Aspects of the spontaneous symmetry breaking in a S U(2) × U(1)-gauge model involving six real scalar fields

Abstract

Starting with an interacting SU(2) × U(1)-gauge model comprising four 1-forms and six real scalar fields, we closely investigate the standard mass-generation mechanism. Assuming that the scalar fields transform under an irreducible and orthogonal representation of the gauge group, we show that the outputs strongly rely on the choice of the vacuum expectation values for the scalar fields, as follows. Initially, by choosing a vacuum expectation configuration with a single non-vanishing component and applying the standard mass-generation mechanism we get a physical field spectrum consisting in three massive 1-forms, a massless 1-form and three real scalar fields, among which only one is massive. Repeating the same procedure, but for a vacuum expectation configuration with two different non-vanishing components, we exhibit a physical field spectrum consisting in four massive 1-forms with distinct masses and two real scalar fields, among which only one is massive. Finally, by considering a vacuum expectation configuration with two equal non-vanishing components, the same mechanism displays three massive 1-forms, among which two with the same mass, a massless 1-form and three physical scalar fields, among which only one is massive.