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

We interpret the $B_{s1}(5778)$ as an $S$-wave $B^{*}\overline{K}$ 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 $B_{s1}(5778)\to B_s^{*}\pi$ and the radiative decays $B_{s1}(5778)\to B_s\gamma$ and $B_{s1}(5778)\to B_s^{*}\gamma$, which will be instructive for the forthcoming experiments.

Figure 1

One-particle-exchange diagrams induced by vector mesons $\rho$ and $\omega$.

Figure 2

Numerical results of the normalized Lorentz-scalar function $\tilde{f}(p_t)$ for $B_{s1}(5778)$ in the $B^{*}\overline{K}$ molecular picture for (a) the monopole form factor, (b) the dipole form factor, and (c) the exponential form factor.

Figure 3

Diagrams contributing to the $B_{s1}\to B_s^{*0}{\pi }^0$ decay induced by (a) $B$, (b) $B^{*}$ and (c) $K^{*}$ mesons.

Figure 4

Diagrams contributing to the $B_{s1}\to B_s^0\gamma$ decay induced by (a) $B^{*}$, (b) $K^{*}$ and (c) $K$ mesons.

Figure 5

Diagrams contributing to the $B_{s1}\to B_s^{*0}\gamma$ decay induced by (a) $B$, (b) $K^{*}$, (c) $B^{*}$ and $K$ mesons.