{"paper":{"title":"Exact results for $Z_m^{\\rm OS}$ and $Z_2^{\\rm OS}$ with two mass scales and up to three loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Kay Sch\\\"onwald, Matteo Fael, Matthias Steinhauser","submitted_at":"2020-08-03T18:00:24Z","abstract_excerpt":"We consider the on-shell mass and wave function renormalization constants $Z_m^{\\rm OS}$ and $Z_2^{\\rm OS}$ up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters $\\sqrt{1-\\tau^2}$ and $\\sqrt{1-\\tau^2}/\\tau$ which extends the findings from Ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order ${\\cal O}(\\epsilon^2)$ and ${\\cal O}(\\epsilon)$ at two- and three-loop order which are crucial ingrediants for a future four-loop calculati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01102","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.01102/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}