Paper I W and Z Boson Masses as Integer Harmonics of the Neutral Pion: Statistical Analysis and Electroweak Implication

Paper I in the Harmonic Structure of the Standard Model series.

We report that the W and Z boson masses, expressed in units of the neutral pion
mass (mπ⁰ = 134.9768 MeV, PDG 2025), yield near-integer approximations mW/mπ⁰
= 595.43 ≈ 595 (deviation 0.072%) and mZ/mπ⁰ = 675.58 ≈ 675 (deviation
0.086%). The reduced ratio 595/675 = 119/135 reproduces the on-shell Weinberg
angle: sin²θW = 1−(119/135)² = 0.22299, vs the measured on-shell value 0.22290 ±
0.00030 — agreement within 0.30σ. We note that 595×mπ = 80,311 MeV sits 58
MeV (4.4σ) below the PDG world average of 80,369.2 ± 13.3 MeV; we report this as
tension and not agreement. The on-shell scheme is the appropriate comparison for a
tree-level prediction; the gap to MS-bar (0.23122) is precisely what one-loop
radiative corrections are expected to close. A Monte Carlo analysis of 20,000
simulated particle spectra, using 17 pre-specified candidate bases, confirms the joint
proximity is not coincidental (p < 8×10⁻⁴, Bonferroni-corrected). A companion
neutrino mass prediction Σmᵢ = 59.46 meV is testable by Euclid DR1 in June 2026.

Updated: Section 2.3 added — uniqueness analysis demonstrating the neutral pion is the sole QCD-scale particle for which both W/m and Z/m are near-integer and the implied Weinberg angle agrees with PDG 2025 measurement. All other candidates (kaon, rho, omega, eta, proton) fail by 2.6σ or more.