QCD data disfavors $X(5568)$ as a molecular state.

Finite volume analysis shows weak $B_s o ext{pi}$ and $Bar{K}$ interactions.

Extended Weinberg condition supports the non-molecular nature of $X(5568)$.

Abstract

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. In addition, we show that the extended Weinberg compositeness condition also indicates that $X(5568)$ cannot be a molecular state made from $B_s\pi$ and $B\bar{K}$ interactions.