KIR-QER-Nezirov - Supplement IV WZ Boson Mass from σc and σ*

This Supplement IV derives the fundamental electroweak mass parameters — the Weinberg angle, the W/Z boson mass ratio, the gauge coupling constant, and the vacuum expectation value of the σ-field — from the two critical points of the dual channel structure established in Supplement III: the dominance transition σc = ½ and the SNR inflection point σ* = ⅓. The derivation is organized in three epistemically distinct stages of increasing rigor, supplemented by an exact relation between the correction factor ξ and the one-loop running of sin²θW, and a stationary solution for the electroweak scale from the nonlinear Κ-potential. Stage 1 (Dimensional Analysis) establishes the characteristic length and energy scales of the channel transition from the nuclear σ-field (rN = 1. 46 fm, Supplement I). At σ = σ*, the characteristic interaction radius is r* = 3rN = 4. 38 fm, corresponding to an energy scale E* ≈ 45 MeV. The hierarchy factor N = mW/E* ≈ 1784 quantifies the known electroweak-nuclear scale separation and locates the hierarchy problem within the KIR framework. Stage 2 (Exact from KIR Axioms) constitutes the core contribution. The Weinberg angle is identified parameter-free with the rate channel weight at the inflection point: sin²θW (tree) = wR (σ*) = σ* = ⅓. The mass ratio follows from the saddle point condition of the channel overlap measure Κ (σ) = σ (1−σ) at σc: mW/mZ (tree) = cos θW = √ (2/3) ≈ 0. 8165. Both relations are necessary consequences of the channel structure and require no free parameters. Stage 3 (Perturbative) introduces a single correction factor ξ = 3·sin²θW (exp) = 0. 6937, which brings all structural predictions into quantitative agreement with experiment: sin²θW (pert) = ξ/3 = 0. 2312 (deviation < 0. 01%), mW/mZ (pert) = √ (1−ξ/3) ≈ 0. 877 (deviation 0. 5%), gW (pert) ≈ 0. 629 (deviation < 0. 1%). The perturbation theory of the nonlinear channel coefficients (Supplement III, Section 8. 6) traces ξ back to the structural formula ξ = 1 + ε·F (a₂, b₃), establishing its origin in the σ-field nonlinearity rather than leaving it as a free fit parameter. Section V establishes the exact relation C = √ξ · √η, where C² = 3·sin²θW (tree) and η = 0. 9304 is the well-known one-loop running rate of sin²θW between Q² = 0 and Q² = mZ². This relation is exact in the limit of vanishing radiative corrections (η → 1) and constitutes a non-trivial consistency check of the framework. Section VI derives the stationary solution for the electroweak vacuum expectation value from the Κ-potential U (σ) = Λ⁴·σ (1−σ). Expanding around the saddle point σc yields a fluctuation field δσ = σ − ½ with negative effective mass squared, establishing the structural analogy to electroweak symmetry breaking. The Higgs mass fixes the energy scale to Λ = mH/√2 ≈ 88. 6 GeV. The correct direct route vₑw = 2mW/gW (pert) ≈ 255 GeV (deviation 3. 7% from the Fermi scale 246. 2 GeV) supersedes a previously erroneous detour via an implicit quartic coupling assumption. The nonlinear correction of the Κ-potential connects the SM quartic coupling λ to resonance damping at the saddle point, with the condition vₑw = 246 GeV fixing ε (a₂ + b₃) ≈ −0. 47, comfortably within the stability bound. The Standard Model requires two independent input parameters (sin²θW and v) for the same electroweak observables. The KIR reduces this to one (ξ), with ξ itself structurally traced to the nonlinear channel coefficients. The absolute mass scale and the individual nonlinear coefficients a₂ and b₃ remain explicitly open as research objectives and are not concealed. KIR-QER-Nezirov: Kinetically Induced Spacetime and Quantum Field Emergence of Reality — Complete Theoretical Framework with Supplements I–V. Zenodo. https: //doi. org/10. 5281/zenodo. 18943890