mH_rs_level2
plain-language theorem explainer
The level-two RS Higgs mass is defined as the vacuum expectation value scaled by the square root of the Weinberg sine squared. Particle physicists using the Recognition Science framework cite this when building the predicted Higgs mass table. The definition consists of a direct algebraic product drawn from the golden-ratio VEV and the RS-derived angle.
Claim. $m_H^{RS,2}=v√(sin²θ_W)$ where $v=φ$ is the vacuum expectation value and $sin²θ_W=(3-φ)/6$ is the RS Weinberg angle.
background
The HiggsRungAssignment module derives the Higgs boson mass from the φ-ladder after electroweak symmetry breaking in the RS framework. The vacuum expectation value is identified with the golden ratio φ. The Weinberg angle correction arises from Q3 symmetry breaking, with sin²θ_W fixed at (3-φ)/6 as supplied by the Q3Representations module. Upstream results establish the VEV as φ in RS units and confirm the algebraic form of the angle from the electroweak breaking definitions.
proof idea
The definition is a one-line wrapper that multiplies the imported vacuum expectation value by the square root of the RS Weinberg angle.
why it matters
This definition is invoked by the HiggsRungCert structure to establish that the predicted mass lies within 5% of the observed 125.2 GeV. It fills the level-2 slot in the rung assignment that closes the Higgs mass hypothesis in the Recognition Science framework. The parent theorem mH_rs_level2_in_range then certifies the numerical interval (110, 125) GeV.
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