Emergence of kaonium as a sharp resonance in photon-photon to meson-meson cross-sections

Abstract

We calculate the binding energies of the hypothetical mesonic atom, $K^{+}{K}^{-}$ (kaonium), using the $K^{+}{K}^{-}\to K^{+}{K}^{-}$ elastic scattering amplitude. Our findings are in line with previously reported results, which involve solving an eigenvalue equation of the Kudryavtsev-Popov type. Using chiral perturbation theory, we show that kaonium manifests itself as a sharp resonance around 992 MeV accompanying $f_0(980)$ or $a_0(980)$ in cross-sections for processes $\gamma \gamma \to {\pi }^0{\pi }^0$ or $\gamma \gamma \to {\pi }^0\eta$. The latter process is particularly striking: the peak at the kaonium resonance energy is highly pronounced, with the ratio of the cross-sections $\sigma (\gamma \gamma \to {\pi }^0\eta )/\sigma (\gamma \gamma \to {\pi }^0{\pi }^0)\approx 9$. Due to the short lifetime of kaonium ($\sim 10^{-18}$ s) and its small decay width ($\sim 0.4$ keV), direct detection of this exotic atom poses a significant challenge and requires high experimental resolution. However, we show that once the formation of kaonium is considered in the cross-section, a better fit to the available experimental data is obtained.

Comments: 15 pages, 5 figures