Two-measure approach to breaking scale-invariance in a standard-model extension

Abstract

Abstract We introduce Weyl's scale-invariance as an additional global symmetry in the standard model of electroweak interactions. A natural consequence is the introduction of general relativity coupled to scalar fields a la Dirac, that includes the Higgs doublet and a singlet σ-field required for implementing global scale-invariance. We introduce a mechanism for ‘spontaneous breaking’ of scale-invariance by introducing a coupling of the σ-field to a new metric-independent measure Φ defined in terms of four scalars ϕ i ( i = 1 , 2 , 3 , 4 ) . Global scale-invariance is regained by combining it with internal diffeomorphism of these four scalars. We show that once the global scale-invariance is broken, the phenomenon (a) generates Newton's gravitational constant G N and (b) triggers spontaneous symmetry breaking in the normal manner resulting in masses for the conventional fermions and bosons. In the absence of fine-tuning the scale at which the scale-symmetry breaks can be of order Planck mass. If right-handed neutrinos are also introduced, their absence at present energy scales is attributed to their mass terms tied to the scale where scale-invariance breaks.