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Recent experiments have discovered various exotic hadrons near scattering thresholds, stimulating interest in their internal structure. For short-range $s$-wave interactions, the structure of near-threshold states has been clarified based on the low-energy universality: shallow bound states below threshold tend to be dominated by the hadronic molecular component [1], whereas narrow resonances slightly above threshold do not [2]. Near-threshold states also appear in systems with the Coulomb plus short-range interactions, such as two-baryon systems with heavy quarks studied in lattice QCD [3] and exotic nuclei [4]. For charged systems, the Coulomb interaction modifies the scattering amplitude even in the low-energy region, and the structure of near-threshold states cannot be understood by directly applying the pure short-range results.
In this work, we investigate near-threshold states in systems with Coulomb plus short-range interactions, describing the scattering amplitude using the Coulomb scattering length and the Coulomb effective range [5,6,7]. To quantify their internal structure, we evaluate the compositeness, which characterizes the molecular nature of the eigenstate [8]. We show that the behavior of the compositeness near the threshold is governed by the competition between the short-range and Coulomb interactions. In particular, when the Bohr radius is larger than the magnitude of the effective range, the compositeness increases in the near-threshold region as a remnant of the short-range low-energy universality, whereas this enhancement disappears when the Coulomb interaction becomes dominant with smaller Bohr radius [6,7]. Applying this framework to exotic hadrons and hypernuclei, we obtain results consistent with experimental observations, precise few-body calculations, and findings from the lattice QCD studies, and show that the molecular nature of near-threshold states can be understood as a common consequence of the remnant of the low-energy universality.
[1] T. Kinugawa and T. Hyodo, Phys. Rev. C 109, 045205 (2024).
[2] T. Kinugawa and T. Hyodo, arXiv:2403.12635 [hep-ph].
[3] Y. Lyu, H.Tong, et al. [HAL QCD Coll.], Phys. Rev. Lett. 127 (2021) 072003.
[4] E. Hiyama, M. Isaka, T. Doi, and T. Hatsuda, Phys. Rev. C 106, 064318 (2022).
[5] R. Higa, H. W. Hammer, and U. van Kolck, Nucl. Phys. A 809, 171 (2008).
[6] T. Kinugawa and T. Hyodo, arXiv:2507.22399 [hep-ph].
[7] T. Kinugawa and T. Hyodo, arXiv:2602.20678 [hep-ph].
[8] T. Kinugawa, T. Hyodo, Eur. Phys. J. A 61, 154 (2025).
