  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
