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arXiv · 2511.01623

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·Hartmut Wittig
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Abstract

We present an update of our lattice QCD determination of the hadronic contribution to the running of the electromagnetic coupling, $\Delta\alpha_{\mathrm{had}}^{(5)}(-Q^2)$, and of the electroweak mixing angle in the space-like momentum region up to $Q^2=12\ \mathrm{GeV}^2$. The calculation is based on CLS ensembles with $N_f=2+1$ flavours of $O(a)$-improved Wilson fermions, covering five lattice spacings between $0.039$ and $0.085$ fm and a range of pion masses, including the physical point. A refined analysis employing a telescopic window strategy allows for a clean separation of systematic effects across Euclidean distance scales. Statistical precision is further enhanced through low-mode averaging, combined with a spectral reconstruction of the vector-vector correlator at long distances on the most chiral ensembles. We confirm significant tensions of up to $7\sigma$ at space-like virtualities around $Q^2= 1\ \mathrm{GeV}^2$ between our lattice results for $\Delta\alpha_{\mathrm{had}}^{(5)}(-Q^2)$ and the corresponding data-driven estimates based on $e^+e^-$ cross section data. Combining our lattice data with perturbative QCD via the Euclidean split technique, we obtain at the $Z$-pole $\Delta\alpha_{\mathrm{had}}^{(5)}(M_Z^2) = 0.027813(33)_{\mathrm{lat}}(35)_{\mathrm{pQCD}}$, which is more than two times more precise than recent data-driven estimates. Our result deviates slightly, by $1-2\sigma$, from the value produced by global electroweak fits. For the electroweak mixing angle, we present the hadronic contribution to its running and provide a precise determination of the octet-singlet mixing component $\bar\Pi^{(0,8)}$, in good agreement with phenomenological models but with significantly higher precision.

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Alessandro Conigli, Dalibor Djukanovic, Georg von Hippel, Simon Kuberski, Harvey B. Meyer, Kohtaroh Miura, Konstantin Ottnad, Andreas Risch, Hartmut Wittig. 2025-11-03. Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings. https://doi.org/10.1103/bk78-wtvd

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