${\bar{B}}^0\to {\bar{K}}^{(\ast )0}X$, $B^{-}\to K^{(\ast )-}X$, ${\bar{B}}_s^0\to \eta ({\eta }^{\prime },\varphi )X$ from the $X(3872)$ molecular perspective

Abstract

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

Comments: 15 pages, 5 figures, 2 tables; V2: discussions added, references added, version published in Phys. Rev. D