Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings
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We present a high-precision lattice QCD determination of the hadronic vacuum polarization in the Euclidean region, computed on CLS ensembles with improved Wilson fermions. Using an extended set of gauge ensembles, a telescopic window strategy, low-mode averaging, and spectral reconstruction on the lightest ensembles, we achieve sub-percent precision over a broad momentum range. We confirm significant tensions at space-like virtualities between our lattice results and the corresponding data-driven estimates based on $e^+ e^-$ cross section data. Combining our lattice determination with perturbative QCD through the Euclidean splitting technique, we obtain a high-precision estimate of the hadronic contribution to the running of the electromagnetic coupling at the Z pole. We also obtain a high-accuracy determination of the octet–singlet mixing component of the vacuum polarization, consistent with phenomenological expectations but with substantially reduced uncertainties. These results provide valuable input for precision electroweak studies.
