New perturbative upper bound on M_H from fermionic Higgs decays at two loops

Abstract

We present the dominant two-loop ${\rm O}\left(G_F^2M_H^4\right)$ electroweak corrections to the fermi\-onic decay widths of a high-mass Higgs boson in the Standard Model. The corrections are negative and quite significant, and are larger in magnitude than the one-loop electroweak corrections for $M_H\gsim 400\ {\rm GeV}$. This indicates the onset of a breakdown of perturbation theory in the Higgs sector of the Standard Model at this surprisingly low value of the Higgs-boson mass.