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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},
}