The $B^{+(0)} \to \bar D^{0(-)} D^{*}_{s0}(2317)^+$ decays and the molecular structure of $D^*_{s0}(2317)$

TL;DR

The paper addresses whether the $D^*_{s0}(2317)$ resonance is predominantly a $DK$- and $D_s\eta$-molecular state by examining $B^{+(0)} \to \bar{D}^{0(-)} D^{*}_{s0}(2317)^+$ decays. It develops a formalism that decouples the weak decay from the strong formation of the resonance, using experimental $B\to \bar{D}DK$ branching fractions to fix weak vertices and modeling the DK to $D^*_{s0}$ transition via final-state interactions with loop functions $G_{KD}$ and couplings $g_{KD}$. A Monte Carlo propagation of experimental uncertainties yields a theoretical branching fraction of $\mathcal{B}[B^+\to \bar{D}^0 D^*_{s0}(2317)^+]_{\rm theo.}=(0.58\pm0.16)\times 10^{-3}$, compatible with the measured value within errors and suggesting a sizeable KD molecular component. The results align with lattice QCD indications of a large $DK$ component (about $72\%$) in $D^*_{s0}(2317)$ and bolster the molecular interpretation, while allowing some nonmolecular admixture within experimental uncertainties.

Abstract

We have conducted a study of the $B^{+(0)} \to \bar D^{0(-)} D^{*}_{s0}(2317)^+$ reactions from the perspective that the $D^*_{s0}(2317)$ resonance is a molecular state of the $KD$ and $D_s η$ components. We have followed a method to evaluate the branching fractions obtaining information from the experimental data on the $B^+\to \bar D^0 K^+ D^0$, $B^+\to \bar D^0 K^0 D^+$, $B^0 \to D^- K^+ D^0$, $B^0 \to D^- K^0 D^+$ reactions, which have the $D^0 K^+$ and $D^+ K^0$ pairs in the final state. The approach concentrates the dynamics of the weak process in the branching ratios of these reactions and pays attention to the propagation of the $DK$ components and their strong interaction to form the $D^*_{s0}(2317)$ resonance. We find branching ratios for the $B^{+(0)} \to \bar D^{0(-)} D^{*}_{s0}(2317)^+$ reactions, which are compatible with the experimental data, but considering errors there is room for contributions of other nonmolecular components, although a sizeable fraction from the molecular components is a solid conclusion.

Figures (4)

• Figure 1: $B^-$ decay with external emission and hadronization of the $\bar{c} s$ quark pair.
• Figure 2: External emission for $B^-$ decay with hadronization of $c\bar{u}$ quark pair.
• Figure 3: Internal emission for $B^-$ decay with $c\bar{c}$ hadronization.
• Figure 4: Final state interaction for $B^+\to \bar{D}^0 D^{*+}_{s0}$ through rescattering of the $KD$ components.