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 state at next-toleading 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.