Running of the Electroweak Gauge Couplings from First Principles

Abstract

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 $Q^2\lesssim 12{\mathrm{GeV}}^2$. At $Q^2\simeq 1{\mathrm{GeV}}^2$, our determination deviates by up to $7\sigma$ from estimates based on $e^{+}{e}^{-}$ measurements. Combining lattice QCD with perturbative QCD via the Euclidean split technique, we obtain for the electromagnetic coupling $\Delta {\alpha }_{\mathrm{had}}^{(5)}(M_Z^2)=0.027821(34{)}_{\mathrm{lat}}(35{)}_{\mathrm{pQCD}}$, 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.

Comments: Updated to match the published version in Physical Review Letters. Bibliographic information and supplemental-material link updated. Published with companion PRD arXiv:2511.01623