Nature of $X(3872)$ in $B^0 \to K^0 X(3872)$ and $B^+ \to K^+ X(3872)$ decays

TL;DR

This paper studies the decay processes of B mesons into K mesons and the X(3872) resonance, considering both short-distance and long-distance mechanisms, to understand the resonance's nature.

Contribution

It introduces a combined analysis of short-distance hadronization and long-distance D D* rescattering effects in B decays to X(3872), explaining the observed decay ratio.

Findings

The decay ratio B(B^0→K^0X(3872))/B(B^+→K^+X(3872)) is approximately 0.5.

The difference in D D* threshold effects explains the decay ratio.

Predictions for B_s^0 decays to η(η')X(3872) are provided.

Abstract

We investigate the decays of $B^0 \to K^0 X(3872)$ and $B^+ \to K^+ X(3872)$ based on the picture where the $X(3872)$ resonance is strongly coupled to the $D\bar{D}^* + c.c.$ channel. In addition to the decay mechanism where the $X(3872)$ resonance is formed from the $c\bar{c}$ pair hadronization with the short-distance interaction, we have also considered the $D\bar{D}^*$ rescattering diagrams in the long-distance scale, where $D$ and $\bar{D}^*$ are formed from $c$ and $\bar{c}$ separately. Because of the difference of the mass thresholds of charged and neutral $D\bar{D}^*$ channels, and the rather narrow width of the $X(3872)$ resonance, at the $X(3872)$ mass, the loop functions of $D^0\bar{D}^{*0}$ and $D^+\bar{D}^{*-}$ are much different. Taking this difference into account, the ratio of $\mathcal{B}[B^0\to K^0X(3872)]/\mathcal{B}[B^+ \to K^+ X(3872)] \simeq 0.5$ can be naturally obtained. Based on this result, we also evaluate the decay widths of $B_s^0 \to \eta(\eta') X(3872)$. It is expected that future experimental measurements of these decays can be used to elucidate the nature of the $X(3872)$ resonance.