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Among all the known forces that contribute, the limited understanding of the strong nuclear force is a key source of inaccuracy. At the fundamental level, the strong force is described by quantum chromodynamics, the theory of quarks and gluons. Their coupling,\n                    <jats:italic>\u03b1<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    , becomes weaker at high energies (asymptotic freedom), enabling power series expansions in\n                    <jats:italic>\u03b1<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    , but the confinement of quarks in hadronic bound states usually requires additional model assumptions. Consequently, determinations of\n                    <jats:italic>\u03b1<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    from experiment mostly remain with large systematic theory errors\n                    <jats:sup>1,2<\/jats:sup>\n                    . Here we report the model-free determination of\n                    <jats:italic>\u03b1<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    with unprecedented precision from low-energy experimental input combined with large-scale numerical simulations of the first-principles formulation of quantum chromodynamics on a space\u2013time lattice. The uncertainty, about half that of all other results combined\n                    <jats:sup>3<\/jats:sup>\n                    , originates predominantly from the statistical Monte Carlo evaluation and has a clear probabilistic interpretation. The result for\n                    <jats:italic>\u03b1<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    describes both low-energy hadronic physics with the help of lattice quantum chromodynamics and high-energy scattering using the perturbative expansion. By removing a source of theoretical uncertainty, our estimate of\n                    <jats:italic>\u03b1<\/jats:italic>\n                    <jats:sub>s<\/jats:sub>\n                    could enable markedly improved analyses of many high-energy experiments\n                    <jats:sup>4<\/jats:sup>\n                    . This will contribute to the likelihood that small effects of yet unknown physics are uncovered, as well as enable stringent precision tests of the Standard Model.\n                  <\/jats:p>","DOI":"10.1038\/s41586-026-10339-4","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T15:03:19Z","timestamp":1775660599000},"page":"328-334","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["High-precision calculation of the quark\u2013gluon coupling from lattice QCD"],"prefix":"10.1038","volume":"652","author":[{"given":"Mattia","family":"Dalla Brida","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roman","family":"H\u00f6llwieser","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9564-0769","authenticated-orcid":false,"given":"Francesco","family":"Knechtli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tomasz","family":"Korzec","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1654-1816","authenticated-orcid":false,"given":"Alberto","family":"Ramos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7007-2980","authenticated-orcid":false,"given":"Stefan","family":"Sint","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rainer","family":"Sommer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,8]]},"reference":[{"key":"10339_CR1","unstructured":"Altarelli, G. 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