Abstract
We point out that the gauge-invariance of the subleading Lagrangian of soft-collinear effective theory is realised in an intricate way through momentum-conservation violating contributions. Although these terms are disregarded in diagrammatic calculations, the gauge invariance of any physical transition amplitude is preserved due to the soft equations of motion. When not working with gauge-invariant building blocks, individual manifestly gauge-invariant constituent terms in the Lagrangian may give rise to gauge-dependent matrix elements starting at \( \mathcal{O} \)(λ2). Implications for a gauge-invariant definition of radiative jet functions are discussed.
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Acknowledgments
We thank Martin Beneke, Thorsten Feldmann, Matthias Neubert, and Robert Szafron for inspiring discussions, Thorsten Feldmann and Robert Szafron for valuable comments on the manuscript, and Martin Beneke for comments which triggered this project, careful reading of the manuscript, and helpful feedback on the article. This work has been supported by the Cluster of Excellence Precision Physics, Fundamental Interactions, and Structure of Matter (PRISMA+ EXC 2118/1) funded by the German Research Foundation (DFG) within the German Excellence Strategy (Project ID 39083149), and has received funding from the European Research Council (ERC) under the European Union’s Horizon 2022 Research and Innovation Programme (Grant agreement No.101097780, EFT4jets).
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Böer, P., Hager, P. On the gauge-invariance of SCET beyond leading power. J. High Energ. Phys. 2023, 197 (2023). https://doi.org/10.1007/JHEP08(2023)197
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DOI: https://doi.org/10.1007/JHEP08(2023)197