Leading hadronic contributions to the running of the electroweak coupling constants from lattice QCD

TL;DR

This paper presents a lattice QCD calculation of the leading hadronic contributions to the running of the electromagnetic and weak coupling constants, achieving results consistent with phenomenology but with larger systematic uncertainties.

Contribution

It provides the first four-flavor lattice QCD determination of these contributions, highlighting the impact of systematic errors on precision.

Findings

Results agree with phenomenological analyses

Systematic uncertainties dominate the error budget

Lattice QCD can reliably compute electroweak running contributions

Abstract

The quark-connected leading-order hadronic contributions to the running of the electromagnetic fine structure constant, $\alpha_{\rm QED}$, and the weak mixing angle, $\theta_W$, are determined by a four-flavour lattice QCD computation with twisted mass fermions. Full agreement of the results with a phenomenological analysis is observed with an even comparable statistical uncertainty. We show that the uncertainty of the lattice calculation is dominated by systematic effects which then leads to significantly larger errors than obtained by the phenomenological analysis.