We consider hard three-loop nonlogarithmic corrections of order $m{\alpha }^7$ to hyperfine splitting in positronium. All these contributions are generated by the graphs with photon and/or electron loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge-invariant sets of diagrams. The total result for all these diagrams is $\mathrm{\Delta }E=-1.2917(1)m{\alpha }^7/{\pi }^3=-5.672\mathrm{kHz}$.

• Received 1 April 2014

DOI:https://doi.org/10.1103/PhysRevD.89.111301