Zeeman-like effect in a spontaneous symmetry-breaking scheme

Abstract

Starting with an interacting theory comprising an Abelian 1-form and four real scalar fields, we closely investigate the standard mass-generation mechanism. We show that the outputs strongly rely on the rigid symmetry group of the interacting potential for the scalar fields, as follows. Initially, by considering of an interacting potential that is S O (4)-invariant and applying the standard mass-generation mechanism, we get a physical massive one-form and three physical scalar fields, among which only one is massive. Repeating the same procedure, but for a potential that is invariant only under S O (2) × S O (2), we obtain the same physical field spectrum, namely, a massive one-form and three massive scalar fields, but among which at least two display the same mass. Finally, by taking into account a potential that is manifestly S O (2)-invariant, we exhibit a Zeeman-like effect in the mass-spectrum of the physical scalar fields, i.e., all the three masses corresponding to the scalar degrees of freedom are distinct.