Next to leading order contributions to the pionium lifetime are considered within non-relativistic effective field theory. A more precise determination of the coupling constants is then needed in order to be consistent with the relativistic $\pi -\pi$ scattering amplitude which can be obtained from chiral perturbation theory. The relativistic correction is found to be 4.1% and corresponds simply to a more accurate value for the non-relativistic decay momentum.

• Received 9 June 1999

DOI:https://doi.org/10.1103/PhysRevD.61.077506