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May 1, 20260 citationsOpen Access

Topological Determination of W and Z Boson Masses, the Weinberg Angle, and Charged-Lepton Mass Ratios

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ANAlexander Nachtigall

Key Points

  • The study aims to predict the masses of W and Z bosons and charged-lepton ratios without traditional electroweak constants.
  • Utilized an information-theoretic framework based on CP^n cascades.
  • Mapped dimensionless mass ratios to physical masses using the Higgs vacuum expectation value.
  • Derived predictions without conventional electroweak fit constants.
  • Predicted W boson mass ratio matches empirical value (0.32636 vs PDG 0.32636, +0.002%).
  • Predicted Z boson mass ratio aligns closely with empirical value (0.37066 vs PDG 0.37035, +0.08%).
  • Predicted Weinberg angle sin^2 theta_W is consistent with experimental results (0.2247 vs PDG 0.22337, +0.6%).

Abstract

We present an information-theoretic account of electroweak and charged-lepton mass scales in which the relevant observables are first predicted as dimensionless ratios on a CPⁿ cascade. A single empirical GeV anchor (the Higgs vacuum expectation value v = 246. 22 GeV) then maps these ratios onto physical masses; no electroweak fit constants (GF, alpha (MZ), sin² thetaW) are used as inputs. The framework predicts: mW⁰ / v = 31 / (alpha^-1 ln 2) = 0. 32636 (PDG 0. 32636, +0. 002%) ; mZ / v = lambda₂ (T) / Tr (T) = 0. 37066 (PDG 0. 37035, +0. 08%) ; sin² thetaW = 0. 2247 (PDG 0. 22337, +0. 6%) ; mₘu/mₑ = 206. 748 (PDG 206. 7683, -0. 010%) ; mₜau/mₑ = 3476. 796 (PDG 3477. 23, -0. 013%). The capacitive integer core alpha^-1core = |11+4i|² = 137 and the dipole trace 109 + 137 = 246 are Born projections of the Higgs dipole; the procedural decimals delta = 0. 036 arise from a cosine-square fixed point at the CP⁴ exchanger. The same dressed phase delta governs the Z-mass eigenvalue of the asymmetric semantic tensor, the leading-order Weinberg angle, and the muon and tau mass corrections. A readout-induced uplift mW¹ = mW⁰ (1 + 4 alpha / 31) = 80. 433 GeV coincides with the CDF II result (80. 4335 +- 0. 0094 GeV) to 0. 07 sigma, while the current ATLAS, CMS, and LHCb measurements remain much closer to the floor mW⁰. The paper's main claim is therefore a joint topological determination of W floor, W readout uplift, Z eigenvalue, sin² thetaW, and charged-lepton ratios from a single dipole trace and a single dressed phase. Not peer reviewed. Prepared with the assistance of artificial intelligence.

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Cite This Study

Alexander Nachtigall (2026) studied this question.

synapsesocial.com/papers/69f44223967e944ac5565e2ahttps://doi.org/10.5281/zenodo.19817994
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