The hadronic contribution to the running of the electromagnetic coupling and electroweak mixing angle

TL;DR

This paper provides a precise theoretical calculation of the hadronic contributions to the running of the electromagnetic coupling and weak mixing angle across a range of energies, crucial for interpreting experimental results and probing new physics.

Contribution

It offers the first comprehensive theoretical determination of the hadronic effects on the running of fundamental couplings in the space-like region with quantified uncertainties.

Findings

Achieved 2% uncertainty at low energies

Achieved 1% uncertainty at higher energies

Results are relevant for current and future precision experiments

Abstract

As present and future experiments, on both the energy and precision frontiers, look to identify new physics beyond the Standard Model, we require more precise determinations of fundamental quantities, like the QED and electroweak couplings at various momenta. These can be obtained either entirely from experimental measurements, or from one such measurement at a particular virtuality combined with the couplings' virtuality dependence computed within the SM. Thus, a precise, entirely theoretical determination of the running couplings is highly desirable, even more since the preliminary results of the E989 experiment in Fermilab were published. We give results for the hadronic contribution to the QED running coupling $\alpha(Q^2)$ and weak mixing angle $\sin^2\theta_W(Q^2)$ in the space-like energy region $(0, 7]~\text{GeV}^2$ with a total relative uncertainty of $2\%$ at energies $Q^2 \ll 1~\text{GeV}^2$, and $1\%$ at $Q^2 > 1~\text{GeV}^2$.