Analytic Evaluation of the Orthopositronium-to-Three-Photon Decay Amplitudes to One-Loop Order

The three independent amplitudes describing the decay of orthopositronium to three photons are evaluated in analytic form to one-loop order. The amplitudes are used to obtain the order- $\alpha$ and order- ${\alpha }^2$ “square” contributions to the orthopositronium decay rate as integrals over the two-dimensional phase space. The results for the decay rate contributions are ${\gamma }_1=-10.286\mathrm{}606\left(10\right)\left(\alpha /\pi \right){\gamma }_{\mathrm{LO}}$ and ${\gamma }_2\left(\mathrm{square}\right)=28.860\mathrm{}\left(2\right)(\alpha /\pi {)}^2{\gamma }_{\mathrm{LO}}$, where ${\gamma }_{\mathrm{LO}}$ is the lowest order rate.