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def

wolfenstein_rho

definition
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module
IndisputableMonolith.StandardModel.CKMMatrix
domain
StandardModel
line
60 · github
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IndisputableMonolith.StandardModel.CKMMatrix on GitHub at line 60.

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  57noncomputable def wolfenstein_A : ℝ := 0.82
  58
  59/-- The Wolfenstein parameter ρ ≈ 0.14. -/
  60noncomputable def wolfenstein_rho : ℝ := 0.14
  61
  62/-- The Wolfenstein parameter η ≈ 0.35 (CP violation phase). -/
  63noncomputable def wolfenstein_eta : ℝ := 0.35
  64
  65/-! ## The Wolfenstein Parametrization -/
  66
  67/-- The CKM matrix in Wolfenstein parametrization (to O(λ³)):
  68
  69     ⎛ 1 - λ²/2      λ           Aλ³(ρ - iη) ⎞
  70V =  ⎜   -λ        1 - λ²/2         Aλ²       ⎟
  71     ⎝ Aλ³(1-ρ-iη)   -Aλ²            1         ⎠
  72-/
  73noncomputable def V_ud : ℂ := 1 - wolfenstein_lambda^2 / 2
  74noncomputable def V_us : ℂ := wolfenstein_lambda
  75noncomputable def V_ub : ℂ := wolfenstein_A * wolfenstein_lambda^3 *
  76  (wolfenstein_rho - I * wolfenstein_eta)
  77noncomputable def V_cd : ℂ := -wolfenstein_lambda
  78noncomputable def V_cs : ℂ := 1 - wolfenstein_lambda^2 / 2
  79noncomputable def V_cb : ℂ := wolfenstein_A * wolfenstein_lambda^2
  80noncomputable def V_td : ℂ := wolfenstein_A * wolfenstein_lambda^3 *
  81  (1 - wolfenstein_rho - I * wolfenstein_eta)
  82noncomputable def V_ts : ℂ := -wolfenstein_A * wolfenstein_lambda^2
  83noncomputable def V_tb : ℂ := 1
  84
  85/-! ## φ-Connection Hypotheses -/
  86
  87/-- Hypothesis 1: λ = sin(θ_c) = 1/(2φ)
  88
  89    1/(2 × 1.618) = 1/3.236 = 0.309
  90