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

doi:10.1007/978-3-030-80219-6_5

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

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Abstract

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.

Original language	English
Title of host publication	Anti-Differentiation and the Calculation of Feynman Amplitudes
Number of pages	16
Publisher	Springer
Publication date	10 Jul 2021
Pages	107-123
ISBN (Print)	978-3-030-80218-9
DOIs	https://doi.org/10.1007/978-3-030-80219-6_5
Publication status	Published - 10 Jul 2021

Series	Texts and Monographs in Symbolic Computation
ISSN	0943-853X

Bibliographical note

16 pages, 5 figures, talk given at the workshop "Antidifferentiation and the Calculation of Feynman Amplitudes"

Keywords

hep-th

Access to Document

10.1007/978-3-030-80219-6_5

http://arxiv.org/pdf/2103.15423v1

Cite this

Bourjaily, J. L., He, Y-H., McLeod, A. J., Spradlin, M., Vergu, C., Volk, M., Hippel, M. V., & Wilhelm, M. (2021). Direct Integration for Multi-leg Amplitudes: Tips, Tricks, and When They Fail. In Anti-Differentiation and the Calculation of Feynman Amplitudes (pp. 107-123). Springer. Texts and Monographs in Symbolic Computation https://doi.org/10.1007/978-3-030-80219-6_5

Direct Integration for Multi-leg Amplitudes : Tips, Tricks, and When They Fail. / Bourjaily, Jacob L.; He, Yang-Hui; McLeod, Andrew J.; Spradlin, Marcus; Vergu, Cristian; Volk, Matthias; Hippel, Matt von; Wilhelm, Matthias.

Anti-Differentiation and the Calculation of Feynman Amplitudes. Springer, 2021. p. 107-123 (Texts and Monographs in Symbolic Computation).

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Bourjaily, Jacob L. ; He, Yang-Hui ; McLeod, Andrew J. ; Spradlin, Marcus ; Vergu, Cristian ; Volk, Matthias ; Hippel, Matt von ; Wilhelm, Matthias. / Direct Integration for Multi-leg Amplitudes : Tips, Tricks, and When They Fail. Anti-Differentiation and the Calculation of Feynman Amplitudes. Springer, 2021. pp. 107-123 (Texts and Monographs in Symbolic Computation).

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