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

Abstract

Lately, the LHCb Collaboration reported the discovery of two new states in the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decay, i.e., $X_0(2866)$ and $X_1(2904)$. In the present work, we study whether these states can be understood as $D^{\ast }{\bar{K}}^{\ast }$ molecules from the perspective of their two-body strong decays into $D^{-}{K}^{+}$ via triangle diagrams and three-body decays into $D^{\ast }\bar{K}\ddot{I}€$. The coupling of the two states to $D^{\ast }{\bar{K}}^{\ast }$ 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 $D^{\ast }{\bar{K}}^{\ast }$ 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 $D^{\ast }{\bar{K}}^{\ast }$ molecule.

5 pages, 2 figures