Calculation of the two-photon-annihilation contribution to the positronium hyperfine interval at ordermα6

The two-photon-annihilation contribution to the positronium hyperfine interval is obtained in analytic form at order m${\mathrm{\alpha }}^6$ using the Fried-Yennie gauge. The contribution to the hyperfine interval is -0.0325m${\mathrm{\alpha }}^6$=-0.606 MHz. This differs from the result of an earlier Feynman gauge evaluation. The errors in the earlier calculation are identified. The corrected Feynman gauge result agrees with the Fried-Yennie gauge result.