IndisputableMonolith.Physics.GaugeBosonMassesFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Gauge Boson Masses from RS — A1 SM Depth
   6
   7m_Z/m_W = 6/(3+φ), sin²θ_W = (3-φ)/6.
   8
   9Lean status: 0 sorry, 0 axiom.
  10-/
  11
  12namespace IndisputableMonolith.Physics.GaugeBosonMassesFromRS
  13open Constants
  14
  15noncomputable def massRatio : ℝ := 6 / (3 + phi)
  16
  17theorem massRatio_pos : 0 < massRatio :=
  18  div_pos (by norm_num) (by linarith [phi_gt_onePointSixOne])
  19
  20theorem massRatio_gt_one : massRatio > 1 := by
  21  unfold massRatio
  22  have h1 := phi_gt_onePointSixOne
  23  have h2 := phi_lt_onePointSixTwo
  24  have hd : (0:ℝ) < 3 + phi := by linarith
  25  rw [gt_iff_lt, lt_div_iff₀ hd]
  26  -- Need 3+φ < 6, i.e., φ < 3
  27  linarith
  28
  29noncomputable def sin2thetaW_RS : ℝ := (3 - phi) / 6
  30
  31theorem sin2thetaW_pos : 0 < sin2thetaW_RS := by
  32  unfold sin2thetaW_RS
  33  apply div_pos _ (by norm_num)
  34  linarith [phi_lt_onePointSixTwo]
  35
  36theorem sin2thetaW_band :
  37    (0.228 : ℝ) < sin2thetaW_RS ∧ sin2thetaW_RS < 0.232 := by
  38  unfold sin2thetaW_RS
  39  have h1 := phi_gt_onePointSixOne
  40  have h2 := phi_lt_onePointSixTwo
  41  constructor
  42  · have : (3 - phi) / 6 > (3 - 1.62) / 6 := by
  43      apply div_lt_div_of_pos_right _ (by norm_num)
  44      linarith
  45    linarith
  46  · have : (3 - phi) / 6 < (3 - 1.61) / 6 := by
  47      apply div_lt_div_of_pos_right _ (by norm_num)
  48      linarith
  49    linarith
  50
  51structure GaugeBosonMassCert where
  52  ratio_pos : 0 < massRatio
  53  ratio_gt_one : massRatio > 1
  54  sin2theta_band : (0.228 : ℝ) < sin2thetaW_RS ∧ sin2thetaW_RS < 0.232
  55
  56noncomputable def gaugeBosonMassCert : GaugeBosonMassCert where
  57  ratio_pos := massRatio_pos
  58  ratio_gt_one := massRatio_gt_one
  59  sin2theta_band := sin2thetaW_band
  60
  61end IndisputableMonolith.Physics.GaugeBosonMassesFromRS
  62