{"paper":{"title":"Singularity-free Next-to-leading Order $\\Delta S= 1$ Renormalization Group Evolution and $\\epsilon_{K}^{\\prime}/\\epsilon_{K}$ in the Standard Model and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ex"],"primary_cat":"hep-ph","authors_text":"Paul Tremper, Teppei Kitahara, Ulrich Nierste","submitted_at":"2016-07-22T16:29:27Z","abstract_excerpt":"The standard analytic solution of the renormalization group (RG) evolution for the $\\Delta S = 1$ Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of $\\epsilon_K^{\\prime}$, the measure of direct $CP$ violation in $K\\to \\pi\\pi$ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio $\\epsilon_{K}^{\\prime}/\\epsilon_{K}$ (with $\\epsilon_{K}$ quantifyi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06727","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}