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arXiv · hep-ph/0307288

Lifetime of Kaonium

S. Krewald·R. H. Lemmer·F. P. Sassen
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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 $SU(3)_V\times SU(3)_A$ 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 $K\bar K$ 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 $0.8\times 10^{-16}$ sec for annihilation in a pure Coulomb field down to $3.1\times 10^{-18}$ 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 $1.1\times 10^{-18}\textrm{sec}$.

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S. Krewald, R. H. Lemmer, F. P. Sassen. 2003-10-08. Lifetime of Kaonium. https://doi.org/10.1103/physrevd.69.016003

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