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

We calculate the binding energies of the hypothetical mesonic atom, K + K − (kaonium), using the K + K − → 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 γ γ → π 0 π 0 or γ γ → π 0 η . The latter process is particularly striking: the peak at the kaonium resonance energy is highly pronounced, with the ratio of the cross sections σ ( γ γ → π 0 η ) / σ ( γ γ → π 0 π 0 ) ≈ 9 . Due to the short lifetime of kaonium ( ∼ 10 − 18 s ) and its small decay width ( ∼ 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.