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@ARTICLE{Papathanasiou:620219,
author = {Papathanasiou, Georgios and Weinzierl, Stefan and Wu,
Konglong and Zhang, Yang},
title = {{R}ationalisation of multiple square roots in {F}eynman
integrals},
reportid = {PUBDB-2025-00092, arXiv:2501.07490. DESY-25-001.
MITP-25-004. USTC-ICTS/PCFT-24-28},
year = {2025},
note = {26 pages. Prepared for submission to JHEP},
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.},
cin = {T},
cid = {I:(DE-H253)T-20120731},
pnm = {611 - Fundamental Particles and Forces (POF4-611) / DFG
project G:(GEPRIS)390783311 - EXC 2094: ORIGINS: Vom
Ursprung des Universums bis zu den ersten Bausteinen des
Lebens (390783311)},
pid = {G:(DE-HGF)POF4-611 / G:(GEPRIS)390783311},
experiment = {EXP:(DE-MLZ)NOSPEC-20140101},
typ = {PUB:(DE-HGF)25},
eprint = {2501.07490},
howpublished = {arXiv:2501.07490},
archivePrefix = {arXiv},
SLACcitation = {$\%\%CITATION$ = $arXiv:2501.07490;\%\%$},
doi = {10.3204/PUBDB-2025-00092},
url = {https://bib-pubdb1.desy.de/record/620219},
}