Abstract
This paper derives a next-to-leading power (NLP) soft theorem for multi-photon emission to all orders in the electromagnetic coupling constant, generalising the leading-power theorem of Yennie, Frautschi, and Suura. Working in the QED version of heavy-quark effective theory, multi-emission amplitudes are shown to reduce to single- and double-radiation contributions only. Single soft-photon emission, in turn, is described by the recent all-order extension of the Low-Burnett-Kroll theorem, where the tree-level formula is supplemented with a one-loop exact soft function. The same approach is used in this article to prove that the genuine double-emission contribution is tree-level exact. As a validation and a first non-trivial application of the multi-photon theorem, the real-real-virtual electron-line corrections to muon-electron scattering are calculated at NLP in the soft limit.
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Acknowledgments
I thank Mathieu Pellen, Marco Rocco, Maximilian Stahlhofen, and Yannick Ulrich for the careful reading of the manuscript as well as valuable suggestions for improvement. I was supported by the German Federal Ministry for Education and Research (BMBF) under contract no. 05H21VFCAA.
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Engel, T. Multiple soft-photon emission at next-to-leading power to all orders. J. High Energ. Phys. 2024, 4 (2024). https://doi.org/10.1007/JHEP03(2024)004
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DOI: https://doi.org/10.1007/JHEP03(2024)004