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. [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.

中文翻译：

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电子-正电子湮灭的光子在Ô（α ³）重新

我们将现代多环方法准确地应用于2和3个光子的电子-正电子an灭的总截面计算 $s/{米}^2$ 准确地 $Ø（{\alpha }^3）$。检查我们的结果的渐近性，我们发现与Ref。达成一致。[1]并发现参考结果中的错误。[2]，[3]。此错误是由于术语引起的，因此参考文献的差分横截面中省略了这些术语。[2]，[3]，它们在运动学区域达到峰值，所有三个光子都准平行于碰撞轴。恢复这些条款后，我们发现Ref的更正结果具有一致性。[3]与我们的结果。