Effects of multiple Higgs bosons on tree unitarity

The abundance of new Higgs bosons in many extensions of the electroweak theory motivate an investigation of their effect on partial-wave scattering amplitudes. For SU(2)×U(1), tree unitarity is shown to be valid for $W$ and $Z$ amplitudes provided three quartic couplings from the Higgs potential are small ($\left|f\right|<\mathrm{}16\mathrm{}\pi$). The mass spectrum of the Higgs boson is almost unconstrained but for the simple requirement that at least one neutral scalar must have a mass $M<\mathrm{}1\mathrm{}$ TeV. Similar results are obtained in a general broken guage theory for the scattering of arbitrary combinations of scalar and vector bosons.