# Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case

@article{Abreu2017DiagrammaticHA,
title={Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case},
author={Samuel Abreu and Ruth Britto and Claude Duhr and Einan Gardi},
journal={Journal of High Energy Physics},
year={2017},
volume={2017},
pages={1-74}
}
• Published 25 April 2017
• Mathematics
• Journal of High Energy Physics
A bstractWe 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…

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