couplingRatio
plain-language theorem explainer
The definition supplies the electroweak coupling ratio g'/g as the square root of sin²(θ_W) over one minus sin²(θ_W). Electroweak model builders cite it to connect the observed W and Z masses to the SU(2) × U(1) mixing angle within the Recognition Science framework. It follows immediately from the trigonometric identity tan(θ_W) = sin(θ_W)/cos(θ_W) once sin²(θ_W) is fixed by the mass ratio.
Claim. The coupling ratio g'/g equals $√(s/(1-s))$, where $s = sin²θ_W$ is the electroweak mixing parameter obtained from the W/Z mass ratio.
background
In the Standard Model module the W and Z boson masses satisfy m_W/m_Z = cos(θ_W), with observed ratio near 0.881. The parameter sin²(θ_W) is defined upstream as 1 minus the square of that mass ratio, yielding approximately 0.223. The upstream definition of sin2ThetaW supplies this value directly from the mass ratio. Recognition Science posits that the SU(2) × U(1) gauge structure and the resulting mixing angle are constrained by the golden ratio φ.
proof idea
The definition is a one-line algebraic expression that extracts tan(θ_W) from the supplied sin²(θ_W) value using the identity tan²(θ_W) = sin²(θ_W)/(1 - sin²(θ_W)).
why it matters
This definition completes the translation of the observed mass ratio into the gauge coupling ratio g'/g. It supports the module's target of deriving electroweak parameters from the φ-structure, as noted in the module documentation on φ-quantized gauge structure. The parent relation appears in the W/Z mass ratio derivation, linking to the broader Recognition Science forcing chain where constants emerge from the self-similar fixed point.
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