Two-loop O(${\mathit{G}}_{\mathit{F}}^2$${\mathit{M}}_{\mathit{H}}^4$) corrections to the fermionic decay rates of the Higgs boson

We calculate the dominant O(${\mathit{G}}_{\mathit{F}}^2$ ${\mathit{M}}_{\mathit{H}}^4$) two-loop electroweak corrections to the fermionic 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 ${\mathit{w}}^{\pm }$ 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 ${\mathit{M}}_{\mathit{H}}$>1114 GeV, and increase in relative magnitude as ${\mathit{M}}_{\mathit{H}}^2$ for larger values of ${\mathit{M}}_{\mathit{H}}$. We conclude that the perturbation expansion in powers of ${\mathit{G}}_{\mathit{F}}$ ${\mathit{M}}_{\mathit{H}}^2$ breaks down for ${\mathit{M}}_{\mathit{H}}$≊1100 GeV. We discuss briefly the QCD and the complete one-loop electroweak corrections to H→bb¯,tt¯, 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.