Energy shift and decay width of kaonium from coupled-channel one-loop chiral amplitudes

Using two fitted coupled-channel one-loop chiral amplitudes, we investigate the strong-interaction energy shift and decay width of the hypothetical Coulomb-bound $K^{+}{K}^{-}$ hadronic atom, kaonium. We obtain ground-state widths of 1.67 and 0.92 keV, which are both larger than previous kaonium predictions, including the 0.30 keV result obtained from a non-perturbative treatment based on leading-order chiral perturbation theory. Although the $K^{+}{K}^{-}$ scattering lengths obtained from the two one-loop amplitudes have nearly equal imaginary parts, their real parts have opposite signs; thus, the leading absorptive contributions to the widths are similar, while the Coulomb corrections act in opposite directions. The kaonium width therefore depends on both the real and imaginary parts of the near-threshold strong amplitude. Despite the increased ground-state width, the first three $s$-wave levels remain separated. In photon fusion, at fixed pole area and resonance position, the increase in the intrinsic width has a negligible effect on the line shape after including Belle’s experimental resolution.