Positronium energy levels at order mα7: Light-by-light scattering in the two-photon-annihilation channel

Recent and ongoing experimental work on the positronium spectrum motivates new efforts to calculate positronium energies at the level of O(alpha(3)) corrections to the lowest-order result. We have obtained results for one set of such corrections involving light-by-light scattering of the photons produced in a two-photon virtual annihilation process. Our result is an energy shift 1.58377 (8)m alpha(7)/pi(3) for the n = 1 singlet state, correcting the ground-state hyperfine splitting by -6.95 kHz. We also obtained a new and more precise result for the light-by-light scattering correction to the real decay of parapositronium into two photons.