Standard Model of the Electroweak Interaction: Theoretical Developments

Abstract

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 $Ø(G_F^2M_H^2M_W^2)$, $Ø(G_F^2m_t^4)$, $Ø(α_sG_FM_W^2)$, 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 concentrate on $Γ\left(H\to f\bar f\,\right)$ and consider in $Ø(α_sG_Fm_t^2)$ the universal corrections and those which are specific for the $\scriptstyle b\bar b$ mode, as well as $Ø(α_s^2)$ corrections in the $q\bar q$ channels including the finite-$m_q$ terms.