Effect of thett¯threshold on electroweak parameters

Threshold effects in $e^{+}{e}^{-}\to t\overline{t}$ induce contributions to key electroweak parameters such as $\Delta \rho$, $\Delta r$, and ${{sin}^2\theta }_W$ beyond the scope of perturbative calculations of $O\left(\alpha \right)$ and $O\left(\alpha {\alpha }_s\right)$. We quantitatively analyze these effects using once-subtracted dispersion relations which manifestly satisfy relevant Ward identities. The derivation and properties of the dispersion relations are discussed at some length. We find that the threshold effects enhance the familiar perturbative $O\left(\alpha {\alpha }_s\right)$ corrections by between 25% and 40%, depending on the $t$-quark mass. The shift in the predicted value of the $W$-boson mass due to the threshold effects ranges from -8 MeV at $m_t=91\mathrm{} \mathrm{GeV}\mathrm{to} -45\mathrm{} \mathrm{MeV}$ at $m_t=250\mathrm{}$ GeV.