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In this work, we study the $B\bar{K}$ molecule in the Bethe-Salpeter (BS)equation approach. With the kernel containing one-particle-exchange diagramsand introducing two different form factors (monopole form factor and dipoleform factor) in the vertex, we solve the BS equation numerically in thecovariant instantaneous approximation. We investigate the isoscalar andisovector $B\bar{K}$ systems, and we find $X(5568)$ cannot be a $B\bar{K}$molecule.

Studying the bound state of the $B\bar{K}$ system in the Bethe-Salpeter formalism