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

TL;DR

This paper derives analytical formulas for total cross sections of specific electron-photon scattering processes involving muons, photons, and electrons, using advanced multiloop calculation techniques, and compares asymptotic behaviors with existing results.

Contribution

It introduces new multiloop calculation methods to obtain analytical expressions for cross sections of $e ext{-} ext{gamma}$ processes involving different particles, including complex integral representations.

Findings

Analytical expressions for cross sections involving muons, photons, and electrons.

Expressions involve classical polylogarithms and elliptic integrals.

Results include threshold and high-energy asymptotics, matching previous findings.

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.