{"paper":{"title":"Analytic Form of the QCD Instanton Determinant for Small Quark Mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Choonkyu Lee, Hyunsoo Min, Jin Hur","submitted_at":"2009-09-30T06:16:34Z","abstract_excerpt":"We use a novel method to calculate analytically the QCD instanton prefactor due to a quark field carrying a small mass parameter $m$. In the SU(2) instanton background of size $\\rho$, the spinor effective action $\\Gamma^F$ (in the minimal subtraction scheme), which gives rise to the prefactor $\\exp (-\\Gamma^F)$, is shown to have the small-$m \\rho$ behavior\n  \\Gamma^F = -\\ln (m /\\mu) - \\ln (\\mu\\rho)/3 -2 \\alpha(1/2) -(m \\rho)^2 \\{\\ln (m \\rho /2) +\\gamma+1/2\\} -2 (m \\rho)^4 \\{-\\ln ^2(m \\rho)/4+\\ln (m \\rho) (1/2-\\gamma +\\ln 2)/2+C \\} +O((m \\rho)^6), where $\\gamma=0.577216...$, $\\alpha(1/2)=0.1458"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5515","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"}