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 $\O(G_F^2M_H^2M_W^2)$, $\O(G_F^2m_t^4)$, $\O(\alpha_sG_FM_W^2)$, and those due to virtual $t\bar t$ threshold effects, as well as specific corrections to $\Gamma\left(Z\to b\bar b\right)$ of $\O(G_F^2m_t^4)$, $\O(\alpha_sG_Fm_t^2)$, and $\O(\alpha_s^3)$ including finite-$m_b$ effects. We also present an update of the hadronic contributions to $\Delta\alpha$. 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 $\Gamma\left(H\to f\bar f\,\right)$ and consider in $\O(\alpha_sG_Fm_t^2)$ the universal corrections and those which are specific for the $\scriptstyle b\bar b$ mode, as well as $\O(\alpha_s^2)$ corrections in the $q\bar q$ channels including the finite-$m_q$ terms.