{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:04:45Z","timestamp":1760234685274,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T00:00:00Z","timestamp":1622419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in e+e\u2212 collisions. An improvement in the precision of calculations of the Standard Model (SM) electroweak pseudo-observables, such as scattering asymmetries, effective weak mixing angles, and decay widths, related to the Z-boson will meet severe experimental requirements at the planned e+e\u2212 colliders and will increase the chance to detect non-standard effects in experimental analysis. To reach this goal, one has to calculate the next order of perturbative SM theory, namely three-loop Feynman integrals. We discuss the complexity of the problem, as well as the methods crucial for completing three-loop calculations. We show several numerical solutions for some three-loop Feynman integrals using sector decomposition, Mellin\u2013Barnes (MB), and differential equation methods.<\/jats:p>","DOI":"10.3390\/sym13060975","type":"journal-article","created":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T21:42:06Z","timestamp":1622497326000},"page":"975","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Toward Three-Loop Feynman Massive Diagram Calculations"],"prefix":"10.3390","volume":"13","author":[{"given":"Ievgen","family":"Dubovyk","sequence":"first","affiliation":[{"name":"Institute of Physics, University of Silesia, 40-007 Katowice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3542-2786","authenticated-orcid":false,"given":"Johann","family":"Usovitsch","sequence":"additional","affiliation":[{"name":"PRISMA Cluster of Excellence, Institut f\u00fcr Physik, Johannes Gutenberg-Universit\u00e4t Mainz, D-55099 Mainz, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7228-4768","authenticated-orcid":false,"given":"Krzysztof","family":"Grzanka","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Silesia, 40-007 Katowice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,31]]},"reference":[{"key":"ref_1","unstructured":"Electroweak, The SLD, Heavy Flavour Groups, ALEPH Collaboration, DELPHI Collaboration, L3 Collaboration, OPAL Collaboration, SLD Collaboration, LEP Electroweak Working Group, and The SLD Electroweak (2006). 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