Pionium lifetime and ππ scattering lengths in generalized chiral perurbation theory
Abstract
The relationship between the pionium lifetime and the ππ scattering lengths is established, including the sizable electromagnetic corrections. The bound state formalism that is used is that of constraint theory which provides a covariant three-dimensional reduction of the Bethe--Salpeter equation. The framework of generalized chiral perturbation theory allows then an analysis of the lifetime value as a function of the ππ scattering lengths, the latter being dependent on the quark condensate value.
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