Two-loop $\mathrm{O}\left(G_F^2{M}_H^4\right)$ corrections to the fermionic decay rates of the Higgs boson

Abstract

We calculate the dominant $\mathrm{O}\left(G_F^2{M}_H^4\right)$ two-loop electroweak corrections to the fermi\-onic decay widths of a heavy Higgs boson in the Standard Model. Use of the Goldstone-boson equivalence theorem reduces the problem to one involving only the physical Higgs boson $H$ and the Goldstone bosons $w^{\pm }$ and $z$ of the unbroken theory. The two-loop corrections are opposite in sign to the one-loop electroweak corrections, exceed the one-loop corrections in magnitude for $M_H>1114\mathrm{GeV}$, and increase in relative magnitude as $M_H^2$ for larger values of $M_H$. We conclude that the perturbation expansion in powers of $G_F{M}_H^2$ breaks down for $M_H\approx 1100\mathrm{GeV}$. We discuss briefly the QCD and the complete one-loop electroweak corrections to $H\to b\bar{b},t\bar{t}$, and comment on the validity of the equivalence theorem. Finally we note how a very heavy Higgs boson could be described in a phenomenological manner.

Comments: 24 pages, RevTeX file, 4 figures in a separate compressed uuencoded Postscript file or available by mail on request. Fig. 1 not included see Figs. 1, 2 in Phys. Rev. D 48, 1061 (1993)