Evaluating four-loop conformal Feynman integrals by \(D\)-dimensional differential equations
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Publication:1636356
DOI10.1007/JHEP10(2016)115zbMATH Open1390.81280arXiv1607.06427MaRDI QIDQ1636356
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Publication date: 12 June 2018
Published in: (Search for Journal in Brave)
Abstract: We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.
Full work available at URL: https://arxiv.org/abs/1607.06427
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