Unitarity constraints on heavy Higgs bosons

We calculate the complete set of O(${\mathrm{G}}_{\mathrm{F}}$ ${\mathrm{M}}_{\mathrm{H}}^2$) corrections to the elastic scattering of longitudinally polarized W bosons in the limit s,${\mathrm{M}}_{\mathrm{H}}^2$≫${\mathrm{M}}_{\mathrm{W}}^2$, for any value of s/${\mathrm{M}}_{\mathrm{H}}^2$. For any Higgs-boson mass such that ${\mathrm{M}}_{\mathrm{H}}$≫${\mathrm{M}}_{\mathrm{W}}$, there exists a critical energy above which partial-wave unitarity is violated and the one-loop correction to the J=0 partial wave is large, indicating the breakdown of perturbation theory.