The hadronic running of the electroweak couplings from lattice QCD

TL;DR

This paper computes the hadronic vacuum polarization contribution to the running of electroweak couplings using lattice QCD, providing results that are consistent with traditional methods and relevant for precision tests of the Standard Model.

Contribution

It presents a non-perturbative lattice QCD calculation of the hadronic contribution to electroweak coupling running up to 7 GeV^2, offering an alternative to R-ratio estimates.

Findings

Observed a 3.5 sigma tension with R-ratio estimates in 3-7 GeV^2 range.

Result at the Z pole, Δα_had^(5)(M_Z^2)=0.02773(15), agrees with R-ratio based results.

Demonstrated the utility of lattice QCD for precision electroweak calculations.

Abstract

The energy dependency (running) of the strength of electromagnetic interactions $\alpha$ plays an important role in precision tests of the Standard Model. 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 Beyond Standard Model 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.