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The vacuum polarization functions $\Pi(q^2)$ of charged and neutral gaugebosons which arise from top and bottom quark loops lead to important shifts inrelations between electroweak parameters which can be measured withever-increasing precision. The large mass of the top quark allows approximationof these functions through the first two terms of an expansion in$M_Z^2/M_t^2$. The first three terms of the Taylor series of $\Pi(q^2)$ areevaluated analytically up to order $\as^2$. The first two are required toderive the approximation, the third can be used to demonstrate the smallness ofthe neglected terms. The paper improves earlier results based on the leadingterm $\propto G_F M_t^2 \as^2$. Results for the subleading contributions to$\dr$ and the effective mixing angle $\sineff$ are presented.

physical review letters

QCD Corrections from the Top Quark to Relations between Electroweak Parameters up to Order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>

QCD Corrections from the Top Quark to Relations between Electroweak Parameters up to Orderαs2