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Rev. Lett."],"accepted":{"date-parts":[[2026,7,1]]},"abstract":"\n We present a high-precision calculation of the hadronic running of electroweak gauge couplings from first principles. Employing lattice QCD in the low-energy regime, we achieve permille precision for virtualities\n \n \n \n \n Q<\/a:mi>\n <\/a:mrow>\n \n 2<\/a:mn>\n <\/a:mrow>\n <\/a:msup>\n \u2272<\/a:mo>\n 12<\/a:mn>\n \u2009<\/a:mtext>\n \u2009<\/a:mtext>\n \n \n GeV<\/a:mi>\n <\/a:mrow>\n \n 2<\/a:mn>\n <\/a:mrow>\n <\/a:msup>\n <\/a:mrow>\n <\/a:math>\n . At\n \n \n \n \n Q<\/c:mi>\n <\/c:mrow>\n \n 2<\/c:mn>\n <\/c:mrow>\n <\/c:msup>\n \u2243<\/c:mo>\n 1<\/c:mn>\n \u2009<\/c:mtext>\n \u2009<\/c:mtext>\n \n \n GeV<\/c:mi>\n <\/c:mrow>\n \n 2<\/c:mn>\n <\/c:mrow>\n <\/c:msup>\n <\/c:mrow>\n <\/c:math>\n , our determination deviates by up to\n \n 7<\/e:mn>\n \u03c3<\/e:mi>\n <\/e:math>\n from estimates based on\n \n \n e<\/g:mi>\n +<\/g:mo>\n <\/g:msup>\n \n e<\/g:mi>\n \u2212<\/g:mo>\n <\/g:msup>\n <\/g:math>\n measurements. Combining lattice QCD with perturbative QCD via the Euclidean split technique, we obtain for the electromagnetic coupling\n \n \n \u0394<\/i:mi>\n \n \n \u03b1<\/i:mi>\n <\/i:mrow>\n \n had<\/i:mi>\n <\/i:mrow>\n \n (<\/i:mo>\n 5<\/i:mn>\n )<\/i:mo>\n <\/i:mrow>\n <\/i:msubsup>\n (<\/i:mo>\n \n \n M<\/i:mi>\n <\/i:mrow>\n \n Z<\/i:mi>\n <\/i:mrow>\n \n 2<\/i:mn>\n <\/i:mrow>\n <\/i:msubsup>\n )<\/i:mo>\n =<\/i:mo>\n 0.027821<\/i:mn>\n (<\/i:mo>\n 34<\/i:mn>\n \n \n )<\/i:mo>\n <\/i:mrow>\n \n lat<\/i:mi>\n <\/i:mrow>\n <\/i:msub>\n (<\/i:mo>\n 35<\/i:mn>\n \n \n )<\/i:mo>\n <\/i:mrow>\n \n pQCD<\/i:mtext>\n <\/i:mrow>\n <\/i:msub>\n <\/i:mrow>\n <\/i:math>\n , which is more than twice as precise as recent phenomenological determinations. We assess improvement scenarios by which the precision target for next-generation electroweak measurements could be reached.\n <\/jats:p>","DOI":"10.1103\/r2cx-tl7s","type":"journal-article","created":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T19:00:41Z","timestamp":1782932441000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Running of the Electroweak Gauge Couplings from First Principles"],"prefix":"10.1103","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3625-5369","authenticated-orcid":true,"given":"Alessandro","family":"Conigli","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/024thra40","id-type":"ROR","asserted-by":"publisher"}],"name":"Helmholtz Institute Mainz"},{"id":[{"id":"https:\/\/ror.org\/02k8cbn47","id-type":"ROR","asserted-by":"publisher"}],"name":"GSI Helmholtz Centre for Heavy Ion 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