Pionium lifetime and \pi\pi scattering lengths in generalized chiral perurbation theory

TL;DR

This paper investigates how electromagnetic corrections affect the relationship between pionium lifetime and cc scattering lengths using a covariant bound state formalism within generalized chiral perturbation theory, linking these to the quark condensate.

Contribution

It introduces a covariant three-dimensional bound state formalism to analyze electromagnetic effects on pionium lifetime within generalized chiral perturbation theory.

Findings

Electromagnetic corrections significantly influence the pionium lifetime

The lifetime depends on cc scattering lengths, which are linked to the quark condensate

The framework allows for a detailed analysis of these relationships

Abstract

The relationship between the pionium lifetime and the $\pi\pi$ 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 $\pi\pi$ scattering lengths, the latter being dependent on the quark condensate value.