${\overline{B}}^0\to {\overline{K}}^{(*)0}X$, $B^{-}\to K^{(*)-}X$, ${\overline{B}}_s^0\to \eta ({\eta }^{\prime },\varphi )X$ from the $X\left(3872\right)$ molecular perspective

We study the decays ${\overline{B}}^0\to {\overline{K}}^{0}X$, $B^{-}\to K^{-}X$, ${\overline{B}}_s^0\to \eta \left({\eta }^{\prime }\right)X$, ${\overline{B}}^0\to {\overline{K}}^{*0}X$, $B^{-}\to K^{*-}X$, ${\overline{B}}_s^0\to \varphi X$, with $X\equiv X\left(3872\right)$, from the perspective of the $X\left(3872\right)$ being a molecular state made from the interaction of the $D^{*+}{D}^{-},D^{*0}{\overline{D}}^0$, and $c.c.$ components. We consider both the external and internal emission decay mechanisms and find an explanation for the ${\overline{K}}^{0}X$ and $K^{-}X$ production rates, based on the mass difference of the charged and neutral $D^{*}\overline{D}$ components. We also find that the internal and external emission mechanisms add constructively in the ${\overline{B}}^0\to {\overline{K}}^{0}X$, $B^{-}\to K^{-}X$ reactions, while they add destructively in the case of ${\overline{B}}^0\to {\overline{K}}^{*0}X$, $B^{-}\to K^{*-}X$ reactions. This feature explains the decay widths of the present measurements and allows us to make predictions for the unmeasured modes of ${\overline{B}}_s^0\to \eta \left({\eta }^{\prime }\right)X\left(3872\right)$ and $B^{-}\to K^{*-}X\left(3872\right)$. The future measurement of these decay modes will help us get a better perspective on the nature of the $X\left(3872\right)$ and the mechanisms present in production reactions of that state.