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Direct Integration for Multi-leg Amplitudes: Tips, Tricks, and When They Fail

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arxiv 2103.15423 v1 pith:Z5MBXO3K submitted 2021-03-29 hep-th

Direct Integration for Multi-leg Amplitudes: Tips, Tricks, and When They Fail

Jacob L. Bourjaily , Yang-Hui He , Andrew J. McLeod , Marcus Spradlin , Cristian Vergu , Matthias Volk , Matt von Hippel , Matthias Wilhelm This is my paper
classification hep-th
keywords integrationdiagramsdirectmethodobstructionalgebraicalternativeamplitudes
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors in which this method, employed with some care, can compute diagrams of up to eight particles and four loops. We also highlight situations in which this method fails due to an algebraic obstruction. In a large number of cases the obstruction can be associated with a Calabi-Yau manifold.

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    Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.