Hyperfine splitting in positronium to ${\cal O}(\alpha^7m_e)$:   one-photon annihilation contribution
  We present the complete result for the ${\cal O}(\alpha^7m_e)$ one-photon annihilation contribution to the hyperfine splitting of the ground state energy levels in positronium. Numerically it increases the prediction of quantum electrodynamics by $217\pm 1$ kHz. 
Marc Baker, Peter Marquard, Alexander Penin, Jan Piclum, and Matthias   Steinhauser
hep-ph