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

Hai Tao Li1,*, Yan-Qing Ma2,3,†, Cheng-Tai Tan2,‡, Jian Wang1,3,§, and Hong-Fei Zhang4,∥

  • *Contact author: haitao.li@sdu.edu.cn
  • †Contact author: yqma@pku.edu.cn
  • ‡Contact author: chengtaitan@stu.pku.edu.cn
  • §Contact author: j.wang@sdu.edu.cn
  • ∥Contact author: hfzhang@mail.gufe.edu.cn
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Phys. Rev. Lett. 136, 021802 – Published 13 January, 2026

DOI: https://doi.org/10.1103/k2mk-mffq

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 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, which explains the rapid convergence 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.

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Phys. Rev. Lett. 136, 021802– Published 13 January, 2026
  • Received 20 November 2025
  • Accepted 23 December 2025
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