Contribution of light-by-light scattering to the ordersO(mα8) andO(mα8ln α) orthopositronium decay rate

The gauge invariant contribution of the six radiatively corrected light-by-light scattering processes to the decay rate of orthopositronium into three photons is calculated. The infrared-safe Yennie gauge is used for the loop photons. The relative order of ${\mathrm{\alpha }}^2$ part of our result, 9.0074(9)(${\mathrm{\alpha }}^2$/${\mathrm{\pi }}^2$)${\mathrm{\Gamma }}_{\mathrm{LO}}$, makes a 0.000350 μ${\mathrm{s}}^{\mathrm{-}1}$ contribution to the decay rate, thus reducing slightly the apparent discrepancy between the theoretical and experimental results. ${\mathrm{\Gamma }}_{\mathrm{LO}}$ is the lowest-order decay rate. The analytically obtained relative order ${\mathrm{\alpha }}^2$ln α part of our result, -${\mathrm{\alpha }}^2$ln(1/α)${\mathrm{\Gamma }}_{\mathrm{LO}}$, is in agreement with earlier evaluations.