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

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 $D_{s0}^{\ast }(2317)$ 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.

16 pages, 3 figures; version to appear in European Physical Journal C

References in corpus (11)

• Dynamically Generated Open and Hidden Charm Meson Systems
• Dynamically generated 0^+ heavy mesons in a heavy chiral unitary approach
• Axial Resonances in the Open and Hidden Charm Sectors
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• Couplings in coupled channels versus wave functions in the case of resonances: application to the two $\Lambda (1405)$ states
• Light meson mass dependence of the positive parity heavy-strange mesons
• Pseudocalar meson and vector meson interactions and dynamically generated axial-vector mesons
• The Delta-resonance in a finite volume
• $B_s{\pi }^{+}$ scattering and search for X(5568) with lattice QCD
• Elementarity of composite systems
• The composite nature of the $\Lambda (1520)$ resonance

Cited by in corpus (2)

• Chiral study of the $a_0(980)$ resonance and $\pi \eta$ scattering phase shifts in light of a recent lattice simulation
• Open-flavor charmed/bottom $sq\bar{q}\bar{Q}$ and $qq\bar{q}\bar{Q}$ tetraquark states