Weak interactions at very high energies: The role of the Higgs-boson mass

We give an $S$-matrix-theoretic demonstration that if the Higgs-boson mass exceeds ${M}_{c}={(8\ensuremath{\pi}\frac{\sqrt{2}}{3}{G}_{F})}^{\frac{1}{2}}$, parital-wave unitarity is not respected by the tree diagrams for two-body scattering of gauge bosons, and the weak interactions must become strong at high energies. We exhibit the relation of this bound to the structure of the Higgs-Goldstone Lagrangian, and speculate on the consequences of strongly coupled Higgs-Goldstone systems. Prospects for the observation of massive Higgs scalars are noted.