Physics Wzboson Ratio Score Card

The W and Z mass ratio

The W and Z bosons are the particles that carry the weak nuclear force, the interaction responsible for radioactive beta decay. Their masses are fundamental constants of the Standard Model of particle physics. The most precise measurements, compiled by the Particle Data Group (PDG), give m_W = 80.377 GeV and m_Z = 91.1876 GeV. The ratio m_W/m_Z is a key quantity because it determines the weak mixing angle, a parameter that quantifies how the weak force mixes with the electromagnetic force.

In Recognition Science, the framework models physical constants as consequences of a single forcing chain. The module P2-WZ takes the measured PDG mass pair as its input and proves two algebraic bounds. First, it proves that m_W/m_Z lies strictly between 0.87 and 0.89. Second, it proves that the weak mixing angle, defined as sin²θ_W = 1 - (m_W/m_Z)², lies strictly between 0.22 and 0.23. These are not approximations; they are exact interval certificates derived from the given mass values.

The module is a data-interface certificate, not a derivation of the masses themselves. It checks that the measured masses are consistent with the framework's expectations. The RS-specific formula for the weak mixing angle, sin²θ_W = (3 - φ)/6 where φ is the golden ratio, is proved in a separate module. This score card only validates the ratio bracket from the PDG inputs.

What this establishes in plain language is a consistency check. The framework's predicted relationship between the W and Z masses is compatible with the best experimental measurements. The proof is machine-checked, with no unproven axioms, and the falsifier is explicit: if a future PDG measurement shifts m_W or m_Z so that their ratio falls outside (0.87, 0.89), the certificate would need updating.

theorem row_WZ_ratio_bracket : massRatio > 0.87 ∧ massRatio < 0.89 := mass_ratio_value

theorem row_sin2_from_WZ_masses : sin2ThetaW > 0.22 ∧ sin2ThetaW < 0.23 := sin2_theta_w_value

What this page does not claim

This module does not derive the W and Z masses from first principles. This module does not prove the RS-specific formula for the weak mixing angle. The interval (0.87, 0.89) is not a prediction of a specific value, only a consistency bound.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Physics/WZBosonRatioScoreCard.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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