Strong decays of $\bar{D}^{*}K^{*}$ molecules and the newly observed $X_{0,1}$ states

TL;DR

This study investigates whether the newly observed $X_{0,1}$ states can be interpreted as $D^*ar{K}^*$ molecular states by analyzing their strong decay patterns, finding partial support for $X_0(2866)$ but not for $X_1(2904)$.

Contribution

The paper provides a novel analysis of the $X_{0,1}$ states as $D^*ar{K}^*$ molecules using decay width calculations and the Weinberg compositeness condition.

Findings

The $X_0(2866)$ has a decay width compatible with a $D^*ar{K}^*$ molecular interpretation.

The $X_1(2904)$ decay width is inconsistent with a $D^*ar{K}^*$ molecular state.

The results suggest a large $D^*ar{K}^*$ component in $X_0(2866)$ but not in $X_1(2904)$.

Abstract

Lately, the LHCb Collaboration reported the discovery of two new states in the $B^+\rightarrow D^+D^- K^+$ decay, i.e., $X_0(2866)$ and $X_1(2904)$. In the present work, we study whether these states can be understood as $D^*\bar{K}^*$ molecules from the perspective of their two-body strong decays into $D^-K^+$ via triangle diagrams and three-body decays into $D^*\bar{K}\pi$. The coupling of the two states to $D^*\bar{K}^*$ are determined from the Weinberg compositeness condition, while the other relevant couplings are well known. The obtained strong decay width for the $X_0(2866)$, in marginal agreement with the experimental value within the uncertainty of the model, hints at a large $D^*\bar{K}^*$ component in its wave function. On the other hand, the strong decay width for the $X_1(2904)$, much smaller than its experimental counterpart, effectively rules out its assignment as a $D^*\bar{K}^*$ molecule.