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 {bar{D}}^*K^* molecules from the perspective of their two-body strong decays into D^-K^+ via triangle diagrams and three-body decays into {bar{D}}^*Kpi . The coupling of the two states to {bar{D}}^*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) state, in marginal agreement with the experimental value within the uncertainty of the model, hints at a large {bar{D}}^*K^* component in its wave function. On the other hand, the strong decay width for the X_1(2904) state, much smaller than its experimental counterpart, effectively rules out its assignment as a {bar{D}}^*K^* molecule.
Highlights
Est LHCb announcement of two structures observed in the D− K + invariant mass of the B+ → D+ D− K + decay points to the likely existence of genuinely exotic mesonic states with a minimum quark content of csud [8,9]
We examine the possibility whether they can be understood as D ∗ K ∗ molecules
In order to obtain the allowed two-body decay widths through the triangle diagrams shown in Fig. 1 and three-body decay widths in Fig. 2, we first compute the coupling constant gX J D ∗ K ∗ (≡ gX J )
Summary
In one earlier study [17], a molecular X0 state with a narrow width and a mass around 2848 MeV was predicted in the unitary coupled channels approach. If within the uncertainties of the model, the so-obtained strong decay widths are consistent with data, it is possible to assign the state under study as a molecular state, otherwise, the possibility is excluded. Such an approach has been widely applied to study newly observed (exotic) hadrons, see, e.g., Refs.
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