The hadronic running of the electroweak couplings from lattice QCD

International audienceThe energy dependency (running) of the strength of electromagnetic interactions $\alpha$ plays an important role in precision tests of the SM. The running of the former to the $Z$ pole is an input quantity for global electroweak fits, while the running of the mixing angle is susceptible to the effects of BSM physics, particularly at low energies. We present a computation of the hadronic vacuum polarization (HVP) contribution to the running of these electroweak couplings at the non-perturbative level in lattice QCD, in the space-like regime up to $Q^2$ momentum transfers of $7\,\mathrm{GeV}^2$. This quantity is also closely related to the HVP contribution to the muon $g-2$. We observe a tension of up to $3.5$ standard deviation between our lattice results for $\Delta\alpha^{(5)}_{\mathrm{had}}(-Q^2)$ and estimates based on the $R$-ratio for $Q^2$ in the $3$ to $7\,\mathrm{GeV}^2$ range. The tension is, however, strongly diminished when translating our result to the $Z$ pole, by employing the Euclidean split technique and perturbative QCD, which yields $\Delta\alpha^{(5)}_{\mathrm{had}}(M_Z^2)=0.027\,73(15)$. This value agrees with results based on the $R$-ratio within the quoted uncertainties, and can be used as an alternative to the latter in global electroweak fits