Study of X(5568) in a unitary coupled-channel approximation of $B \bar{K}$ and $B_s \pi$

Abstract

The potential of the $B$ meson and the pseudoscalar meson is constructed up to the next-to-leading order Lagrangian, and then the $B \bar{K}$ and $B_s \pi$ interaction is studied in the unitary coupled-channel approximation, and a resonant state with a mass about $5568MeV$ and $J^P=0^+$ is generated dynamically, which can be associated with the $X(5568)$ state announced by D0 Collaboration recently. The mass and the decay width of this resonant state depend on the regularization scale in the dimensional regularization scheme, or the maximum momentum in the momentum cutoff regularization scheme. The scattering amplitude of the vector $B$ meson and the pseudoscalar meson is calculated, and an axial-vector state with a mass near $5620MeV$ and $J^P=1^+$ is produced. Moreover, their partners in the charm sector are also discussed.