Lifetime of kaonium

Abstract

The kaon-antikaon system is studied in both the atomic and the strongly interacting sector. We discuss the influence of the structures of the ${f}_{0}(980)$ and the ${a}_{0}(980)$ mesons on the lifetime of kaonium. The strong interactions are generated by vector meson exchange within the framework of the standard ${\mathrm{SU}(3)}_{V}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{A}$ 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 $K\overline{K}$ scattering and annihilation. The presence of two scalar mesons ${f}_{0}(980)$ and ${a}_{0}(980)$ 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 $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\mathrm{sec}$ for annihilation in a pure Coulomb field down to $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\mathrm{sec}$ when the strong interactions are included. The analysis of the two photon decay width of the ${f}_{0}(980)$ suggests a generalization of the molecular picture which reduces the lifetime of kaonium still further to $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18} \mathrm{sec}.$