Strongly Interacting Higgs Sector in the Minimal Standard Model?

The triviality Higgs mass bound is studied with a higher derivative regulator in the spontaneously broken phase of the four dimensional O(4) symmetric scalar field theory with quartic self-interaction. The phase diagram of the O(4) model is determined in a Monte Carlo simulation which interpolates between the hypercubic lattice regulator and the higher derivative regulator in continuum space-time. The same method can be used to calculate the Higgs mass bound in continuum space-time. In a large-N analysis, when compared with a hypercubic lattice, we find a relative increase in the triviality bound of the higher derivative regulator suggesting a strongly interacting Higgs sector in the TeV region with negligible dependence on regulator parameters. When the higher derivative regulator mass is brought close to the Higgs mass the model requires a more elaborate analysis of complex ghost states in scattering amplitudes. Part Two of Extended UCSD-PTH 92-40