$B_s\pi$--$B\bar{K}$ 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.

arXiv comment16 pages, 3 figures; version to appear in European Physical Journal C

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Cited by in corpus (19)

• The $XYZ$ states: experimental and theoretical status and perspectives
• A review of the open charm and open bottom systems
• Open charm and bottom tetraquarks in an extended relativized quark model
• Chiral study of the $a_0(980)$ resonance and $\pi \eta$ scattering phase shifts in light of a recent lattice simulation
• Searching for possible ${\Omega }_c-$like molecular states from ${\Xi }_c^{\ast }\bar{K}/{\Xi }_c{\bar{K}}^{\ast }/{\Xi }_c^{\prime }{\bar{K}}^{\ast }$ interaction
• Spectrum and rearrangement decays of tetraquark states with four different flavors
• Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{\psi s}^{\Lambda }(4338)$ and $P_{cs}(4459)$
• Open-flavor charmed/bottom $sq\bar{q}\bar{Q}$ and $qq\bar{q}\bar{Q}$ tetraquark states
• The decays of the fully open flavor state $T_{c\bar{s}0}^0$ in a $D^{\ast }{K}^{\ast }$ molecule scenario
• Generating a resonance-like structure in the reaction $B_c\to B_s\pi \pi$
• Estimating decay rate of $X^{\pm }(5568)\to B_s{\pi }^{\pm }$ while assuming them to be molecular states
• Study of X(5568) in a unitary coupled-channel approximation of $B\bar{K}$ and $B_s\pi$
• Exploring the mass spectrum and the electromagnetic properties of the possible ${\Xi }_{cc}{K}^{(\ast )}$ and ${\Xi }_{cc}{\bar{K}}^{(\ast )}$ molecules
• The bottomed strange molecules with isospin 0
• How can $X^{\pm }(5568)$ escape detection?
• Studying the bound state of the $B\bar{K}$ system in the Bethe-Salpeter formalism
• Mass Spectrum of Exotic X(5568) State via Artificial Neural Network
• Investigating $S$-wave bound states composed of two pseudoscalar mesons
• Chiral excitations of open-beauty systems