Electron-positron annihilation to photons at O(α3) revisited

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/m2 with the accuracy O(α3). Examining the asymptotics of our results, we find agreement with Ref. [1] and discover mistakes in the results of Refs. [2,3]. This mistake is due to the terms, omitted in differential cross section in Refs. [2,3], which are peaked in the kinematic region with all three photons being quasi-parallel to the collision axis. After restoring these terms, we find an agreement of the corrected result of Ref. [3] with our result.