2019 October 15
We report on progress in the calculation of corrections to positronium energy levels of order $m \alpha^7$. Corrections at this level will be needed for the interpretation of the results of upcoming measurements. A procedure for the calculation of high order corrections has been developed based on the Bethe-Salpeter equation of dimensionally regularized NRQED and the method of regions. We demonstrate the effectiveness of this approach by using it to obtain all pure recoil corrections to positronium energies at $O(m \alpha^6)$ in a unified manner.