The Compton Scattering Total Cross Section at Next-to-Leading Order

TL;DR

This paper provides an analytic formula for the total Compton scattering cross section at next-to-leading order, incorporating real and virtual contributions, and employs advanced multiloop techniques for precise calculation.

Contribution

It presents the first complete analytic next-to-leading order cross section for Compton scattering, combining real and virtual processes with modern multiloop methods.

Findings

Analytic formula for the $ ext{O}(oldsymbol{ extalpha}^3)$ cross section

Inclusion of double-Compton and virtual contributions

Use of differential equations for multiloop integral computation

Abstract

An analytic formula is given for the total scattering cross section of an electron and a photon at order $\alpha^3$. This includes both the double-Compton scattering real-emission contribution as well as the virtual Compton scattering part. When combined with the recent analytic result for the pair-production cross section, the complete $\alpha^3$ cross section is now known. Both the next-to-leading order calculation as well as the pair-production cross section are computed using modern multiloop calculation techniques, where cut diagrams are decomposed into a set of master integrals that are then computed using differential equations.