Order-${\alpha }^2$ corrections to the decay rate of parapositronium are calculated. A QED scattering calculation of the amplitude for electron-positron annihilation into two photons at threshold is combined with the technique of effective field theory to determine a nonrelativistic QED Hamiltonian, which is then used in a bound-state calculation to determine the decay rate. Our result for the two-loop correction is $5.1243\left(33\right)\mathrm{}$ in units of $(\alpha /\pi {)}^2$ times the lowest-order rate. This is consistent with but more precise than the result $5.1\left(3\right)\mathrm{}$ of a previous calculation.

• Received 22 May 2003

DOI:https://doi.org/10.1103/PhysRevA.68.032512