{"paper":{"title":"Lattice determination of the pion mass difference $M_{\\pi^{+}} - M_{\\pi^{0}}$ at order $\\mathcal{O}(\\alpha_{em})$ and $\\mathcal{O}( (m_{d}-m_{u})^{2})$ including disconnected diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-lat","authors_text":"F. Sanfilippo, G. Gagliardi, G. Martinelli, R. Frezzotti, S. Simula, V. Lubicz","submitted_at":"2021-12-02T09:16:44Z","abstract_excerpt":"We present our preliminary results concerning the charged/neutral pion mass difference $M_{\\pi^{+}} - M_{\\pi^{0}}$ at order $\\mathcal{O}(\\alpha_{em})$ in the QED interactions, and for $M_{\\pi^{+}} - M_{\\pi^{0}}$ at order $\\mathcal{O}\\left( (m_{d}-m_{u})^{2}\\right)$ in the strong isospin-breaking term. The latter contribution provides a determination of the $\\rm{SU}(2)$ chiral perturbation theory low-energy constant $\\ell_{7}$, whose present estimate is affected by a rather large uncertainty. The disconnected contributions appearing in the diagrammatic expansion of $M_{\\pi^{+}} - M_{\\pi^{0}}$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.01066","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/2112.01066/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"}