Compositeness of near-threshold exotic hadrons in systems with Coulomb and short-range interactions

We study the universal properties of near-threshold $s$-wave eigenstates in systems with Coulomb plus short-range interactions by analyzing their compositeness. Using a nonrelativistic effective field theory, we derive a relation between the compositeness of near-threshold states and the Coulomb scattering length, the Coulomb effective range, and the Bohr radius. We find that the long-range Coulomb interaction modifies the threshold behavior expected from the low-energy universality of purely short-range systems. When the Coulomb interaction is relatively weak compared with the short-range interaction, a remnant of the low-energy universality associated with the short-range interaction survives, leading to composite-dominant near-threshold eigenstates. In contrast, in the strong-Coulomb regime, this remnant disappears.