{"paper":{"title":"Recoil corrections to $\\mu$H hyperfine splitting","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The full theory of muonic hydrogen hyperfine splitting, with direct recoil and QED corrections and proton structure taken from ordinary hydrogen, yields 182626(5) μeV for the ground state.","cross_cats":[],"primary_cat":"physics.atom-ph","authors_text":"Andrzej Maro\\'n, Krzysztof Pachucki, Mateusz Pa\\'ntak","submitted_at":"2026-04-08T10:43:04Z","abstract_excerpt":"This work attempts to present a complete theory of the $\\mu$H hyperfine splitting, including all contributions above 1 ppm. Quantum electrodynamic and recoil corrections are calculated directly, while the proton structure correction is obtained with the help of the H hyperfine splitting. The resulting theoretical prediction for the ground state of $\\mu$H is $E_\\mathrm{hfs} = 182\\,626(5)$ $\\mu$eV."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting theoretical prediction for the ground state of μH is E_hfs = 182626(5) μeV.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The proton structure correction extracted from ordinary hydrogen hyperfine splitting can be applied to muonic hydrogen with only the quoted 5 μeV uncertainty and without additional model-dependent errors from the different reduced-mass and wave-function regimes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The ground-state hyperfine splitting in muonic hydrogen is predicted as 182626(5) μeV after including all contributions above 1 ppm.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The full theory of muonic hydrogen hyperfine splitting, with direct recoil and QED corrections and proton structure taken from ordinary hydrogen, yields 182626(5) μeV for the ground state.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f8a174925949b3d0aebcdc7bd8a31451be49b317b4d882d7b0256ca1dd6d2d15"},"source":{"id":"2604.06930","kind":"arxiv","version":2},"verdict":{"id":"334167fa-79c3-4129-8091-b73ce747a298","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:53:20.255436Z","strongest_claim":"The resulting theoretical prediction for the ground state of μH is E_hfs = 182626(5) μeV.","one_line_summary":"The ground-state hyperfine splitting in muonic hydrogen is predicted as 182626(5) μeV after including all contributions above 1 ppm.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The proton structure correction extracted from ordinary hydrogen hyperfine splitting can be applied to muonic hydrogen with only the quoted 5 μeV uncertainty and without additional model-dependent errors from the different reduced-mass and wave-function regimes.","pith_extraction_headline":"The full theory of muonic hydrogen hyperfine splitting, with direct recoil and QED corrections and proton structure taken from ordinary hydrogen, yields 182626(5) μeV for the ground state."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.06930/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":2,"snapshot_sha256":"17b5e0f32cb3bf405b9a1ee98a25e95c972948debbc4c20906ddb3a8e2b4b5f7"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}