Hard nonlogarithmic corrections of ordermα7to hyperfine splitting in positronium

Abstract

We consider hard three-loop nonlogarithmic corrections of order $m{\ensuremath{\alpha}}^{7}$ 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 $\mathrm{\ensuremath{\Delta}}E=\ensuremath{-}1.2917(1)m{\ensuremath{\alpha}}^{7}/{\ensuremath{\pi}}^{3}=\ensuremath{-}5.672\text{ }\text{ }\mathrm{kHz}$.