  The mass and meson-current coupling constant of the resonance $X(5568)$, as
well as the width of the decay $X(5568)\to B_s^{\ast}\pi$ are calculated by
modeling the exotic $X(5568)$ resonance as a diquark-antidiquark state $%
X_b=[su][bd]$ with quantum numbers $J^{P}=1^{+}$. The calculations are made
employing QCD two-point sum rule method, where the quark, gluon and mixed
vacuum condensates up to dimension eight are taken into account. The sum rule
approach on the light-cone in its soft-meson approximation is used to explore
the vertex $X_bB_{s}^{\ast}\pi$ and extract the strong coupling $%
g_{X_bB_{s}^{\ast}\pi}$, which is a necessary ingredient to find the width of
the $X_b \to B_s^{\ast}\pi^{+}$ decay process. The obtained predictions are
compared with the experimental data of the D0 Collaboration, and results of
other theoretical works.
