Decays of the π +π - atom

We construct an effective non-relativistic quantum field theory that describes bound states of π ⁺ π ^- pairs and their hadronic decays. We then derive a general expression for the lifetime of the ground stare at next-to-leading order in isospin breaking. Chiral perturbation theory allows one to relate the decay rate to the two S-wave ππ scattering lengths and to several low-energy constants that occur in the chiral Lagrangian. Recent predictions for the scattering lengths give τ= (2.9±0.1) × 10 ^-15 s. This result may be confronted with π ⁺π ^- lifetime measurements, like the one presently carried out at CERN.