Details on the O(me 6 ) Positronium Hyperne Splitting due to Single Photon Annihilation

A detailed presentation is given of the analytic calculation of the single-photon annihilation contributions for the positronium ground state hyperne splitting, to order me 6 in the framework of non-relativistic eective theories. The current status of the theoretical description of the positronium ground state hyperne splitting is reviewed.