Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
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Publication:1707748
DOI10.1007/JHEP12(2017)090zbMATH Open1383.81321arXiv1704.07931OpenAlexW2608389474WikidataQ56226577 ScholiaQ56226577MaRDI QIDQ1707748
Author name not available (Why is that?)
Publication date: 3 April 2018
Published in: (Search for Journal in Brave)
Abstract: We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the dimensional regulator are multiple polylogarithms (MPLs). Our main result is the conjecture that this diagrammatic coaction reproduces the combinatorics of the coaction on MPLs order by order in the Laurent expansion. We show that our conjecture holds in a broad range of nontrivial one-loop integrals. We then explore its consequences for the study of discontinuities of Feynman integrals, and the differential equations that they satisfy. In particular, using the diagrammatic coaction along with information from cuts, we explicitly derive differential equations for any one-loop Feynman integral. We also explain how to construct the symbol of any one-loop Feynman integral recursively. Finally, we show that our diagrammatic coaction follows, in the special case of one-loop integrals, from a more general coaction proposed recently, which is constructed by pairing master integrands with corresponding master contours.
Full work available at URL: https://arxiv.org/abs/1704.07931
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