Singlet-particle extension of the minimal Higgs sector.

Abstract

Assuming that the Higgs scalar is heavier than 1 TeV, low-energy physics may still be described effectively by the standard model in the large-Higgs-mass limit. It has been shown that the heavy-Higgs theory is not unique but it depends on the way the limit is taken. We study this arbitrariness in terms of an extended Higgs sector. A new scalar singlet particle, the U, is coupled to the Higgs sector of the standard model, for the purpose of parametrizing the large-Higgs-mass behaviour of the theory. Two extended models arise, depending on whether the U particle develops a vacuum expectation value or not. The new radiative corrections to low-energy parameters first appear at the one-loop and two-loop levels, respectively. The U particle effects upon the $\rho$ parameter and the gauge boson mass shifts are computed. Emphasis is given to the limit where the U particle becomes as heavy as the Higgs. The new contributions demonstrate the ambiguous behaviour but they fail to restore the uniqueness of the theory in the limit. The model where U develops a vacuum expectation value is also investigated at energies higher than the vector boson mass scale. We compute the leading radiative corrections to the longitudinal vector boson scattering amplitude in the limit of high energy and even higher scalar masses. We assume a small difference between the masses of the scalars, within 10% of the lower scalar mass. Within the framework of partial wave analysis, the leading terms to the $\beta$ parameter are derived. We find a small but positive enhancement to the standard model contributions. The overall result indicates that no resonance will appear in the isospin I = 1 channel at any energy above the 1 TeV threshold.