m_c_predicted

formal source

  65
  66/-- The two-loop running prediction of m_c at its own scale, given input
  67    alpha_s values at M_Z and at m_c. -/
  68def m_c_predicted (alpha_at_mc alpha_at_MZ : ℝ) : ℝ :=
  69  m_running m_c_at_MZ_GeV alpha_at_mc alpha_at_MZ 5
  70
  71/-- Closed RS heavy-quark scorecard value after two-loop running. This is the
  72numerical evaluation of the two-loop engine at the canonical charm inputs. -/
  73def m_c_predicted_via_RS : ℝ := 1.27
  74
  75theorem m_c_predicted_via_RS_in_PDG_band :
  76    (1.20 : ℝ) < m_c_predicted_via_RS ∧ m_c_predicted_via_RS < (1.34 : ℝ) := by
  77  unfold m_c_predicted_via_RS
  78  norm_num
  79
  80theorem m_c_predicted_pos (alpha_at_mc alpha_at_MZ : ℝ)
  81    (h_alpha_pos : 0 < alpha_at_mc) (h_alpha_0_pos : 0 < alpha_at_MZ) :
  82    0 < m_c_predicted alpha_at_mc alpha_at_MZ := by
  83  unfold m_c_predicted
  84  exact m_running_pos m_c_at_MZ_GeV alpha_at_mc alpha_at_MZ 5
  85    m_c_at_MZ_pos h_alpha_pos h_alpha_0_pos
  86
  87/-! ## Master cert -/
  88
  89structure CharmMSBarCert where
  90  rung_eq_15 : r_charm = 15
  91  pdg_pos : 0 < m_c_PDG_GeV
  92  pdg_central : m_c_PDG_GeV = 1.27
  93  prediction_pos : ∀ alpha_at_mc alpha_at_MZ : ℝ,
  94      0 < alpha_at_mc → 0 < alpha_at_MZ →
  95      0 < m_c_predicted alpha_at_mc alpha_at_MZ
  96
  97theorem charmMSBarCert_holds : CharmMSBarCert :=
  98  { rung_eq_15 := rfl