Three loop QCD corrections to electroweak radiative parameters

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 𝒪⁡(𝛼⁢𝛼2 𝑠) corrections to the electroweak radiative parameters Δρ, Δr and Δκ. We improve the accuracy of the calculation at this perturbative order, compared to the existing literature, by the systematic inclusion of the three-loop light-quark contributions, and by using deeper series expansions in the evaluation of some Feynman integrals. We 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 ̅̅̅̅̅̅̅̅̅ MS electric charge at 𝑞2=𝑚2 𝑍 with the inclusion of these 𝒪⁡(𝛼⁢𝛼2 𝑠) corrections.