### Speaker

### Description

The energy dependency (running) of the strength of electromagnetic interactions $\alpha$ and of the mixing with weak interactions $\sin^2\theta_{\mathrm{W}}$ 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 in alternative to the latter in global electroweak fits.

Moreover, the ability to perform an exact flavor decomposition allows us to present the most precise determination to date of the $\mathrm{SU}(3)$-flavor-suppressed HVP function that enters the running of $\sin^2\theta_{\mathrm{W}}$.

In-person participation | Yes |
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