Three loop QCD corrections to electroweak radiative parameters

TL;DR

This paper calculates three-loop QCD corrections to electroweak parameters, refining theoretical predictions for the W boson mass and electric charge at the Z boson scale, with implications for future precision measurements.

Contribution

It provides the first detailed three-loop QCD correction calculations for electroweak parameters, enhancing the accuracy of theoretical predictions in particle physics.

Findings

Shift in W boson mass prediction significant for FCC precision goals.

Improved prediction of the MS-bar electric charge at the Z boson mass scale.

Enhanced theoretical precision at the three-loop order in QCD corrections.

Abstract

We reevaluate the vacuum polarization functions for electroweak gauge bosons at three loops in QCD, employing state-of-the-art perturbative techniques. We apply these results to determine the ${\mathcal{O}}(\alpha \alpha_s^2)$ corrections to the electroweak radiative parameters $\Delta\rho$, $\Delta r$ and $\Delta \kappa$. We improve the accuracy of the calculation at this perturbative order, compared to the existing literature, and present some phenomenological implications of these results. We find a shift in the prediction of the $W$ boson mass, significant in view of the FCC precision targets. We improve the prediction of the $\overline{\mathrm{MS}}$ electric charge at $q^2=m_Z^2$ with the inclusion of these ${\mathcal{O}}(\alpha \alpha_s^2)$ corrections.