Status of Higher-Order Corrections in the Standard Electroweak Theory

We review recent theoretical progress in the computation of radiative corrections beyond one loop within the standard model of electroweak interactions, both in the gauge and Higgs sectors. In the gauge sector, we discuss universal corrections of $Ø(G_F^2M_H^2M_W^2)$, $Ø(G_F^2m_t^4)$, $Ø(α_sG_FM_W^2)$, $Ø(α_s^2G_Fm_t^2)$, and those due to virtual $t\bar t$ threshold effects, as well as specific corrections to $Γ\left(Z\to b\bar b\right)$ of $Ø(G_F^2m_t^4)$, $Ø(α_sG_Fm_t^2)$, and $Ø(α_s^3)$ including finite-$m_b$ effects. We also present an update of the hadronic contributions to $Δα$. Theoretical uncertainties, other than those due to the lack of knowledge of $M_H$ and $m_t$, are estimated. In the Higgs sector, we report on the $Ø(α_sG_Fm_t^2)$ corrections to $Γ\left(H\to f\bar f\,\right)$ including those which are specific for the $b\bar b$ mode, the $Ø(α_s^2)$ corrections to $Γ\left(H\to q\bar q\right)$ including the finite-$m_q$ terms, and the $Ø(α_s)$ corrections to $Γ(H\to gg)$.

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