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Through the extraordinary precision of QED, the SM predicts the energy levels of simple systems such as the hydrogen atom with up to 13\u2009significant digits\n                    <jats:sup>1<\/jats:sup>\n                    , making hydrogen spectroscopy an ideal test bed. The consistency of physical constants extracted from different transitions in hydrogen using QED, such as the proton charge radius\n                    <jats:italic>r<\/jats:italic>\n                    <jats:sub>p<\/jats:sub>\n                    , constitutes a test of the theory. However, values of\n                    <jats:italic>r<\/jats:italic>\n                    <jats:sub>p<\/jats:sub>\n                    from recent measurements\n                    <jats:sup>2\u20137<\/jats:sup>\n                    of atomic hydrogen are partly discrepant with each other and with a more precise value from spectroscopy of muonic hydrogen\n                    <jats:sup>8,9<\/jats:sup>\n                    . This prevents a test of QED at the level of experimental uncertainties. Here we present a measurement of the 2S\u20136P transition in atomic hydrogen with sufficient precision to distinguish between the discrepant values of\n                    <jats:italic>r<\/jats:italic>\n                    <jats:sub>p<\/jats:sub>\n                    and enable rigorous testing of QED and the SM overall. Our result\n                    <jats:italic>\u03bd<\/jats:italic>\n                    <jats:sub>2S\u20136P<\/jats:sub>\n                    \u2009=\u2009730,690,248,610.79(48)\u2009kHz gives a value of\n                    <jats:italic>r<\/jats:italic>\n                    <jats:sub>p<\/jats:sub>\n                    \u2009=\u20090.8406(15)\u2009fm at least 2.5-fold more precise than from other atomic hydrogen determinations and in excellent agreement with the muonic value. The SM prediction of the transition frequency (730,690,248,610.79(23)\u2009kHz) is in excellent agreement with our result, testing the SM to 0.7\u2009parts per trillion (ppt) and, specifically, bound-state QED corrections to 0.5\u2009parts per million (ppm), their most precise test so far.\n                  <\/jats:p>","DOI":"10.1038\/s41586-026-10124-3","type":"journal-article","created":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T16:02:44Z","timestamp":1770825764000},"page":"845-851","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Sub-part-per-trillion test of the Standard Model with atomic hydrogen"],"prefix":"10.1038","volume":"650","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1766-5909","authenticated-orcid":false,"given":"Lothar","family":"Maisenbacher","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2253-7936","authenticated-orcid":false,"given":"Vitaly","family":"Wirthl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9247-8922","authenticated-orcid":false,"given":"Arthur","family":"Matveev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexey","family":"Grinin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6435-659X","authenticated-orcid":false,"given":"Randolf","family":"Pohl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6476-9033","authenticated-orcid":false,"given":"Theodor W.","family":"H\u00e4nsch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9557-5549","authenticated-orcid":false,"given":"Thomas","family":"Udem","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,2,11]]},"reference":[{"key":"10124_CR1","doi-asserted-by":"publisher","first-page":"025002","DOI":"10.1103\/RevModPhys.97.025002","volume":"97","author":"PJ Mohr","year":"2025","unstructured":"Mohr, P. 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