Four-Loop QCD Corrections to the Electroweak<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi></mml:math>Parameter

Abstract

The four-loop QCD corrections to the electroweak rho parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing "nonsinglet" 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. The 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 are thus stabilized.