The hadronic running of the electromagnetic coupling and electroweak mixing angle

TL;DR

This paper reports lattice QCD calculations of the hadronic contributions to the running of the electromagnetic coupling and weak mixing angle, revealing a notable tension with R-ratio estimates in certain momentum ranges.

Contribution

First lattice QCD study using two discretisations to compute hadronic vacuum polarisation functions for electroweak parameters with detailed extrapolation to the physical point.

Findings

Observed up to 3.5 sigma tension with R-ratio estimates for certain momenta.

Provided lattice-based estimates for the hadronic contributions at the Z boson mass scale.

Assessed implications for global electroweak fits.

Abstract

We present results for the hadronic running of the electromagnetic coupling and the weak mixing angle from simulations of lattice QCD with $N_f=2+1$ flavours of $O(a)$-improved Wilson fermions. Using two different discretisations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarisation (HVP) functions $\bar{\Pi}^{\gamma\gamma}$ and $\bar{\Pi}^{Z\gamma}$ for spacelike squared momenta $Q^2\leq 7$ $\mathrm{GeV}^2$. Our results are extrapolated to the physical point using ensembles at four lattice spacings, with pion masses ranging from 130 to 420 MeV. We observe a tension of up to 3.5 standard deviations between our lattice results for $\Delta\alpha_{\rm had}^{(5)}(-Q^2)$ and estimates based on the $\textit{R}$-ratio for space-like momenta in the range $Q^2=3-7\,\rm GeV^2$. To obtain an estimate for $\Delta\alpha_\mathrm{had}^{(5)}(M_Z^2)$, we employ the Euclidean split technique. The implications for comparison with global electroweak fits are assessed.