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One-loop Integrals from Volumes of Orthoschemes
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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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Cited by 2 Pith papers
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Recursive construction of scalar one-loop integrals in dimensional regularisation
A recursion based on hyperbolic simplex volumes expresses every epsilon-expansion coefficient of scalar one-loop Feynman integrals in terms of multiple polylogarithms.
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