Abstract

We present an ab-initio electroweak normalization in which the gauge factors gL, gZ, the neutral mixing angle θW, and the electromagnetic coupling e are fixed by a single coherent background. A quadratic expansion of the pre-geometric action about the self-dual background two-form Σ produces a background stiffness τ (ρ0); projecting the induced Yang–Mills block onto SU(2)L and the Cartan U(1)Z  with fixed projector weights (ωL, ωZ ) yields, in component-canonical trace, 1/g2L = ωL/τ (ρ0) and 1/g2Z = 1/τ (ρ0) (ωZ = 1). The photon direction from the neutral kinetic block then fixes e without external normalization, and α(μ) = e2(μ)/(4π) follows. With these ab-initio boundary conditions at the condensation scale Λq, we evolve the couplings to MZ (and to 0) using a two-loop EFT renormalization group with threshold matching. We report α−1(MZ), α−1(0), and sin2θW (MZ) with internal theory bands; the hadronic vacuum-polarization input entering α(0) is quoted separately. The construction assumes a single neutral U (1) with optional U(1) – U(1) kinetic mixing (handled by canonicalization), mass-matched Abelian matching at Λq , and the validity of the coherent domain below Λq . No electroweak fit inputs are used in setting gL, gZ, θW, or e.

Keywords: ab initio electroweak normalization, electroweak mixing origin, emergent electroweak symmetry, composite stiffness parameters, pre-geometric background, coherence field / scalar coherence,  Weinberg angle from first principles, derivation of the fine-structure constant,  geometric origin of U(1)EM,  canonical SU(2)L× U(1)Z reduction, neutral boson mixing from scalar alignment, nonperturbative electroweak boundary conditions, gauge unification without GUTs, emergent gauge fields, pre-metric field theory, projection geometry, coherently-induced symmetry breaking, non-Abelian to Abelian reduction,  electroweak boson stiffness,  fine-structure constant (α) prediction,  Weinberg angle constraint, axis-model electroweak sector,  scalar-filtered gauge projections,  geometric gauge mixing,  UV boundary condition from coherence