$\bar B^0 \to \bar K^{(*) \,0} X$, $B^- \to K^{(*) \, -} X$, $\bar B_s^0 \to \eta (\eta', \phi) X$ from the $X(3872)$ molecular perspective

TL;DR

This paper investigates B meson decays involving the X(3872) state, proposing it as a molecular D*D bound state, and explains decay rates through interference of decay mechanisms, offering predictions for unmeasured modes.

Contribution

It introduces a molecular model for X(3872) in B decays and analyzes decay mechanisms to explain existing data and predict new decay modes.

Findings

External and internal emission mechanisms interfere constructively or destructively, affecting decay widths.

Mass differences of D*D components explain production rate variations.

Predictions made for unmeasured decay modes to test the molecular hypothesis.

Abstract

We study the decays $\bar B^0 \to \bar K^0 \, X$, $B^- \to K^- \, X$, $\bar B^0_s \to \eta (\eta')\, X$, $\bar B^0 \to \bar K^{*0} \, X$, $B^- \to K^{*-} \, X$ , $\bar B_s^0 \to \phi \, X$, with $X \equiv X(3872)$, from the perspective of the $X(3872)$ being a molecular state made from the interaction of the $D^{*+} D^-, D^{*0} \bar D^0$ 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 $D^* \bar D$ 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 $\bar B^0 \to \bar K^{*0} \, X$, $B^- \to K^{*-} \, X$ reactions. This feature explains the decay widths of the present measurements and allows us to make predictions for the unmeasured modes of $\bar B^0_s \to \eta (\eta')\, X(3872)$ and $B^- \to K^{*-} \, X(3872)$. 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.