$B_{s1}(5778)$ as a $B^{\ast }\bar{K}$ molecule in the Bethe-Salpeter equation approach

Abstract

We interpret the $B_{s1}(5778)$ as an $S$-wave $B^{\ast }\bar{K}$ molecular state in the Bethe-Salpeter equation approach. In the ladder and instantaneous approximations, and with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the vertex, we find the bound state exists. We also study the decay widths of the decay $B_{s1}(5778)\to B_s^{\ast }\pi$ and the radiative decays $B_{s1}(5778)\to B_s\gamma$ and $B_{s1}(5778)\to B_s^{\ast }\gamma$, which will be instructive for the forthcoming experiments.