Preprint

PUBDB-2025-00092

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Rationalisation of multiple square roots in Feynman integrals

Papathanasiou, G.DESY* ; Weinzierl, S. (Corresponding author) ; Wu, K.Extern* ; Zhang, Y.

2025

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Please use a persistent id in citations: doi:10.3204/PUBDB-2025-00092

Report No.: DESY-25-001; MITP-25-004; USTC-ICTS/PCFT-24-28; arXiv:2501.07490

Abstract: Feynman integrals are very often computed from their differential equations. It is not uncommon that the $\varepsilon$-factorised differential equation contains only dlog-forms with algebraic arguments, where the algebraic part is given by (multiple) square roots. It is well-known that if all square roots are simultaneously rationalisable, the Feynman integrals can be expressed in terms of multiple polylogarithms. This is a sufficient, but not a necessary criterium. In this paper we investigate weaker requirements. We discuss under which conditions we may use different rationalisations in different parts of the calculation. In particular we show that we may use different rationalisations if they correspond to different parameterisations of the same integration path. We present a non-trivial example -- the one-loop pentagon function with three adjacent massive external legs involving seven square roots -- where this technique can be used to express the result in terms of multiple polylogarithms.

Note: 26 pages. Prepared for submission to JHEP

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. DFG project G:(GEPRIS)390783311 - EXC 2094: ORIGINS: Vom Ursprung des Universums bis zu den ersten Bausteinen des Lebens (390783311) (390783311)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2025

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