Three loop QCD corrections to electroweak radiative parameters

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 $\mathcal{O}(\hat{I}\pm \hat{I}{\pm }_s^2)$ corrections to the electroweak radiative parameters $\hat{I}”\ddot{I}$, $\hat{I}”r$ and $\hat{I}”\hat{I}º$. 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 $\mathcal{O}(\hat{I}\pm \hat{I}{\pm }_s^2)$ corrections.

9 pages, 3 figures;