Total cross sections of $e\gamma \to eX\bar{X}$ processes with $X=\mu ,\gamma ,e$ via multiloop methods

Abstract

Using modern multiloop calculation methods, we derive the analytical expressions for the total cross sections of the processes $e^{-}\gamma \to e^{-}X\bar{X}$ with $X=\mu ,\gamma$ or $e$ at arbitrary energies. For the first two processes our results are expressed via classical polylogarithms. The cross section of $e^{-}\gamma \to e^{-}{e}^{-}{e}^{+}$ is represented as a one-fold integral of complete elliptic integral $\mathrm{K}$ and logarithms. Using our results, we calculate the threshold and high-energy asymptotics and compare them with available results.

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• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
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