`w_pred`

definition

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module: IndisputableMonolith.Masses.ElectroweakMasses
domain: Masses
line: 121 · github
papers citing: none yet

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IndisputableMonolith.Masses.ElectroweakMasses on GitHub at line 121.

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formal source

 118
 119m_W = m_Z × cos(θ_W) where cos²(θ_W) = (3+φ)/6 -/
 120
 121noncomputable def w_pred : ℝ := z_pred * cos_theta_W_rs
 122
 123/-- The W/Z mass ratio equals cos(θ_W) by construction. -/
 124theorem wz_ratio_eq_cos : w_pred / z_pred = cos_theta_W_rs := by
 125  unfold w_pred
 126  have hzne : z_pred ≠ 0 := ne_of_gt (by linarith [z_mass_bounds.1])
 127  exact mul_div_cancel_left₀ _ hzne
 128
 129/-! ## Summary -/
 130
 131/-- Electroweak verification certificate. -/
 132structure EWCert where
 133  z_in_range : (91075.09 : ℝ) < z_pred ∧ z_pred < 91075.10
 134  z_error : |z_pred - m_Z_exp| / m_Z_exp < 0.0013
 135  wz_is_cos : w_pred / z_pred = cos_theta_W_rs
 136
 137theorem ew_cert_exists : Nonempty EWCert :=
 138  ⟨{ z_in_range := z_mass_bounds
 139     z_error := z_relative_error
 140     wz_is_cos := wz_ratio_eq_cos }⟩
 141
 142end
 143
 144end IndisputableMonolith.Masses.ElectroweakMasses

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