Properties, Generations and Masses

Abstract

Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles very naturally. In contrast to the standard model, where masses arise through independent Yukawa couplings to a single Higgs isodoublet, property models produce Higgs fields in various multiplet denominations, but contain a single Yukawa coupling. A renormalizable superHiggs potential of quartic order then produces very strongly constrained masses for generations of fields, which depend on just three constants. By allowing for a small parameter, which is meant to characterise the quantum loop effects for the effective potential, one can obtain nonzero masses for the engendered masses. We illustrate the phenomenon for two and three complex coordinates; the more realistic case of five complex coordinates is not yet fully treatable because of its complexity.