z_w_ratio
plain-language theorem explainer
The definition supplies the ratio of Z boson mass to W boson mass in GeV. Electroweak physicists cite the quantity when testing the tree-level relation m_Z = m_W / cos θ_W against data near 1.135. It is realized as a direct division of the two fixed numerical constants supplied by the same module.
Claim. Define the ratio $r = m_Z / m_W$, where $m_Z$ denotes the Z-boson mass and $m_W$ the W-boson mass, both in GeV.
background
The module derives W and Z masses from electroweak symmetry breaking in the Recognition Science setting. The Higgs vacuum expectation value at approximately 246 GeV corresponds to a J-cost minimum and sits at a definite rung on the phi-ladder; the weak mixing angle arises from the geometric embedding of the gauge groups, producing the exact tree-level relation m_Z = m_W / cos θ_W. Upstream definitions fix the numerical inputs m_W = 80.3692 GeV and m_Z = 91.1876 GeV.
proof idea
The definition is a one-line wrapper that performs the division of the Z-boson mass constant by the W-boson mass constant.
why it matters
The ratio feeds the downstream approximation theorem that bounds its deviation from 1.135 by 0.01, confirming consistency with the predicted cos θ_W ≈ 0.882. It anchors the electroweak unification scale inside the module and aligns with the phi-ladder placement of the vacuum expectation value together with the eight-tick octave structure of the underlying forcing chain.
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