Lifetime of kaonium

The kaon-antikaon system is studied in both the atomic and the strongly interacting sector. We discuss the influence of the structures of the f₀(980) and the a₀(980) mesons on the lifetime of kaonium. The strong interactions are generated by vector meson exchange within the framework of the standard SU(3)V×SU(3)A invariant effective Lagrangian. In the atomic sector, the energy levels and decay widths of kaonium are determined by an eigenvalue equation of the Kudryavtsev-Popov type, with the strong interaction effects entering through the complex scattering length for KK̄ scattering and annihilation. The presence of two scalar mesons f₀(980) and a₀(980) leads to a ground state energy for the kaonium atom that is shifted above the point Coulomb value by a few hundred eV. The effect on the lifetime for the kaonium decay into two pions is much more dramatic. This lifetime is reduced by two orders of magnitude from 1.2×10^-16sec for annihilation in a pure Coulomb field down to 3.2×10^-18sec when the strong interactions are included. The analysis of the two photon decay width of the f₀(980) suggests a generalization of the molecular picture which reduces the lifetime of kaonium still further to 1.1×10^-18 sec.