Two-loop corrections to the decay rate of parapositronium

Abstract

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 an NRQED Hamiltonian, which is then used in a bound state calculation to determine the decay rate. Our result for the two-loop correction is $5.1243(33)$ in units of $(\alpha /\pi {)}^2$ times the lowest order rate. This is consistent with but more precise than the result $5.1(3)$ of a previous calculation.

26 pages, 7 figures