Total cross sections of eγ → eX X ¯ $$ eX\overline{X} $$ processes with X = μ, γ, e via multiloop methods

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