Abstract
The soft theorem states that scattering amplitude in gauge theory with a soft gauge-boson emission can be factorized into a hard scattering amplitude and a soft factor. In this paper, we present calculations of the soft factor for processes involving two hard colored partons, up to three loops in QCD. To accomplish this, we developed a systematic method for recursively calculating relevant Feynman integrals using the Feynman-Parameter representation. Our results constitute an important ingredient for the subtraction of infrared singularities at N4LO in perturbative QCD. Using the principle of leading transcendentality between QCD and \( \mathcal{N} \) = 4 super Yang-Mills theory, we determine the soft factor in the latter case to three loops with full-color dependence. As a by-product, we also obtain the finite constant \( {f}_2^{(3)} \) in the Bern-Dixon-Smirnov ansatz analytically, which was previously known numerically only.
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Acknowledgments
W.C. and H.X.Z. were supported by National Natural Science Foundation of China under contract No. 11975200. M.X.L. was supported by National Natural Science Foundation of China under contract No. U2230402. T.Z.Y. would like to acknowledge the European Research Council (ERC) for funding this work under the European Union’s Horizon 2020 research and innovation programme grant agreement 101019620 (ERC Advanced Grant TOPUP). H.X.Z. would also like to express gratitude to the Erwin-Schrödinger Institute for Mathematical Physics for their hospitality during the program “Quantum Field Theory at the Frontiers of the Strong Interaction”, where part of this work was completed. We would like to thank Lance J. Dixon for useful discussions.
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Chen, W., Luo, Mx., Yang, TZ. et al. Soft theorem to three loops in QCD and \( \mathcal{N} \) = 4 super Yang-Mills theory. J. High Energ. Phys. 2024, 131 (2024). https://doi.org/10.1007/JHEP01(2024)131
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DOI: https://doi.org/10.1007/JHEP01(2024)131