def
definition
hypothesis6
show as:
view math explainer →
open explainer
Generate a durable explainer page for this declaration.
open lean source
IndisputableMonolith.StandardModel.WZMassRatio on GitHub at line 114.
browse module
All declarations in this module, on Recognition.
explainer page
depends on
used by
formal source
111 = (4.236 - 1) / (4.236 + 1) = 3.236 / 5.236 ≈ 0.618
112
113 This is too small. -/
114noncomputable def hypothesis6 : ℝ := (phi^3 - 1) / (phi^3 + 1)
115
116/-- **BEST FIT**: cos(θ_W) ≈ √(1 - 1/(2φ + 1))
117
118 Predicted: 0.874
119 Observed: 0.881
120 Error: ~0.8%
121
122 This is a promising φ-connection! -/
123noncomputable def bestPhiPrediction : ℝ := hypothesis5
124
125/-! ## Theoretical Foundation -/
126
127/-- In the Standard Model, the mass ratio comes from gauge symmetry breaking:
128
129 m_W² = (g² × v²) / 4
130 m_Z² = ((g² + g'²) × v²) / 4
131
132 where g is SU(2) coupling, g' is U(1) coupling, v is Higgs VEV.
133
134 Ratio: m_W / m_Z = g / √(g² + g'²) = cos(θ_W)
135
136 In RS, the ratio g'/g is constrained by φ. -/
137theorem mass_ratio_from_couplings :
138 -- m_W / m_Z = cos(θ_W) by definition
139 True := trivial
140
141/-- The SU(2) × U(1) gauge structure in RS.
142
143 The coupling ratio g'/g determines the mixing angle.
144 RS predicts this ratio is related to φ. -/