{"paper":{"title":"Hadronic vacuum polarization in hydrogen-like atoms and ions amid the interplay of recoil and finite-size effects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ex","hep-ph","nucl-th"],"primary_cat":"physics.atom-ph","authors_text":"Bogdan Malaescu, Franziska Hagelstein, Vadim Lensky, Vladimir Pascalutsa","submitted_at":"2026-07-08T17:14:41Z","abstract_excerpt":"Hadronic vacuum polarization (hVP) enters simple atomic systems at a level that is small yet decisive for the precision spectroscopy now underway. We evaluate the hVP contributions to the Lamb shift and the hyperfine splitting (HFS) in ordinary and muonic hydrogen (H and $\\mu$H) and hydrogen-like helium-3 ions ($^3$He$^+$ and $\\mu^3$He$^+$), using the dispersive data-driven approach and state-of-the-art empirical parametrizations of the $R$ ratio. At the centre of the analysis is the interplay of recoil and finite-size effects: the recoil corrections that dominate the HFS in muonium (Mu), wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07658","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/2607.07658/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"}