Two-Loop ${\cal O}(\alpha_sG_Fm_t^2)$ Corrections to Higgs Production at LEP

Abstract

We evaluate the two-loop ${\cal O}(\alpha_sG_Fm_t^2)$ correction to the $ZZH$ coupling in the Standard Model by means of a low-energy theorem, assuming that the top quark is much heavier than the Higgs boson. We then construct a heavy-top-quark effective Lagrangian for the $ZZH$ interaction that accommodates the ${\cal O}(G_Fm_t^2)$ and ${\cal O}(\alpha_sG_Fm_t^2)$ corrections and derive from it the corresponding corrections to the $H\to ZZ$ decay as well as those to Higgs-boson production at LEP1, via $Z\to f\bar fH$, and at LEP2, via $e^+e^-\to ZH$. In all cases, the leading ${\cal O}(G_Fm_t^2)$ terms are considerably screened by their QCD corrections, if the on-shell renormalization scheme with $G_F$ as a basic parameter is employed.