{"paper":{"title":"Pion masses in 2-flavor QCD with $\\eta$ condensation","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["hep-ph","hep-th","nucl-th"],"primary_cat":"hep-lat","authors_text":"Michael Creutz, Sinya Aoki","submitted_at":"2014-02-08T09:52:02Z","abstract_excerpt":"We investigate some aspects of 2-flavor QCD with $m_u\\not= m_d$ at low-energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at $m_u=0$ for the fixed $m_d\\not=0$, the neutral pion mass becomes zero at two critical values of $m_u$, between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the \"topological susceptibility\" in the ChPT diverges at these two critical points. We briefly discuss a possibility that $m_u=0$ can be defined by the vanishing the \"to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1837","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":""},"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"}