Compositeness of $T_{cc}$ and $X(3872)$ by considering decay and coupled-channels effects

Abstract

The compositeness of weakly bound states is discussed using the effective field theory from the viewpoint of the low-energy universality. We introduce a model with coupling of the single-channel scattering to the bare state, and study the compositeness of the bound state by varying the bare state energy. In contrast to the naive expectation that the near-threshold states are dominated by the molecular structure, we demonstrate that a non-composite state can always be realized even with a small binding energy. At the same time, however, it is shown that a fine tuning is necessary to obtain the non-composite weakly bound state. In other words, the probability of finding a model with the composite dominant state becomes larger with the decrease of the binding energy in accordance with the low-energy universality. For the application to exotic hadrons, we then discuss the modification of the compositeness due to the decay and coupled-channels effects. We quantitatively show that these contributions suppress the compositeness, because of the increase of the fraction of other components. Finally, as examples of near-threshold exotic hadrons, the structures of $T_{cc}$ and $X(3872)$ are studied by evaluating the compositeness. We find the importance of the coupled-channels and decay contributions for the structures of $T_{cc}$ and $X(3872)$, respectively.

19 pages, 14 figures, published version

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Cited by in corpus (7)

• Compositeness of hadrons, nuclei, and atomic systems
• Isospin violation effect and three-body decays of the $T_{cc}^{+}$ state
• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Hidden-Charm Tetraquarks in a Mixture Model: Coupled-Channel Analysis with $c\bar{c}$ and Hadronic Molecular Components
• Electromagnetic characteristics as probes into the inner structures of the predicted ${\Xi }_c^{{(}^{\prime },\ast )}{D}_s^{(\ast )}$ molecular states
• Closed-channel parameters of Feshbach resonances
• Compositness and wave function of shallow bound states in relation to scattering observables