Decays of theπ+π−atom

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