Decays of the pi+ pi- atom

Abstract

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 \pm 0.1) * 10^{-15} sec. This result may be confronted with pi+ pi- lifetime measurements, like the one presently carried out at CERN.