electroweakBosons
plain-language theorem explainer
The electroweak sector contains four bosons. Researchers deriving gauge boson spectra from the Recognition Science forcing chain would reference this count when matching Standard Model particle content to the J-cost minimum after symmetry breaking. The definition is a direct numerical assignment of 4, resting on the 8/2 splitting noted in the module comment.
Claim. The electroweak boson count equals 4, corresponding to the W, Z, photon, and Higgs after SU(2)_L × U(1)_Y breaking.
background
The module derives W and Z masses from the Higgs mechanism and weak mixing angle θ_W. Electroweak symmetry breaking occurs when the Higgs field acquires a vacuum expectation value v ≈ 246 GeV, reducing the gauge group to U(1)_EM; this step maps to a J-cost minimum in the Recognition Science setting. The angle satisfies sin²θ_W ≈ 0.231, and the mass relation m_Z = m_W / cos(θ_W) follows from the gauge embedding. The φ-ladder places the electroweak scale at a specific rung, yielding the listed predictions m_W ≈ 80.38 GeV and m_Z ≈ 91.19 GeV.
proof idea
The definition is a direct constant assignment of the natural number 4. The comment records the arithmetic 8/2 = 4 as the justification for the boson count in the electroweak sector.
why it matters
This definition fixes the particle content of the electroweak sector for the mass derivations in the module. It supports the concrete predictions m_W ≈ 80.38 GeV, m_Z ≈ 91.19 GeV, and sin²θ_W ≈ 0.231 that follow from the φ-ladder placement of the VEV. The four-boson count aligns with the gauge structure after symmetry breaking and connects to the T5–T8 forcing steps that determine spatial dimensions and the alpha band.
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