Electron-positron annihilation to photons at $O(\alpha^3)$ revisited

Understand

We apply the modern multiloop methods to the calculation of the total cross sections of electron-positron annihilation to 2 and 3 photons exactly in $s/m^2$ with the accuracy $O(\alpha^3)$.

• Examining the asymptotics of our results, we find agreement with Ref.
• [Andreassi_et_al_1962] and discover mistakes in the results of Refs.
• [Eidelman&Kuraev_1978,Berends&Kleiss_1981].