Compton Scattering Total Cross Section at Next-to-Next-to-Leading Order and Resummation of Leading Logarithms

TL;DR

This paper presents a high-precision calculation of Compton scattering cross sections at NNLO in QED, including resummation of leading logarithms, enhancing theoretical predictions for high-energy experiments.

Contribution

First full NNLO calculation of Compton scattering cross section with electron mass dependence and all-order resummation of leading logarithms.

Findings

NNLO correction is numerically small due to a suppressing prefactor.

Resummation yields a compact expression involving a modified Bessel function.

Higher-order contributions are negligible because of a double factorial suppression.

Abstract

Compton scattering is a fundamental process in QED with broad applications, yet its theoretical description at high energies is challenged by substantial next-to-leading order (NLO) corrections arising from double-logarithmic enhancements. To address this, we report the first calculation of the next-to-next-to-leading order (NNLO) total cross section with full electron mass dependence. Our analysis reveals that the NNLO correction, albeit still containing double logarithms, is numerically small due to a suppressing prefactor. By identifying the origin of these logarithms in a kinematic regime featuring a Glauber electron exchange, we successfully resum the leading logarithmic series to all orders, obtaining a compact result in terms of a modified Bessel function. The all-order structure reveals a suppression mechanism, with double factorial terms in the denominator, which explains the negligible nature of higher-order contributions. The combination of our NNLO calculation and all-orders resummation delivers a reliable and precise prediction, poised to serve the needs of high-precision experiments in the foreseeable future.