Multiple soft-photon emission at next-to-leading power to all orders

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.

39 pages, 1 figure, published version

References in corpus (22)

• Automation of next-to-leading order computations in QCD: the FKS subtraction
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• Path integral approach to eikonal and next-to-eikonal exponentiation
• A new approach to evaluate the leading hadronic corrections to the muon g-2
• Two-loop QED corrections to Bhabha scattering
• Three-Loop Chromomagnetic Interaction in HQET
• Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions
• QED at NNLO with McMule
• The QCD form factor of heavy quarks at NNLO
• Massive vector form factors to three loops
• Muon-electron scattering at NNLO: the hadronic corrections
• On the Subleading-Soft Behaviour of QCD Amplitudes
• Muon-electron scattering at NNLO
• Bhabha scattering at NNLO with next-to-soft stabilisation
• Status of the MUonE experiment
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• The LBK theorem to all orders
• Massive three-loop form factors: anomaly contribution
• Single ${\pi }^0$ production in $\mu e$ scattering at MUonE
• Dark Photons and Displaced Vertices at the MUonE Experiment
• Lepton pair production at NNLO in QED with EW effects
• Subleading Effects in Soft-Gluon Emission at One-Loop in Massless QCD

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• Subleading Effects in Soft-Gluon Emission at One-Loop in Massive QCD