{"paper":{"title":"QCD Corrections to QED Vacuum Polarization","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"J. Dias de Deus, P. Castelo Ferreira","submitted_at":"2007-07-27T23:57:01Z","abstract_excerpt":"We compute QCD corrections to QED calculations for vacuum polarization in background magnetic fields. Formally, the diagram for virtual $e\\bar{e}$ loops is identical to the one for virtual $q\\bar{q}$ loops. However due to confinement, or to the growth of $\\alpha_s$ as $p^2$ decreases, a direct calculation of the diagram is not allowed. At large $p^2$ we consider the virtual $q\\bar{q}$ diagram, in the intermediate region we discuss the role of the contribution of quark condensates $\\left< q\\bar{q}\\right>$ and at the low-energy limit we consider the $\\pi^0$, as well as charged pion $\\pi^+\\pi^-$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.4200","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"}