Four-Loop QCD Corrections to the Rho Parameter

TL;DR

The four-loop QCD corrections to the electroweak rho parameter arising from top and bottom quark loops are computed and the missing "nonsinglet" piece is evaluated, and the predictions for the shift of the weak mixing angle and the W-boson mass are stabilized.

Abstract

The four-loop QCD corrections to the electroweak $ρ$-parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing ``non-singlet'' piece. Using algebraic methods the amplitude is reduced to a set of around 50 new master integrals which are calculated with various analytical and numerical methods. Inclusion of the newly completed term halves the final value of the four-loop correction for the minimally renormalized top-quark mass. The predictions for the shift of the weak mixing angle and the W-boson mass is thus stabilized.