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 SU(3) V ϫSU(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 KK 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 1.2ϫ10 Ϫ16 sec for annihilation in a pure Coulomb field down to 3.2ϫ10 Ϫ18 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 1.1ϫ10 Ϫ18 sec.

Masses of di-mesonic molecular states

“…Our calculated predictions for this states are agreed with theoretical predictions in ref. [33][34][35][36] [23] and with ref. [37] (0.13 keV).…”

Two-photon decays of hadronic molecules

“…This was taken as a recipe by many authors and was applied also to calculate the two-photon decay rates of hadronic molecules [9,10]. In this paper we argue that this procedure leads to wrong results.…”

“…[10] #2 . The second argument is that any transition matrix element using the wave function at the origin meets certain problems with gauge invariance.…”

“…In the present paper we demonstrate that the technique used in Refs. [9,10] has a large theoretical uncertainty. We also show that a gauge-invariant treatment of the two-photon decay amplitude of the KK molecule yields the value of the γγ width for the f 0 (980) close to 0.2 keV.…”

Energy-level displacement of excitednpstates of kaonic hydrogen

“…According to [1], the contribution of the elastic background (a K − p 1/2 ) B to the P-wave scattering length a K − p 1/2 should be defined by the contribution of all low-energy interactions (a K − p 1/2 ) CA , which can be described within the Effective Chiral Lagrangian (the ECL) approach [22] or that is equivalent within Current Algebra (CA) [23]- [30], supplemented by soft-kaon theorems (SKT) [26]- [30], and the contribution (a K − p 1/2 ) KK of low-energy exchanges with the exotic scalar mesons a 0 (980) and f 0 (980), which are four-quark states [31,32] or KK molecules [32,33]. The description of strong low-energy interactions of these mesons goes beyond the ECL approach, describing strong low-energy interactions of mesons with qq and baryons with qqq quark structures.…”