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Two-measure approach to breaking scale-invariance in a standard-model extension. (English) Zbl 1369.81116

Summary: 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 à la Dirac, that includes the Higgs doublet and a singlet \(\sigma\)-field required for implementing global scale-invariance. We introduce a mechanism for ‘spontaneous breaking’ of scale-invariance by introducing a coupling of the \(\sigma\)-field to a new metric-independent measure \(\Phi\) defined in terms of four scalars \(\phi^i\) \((i = 1, 2, 3, 4)\). 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 \(G_{\mathrm N}\) 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.

MSC:

81V22 Unified quantum theories
81R40 Symmetry breaking in quantum theory

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