Total cross sections of $e\gamma\to e X\bar{X}$ 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.