Spontaneous Symmetry Breaking and the Emergent Einstein-Standard Model: From Weyl x SU (2)L x U (1)Y Gauge Theory to Geometric Mass Generation

Abstract

We construct a Weyl x SU(2)_L x U(1)_Y invariant theory by extending four-dimensional Weyl quadratic gravity with Weyl-invariant scalar, fermion, Yukawa and gauge sectors. The quadratic structure (R^tilde - mu^2 |phi|^2)^2 allows the Weyl Goldstone mode to be extracted via a Stueckelberg mechanism independent of the Higgs field. Spontaneous breaking of Weyl gauge symmetry reduces the Weyl quadratic curvature to the Einstein-Hilbert action with a positive cosmological constant, generates a mass term for the Weyl gauge field, and simultaneously produces the Higgs potential -mu^2 |phi|^2 + lambda^2 |phi|^4, which is otherwise forbidden by the symmetry. Our framework unifies the Stueckelberg, Higgs and Yukawa mechanisms, reproduces Standard Model mass generation, and predicts additional Higgs-induced contributions to the Weyl gauge field mass, together with a set of Higgs-Weyl couplings. These interactions provide new phenomenological handles, including a vector dark matter candidate, and highlight the geometric origin of mass.