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Running of the Electroweak Gauge Couplings from First Principles

Alessandro Conigli1,2,*, Dalibor Djukanovic1,2, Georg von Hippel3, Simon Kuberski4, Harvey B. Meyer1,3,4, Kohtaroh Miura5, Konstantin Ottnad3,†, Andreas Risch6, and Hartmut Wittig1,2,3

  • *Contact author: aconigli@uni-mainz.de
  • †Present address: Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany.
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Phys. Rev. Lett. 137, 071901 – Published 13 August, 2026

DOI: https://doi.org/10.1103/r2cx-tl7s

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 Q2≲12  GeV2. At Q2≃1  GeV2, our determination deviates by up to 7σ from estimates based on e+e− measurements. Combining lattice QCD with perturbative QCD via the Euclidean split technique, we obtain for the electromagnetic coupling Δαhad(5)(MZ2)=0.027821(34)lat(35)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.

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Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings

Alessandro Conigli, Dalibor Djukanovic, Georg von Hippel, Simon Kuberski, Harvey B. Meyer, Kohtaroh Miura, Konstantin Ottnad, Andreas Risch, and Hartmut Wittig
Phys. Rev. D 114, 034508 (2026)

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Outline

Information

Phys. Rev. Lett. 137, 071901– Published 13 August, 2026
  • Received 14 January 2026
  • Revised 11 April 2026
  • Accepted 1 July 2026
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