Strongly interacting Higgs bosons

The sensitivity of present-energy weak interactions to a strongly interacting heavy-Higgs-boson sector is discussed. The gauged nonlinear $\ensuremath{\sigma}$ model, which is the limit of the linear model as the Higgs-boson mass goes to infinity, is used to organize and catalogue all possible heavy-Higgs-boson effects. As long as the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}$ symmetry of the Higgs sector is preserved, these effects are found to be small, of the order of the square of the gauge coupling times logarithms (but not powers) of the Higgs-boson mass divided by the $W$ mass. We work in the context of a simplified model with gauge group $\mathrm{SU}{(2)}_{L}$; the extension to $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ is briefly discussed.