Abstract
Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar n-gon Feynman integral in n dimensions, for even n, with massless or massive internal and external edges. Furthermore, we evaluate the general six-dimensional hexagon integral in terms of classical polylogarithms.
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Acknowledgments
We are grateful to Jacopo Chen for pointing out an extra factor of 1/2, to Oliver Schlotterer for discussions on the single-valued map, and to Daniil Rudenko for encouraging comments. This work was supported in part by the U.S. Department of Energy under contract DESC0010010 (Task F) and by Simons Investigator Award #376208. CV was supported in part by grant 00025445 from Villum Fonden.
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Ren, L., Spradlin, M., Vergu, C. et al. One-loop integrals from volumes of orthoschemes. J. High Energ. Phys. 2024, 104 (2024). https://doi.org/10.1007/JHEP05(2024)104
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DOI: https://doi.org/10.1007/JHEP05(2024)104