Production of the $X(3872)$ state via the $B^0\to K^{\ast 0}X(3872)$ decay

In this work the production of the state $X(3872)$ is estimated via the reaction $B^0\to K^{\ast 0}X(3872)$ through triangle mechanisms described by the sequence $B^0\to D_s^{(\ast )+}(\to K^{\ast 0}{D}^{(\ast )+})D^{(\ast )-}\to K^{\ast 0}(D^{(\ast )+}{D}^{(\ast )-})\to K^{\ast 0}X(3872)$. The molecular configuration $(D{\bar{D}}^{\ast }-c\mathrm{.}c\mathrm{.})$ of the $X(3872)$ is considered. By means of the effective Lagrangian approach, the branching ratio $\mathcal{B}(B^0\to K^{\ast 0}X(3872))$ is calculated as a function of the strength of the coupling of the charged components $(D^{+}{\bar{D}}^{\ast -}-c\mathrm{.}c\mathrm{.})$ to the $X(3872)$ and compared with experimental data. Besides, employing the decay $B^0\to K^{\ast 0}\psi (2S)$ as a normalization channel, the ratio of branching fractions $R=\frac{\mathcal{B}(B^0\to K^{\ast 0}X(3872))}{\mathcal{B}(B^0\to K^{\ast 0}\psi (2S))}\times \frac{\mathcal{B}(X(3872)\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-})}{\mathcal{B}(\psi (2S)\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-})}$ is also estimated. The findings provide another concrete example for the vital role of charged components in achieving a quantitatively correct description of the $X(3872)$.