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In quantum chromodynamics, the calculation of correlation functions for purely space-like momenta has reached a high level of sophistication, but the calculation at time-like momenta requires refined methods. One of them is the contour deformation method. Here we describe how to employ it for three-point functions. The basic mechanisms are discussed for a scalar theory, but they are the same for more complicated theories and are thus relevant, e.g., for the three-gluon or quark-gluon vertices of quantum chromodynamics. Their inclusion in existing truncation schemes is a crucial step for investigating the analytic structure of elementary correlation functions of quantum chromodynamics and the calculation of its spectrum from them.<\/jats:p>","DOI":"10.3390\/sym15020414","type":"journal-article","created":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T05:31:24Z","timestamp":1675402284000},"page":"414","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["How to Determine the Branch Points of Correlation Functions in Euclidean Space II: Three-Point Functions"],"prefix":"10.3390","volume":"15","author":[{"given":"Markus Q.","family":"Huber","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik, Justus-Liebig-Universit\u00e4t Giessen, 35392 Giessen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5080-382X","authenticated-orcid":false,"given":"Wolfgang J.","family":"Kern","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Graz, NAWI Graz, Universit\u00e4tsplatz 5, 8010 Graz, Austria"},{"name":"Institute of Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstra\u00dfe 36, 8010 Graz, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Reinhard","family":"Alkofer","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Graz, NAWI Graz, Universit\u00e4tsplatz 5, 8010 Graz, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ppnp.2014.02.001","article-title":"Explanation and Prediction of Observables using Continuum Strong QCD","volume":"77","author":"Cloet","year":"2014","journal-title":"Prog. 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