Exotic molecular meson states of B${}^{(\ast )}$ K${}^{(\ast )}$ nature

We evaluate theoretically the interaction of the open bottom and strange systems $\overline{B}\overline{K}$, ${\overline{B}}^{\ast }\overline{K}$, $\overline{B}{\overline{K}}^{\ast }$ and ${\overline{B}}^{\ast }{\overline{K}}^{\ast }$ to look for possible bound states which could correspond to exotic non-quark-antiquark mesons since they would contain at least one b and one s quarks. The s-wave scattering matrix is evaluated implementing unitarity by means of the Bethe-Salpeter equation, with the potential kernels obtained from contact and vector meson exchange mechanisms. The vertices needed are supplied from Lagrangians derived from suitable extensions of the hidden gauge symmetry approach to the bottom sector. We find poles below the respective thresholds for isospin 0 interaction and evaluate the widths of the different obtained states by including the main sources of imaginary part, which are the B* → Bγ decay in the ${\overline{B}}^{\ast }\overline{K}$ channels, the K* → Kπ in the channels involving a K*, plus the box diagrams with $\overline{B}\overline{K}$ and ${\overline{B}}^{\ast }\overline{K}$ intermediate states for the ${\overline{B}}^{\ast }{\overline{K}}^{\ast }$ channels.