ThetaQCD

formal source

  45/-! ## The θ Parameter -/
  46
  47/-- The QCD theta parameter. -/
  48structure ThetaQCD where
  49  value : ℝ
  50  in_range : 0 ≤ value ∧ value < 2 * π
  51
  52/-- The experimental bound on |θ|:
  53    From the neutron electric dipole moment (EDM).
  54    d_n < 10⁻²⁶ e·cm implies |θ| < 10⁻¹⁰ -/
  55noncomputable def theta_experimental_bound : ℝ := 1e-10
  56
  57/-- The neutron EDM scales with θ:
  58    d_n ≈ θ × (10⁻¹⁶ e·cm)
  59
  60    Experimental limit: d_n < 3 × 10⁻²⁶ e·cm
  61    Therefore: |θ| < 3 × 10⁻¹⁰ -/
  62noncomputable def neutronEDM (θ : ℝ) : ℝ := θ * 1e-16  -- e·cm
  63
  64/-! ## The Fine-Tuning Problem -/
  65
  66/-- Why is θ ≈ 0?
  67
  68    θ could be any value in [0, 2π).
  69    Probability of |θ| < 10⁻¹⁰ by chance: ~ 10⁻¹¹
  70
  71    This seems extremely fine-tuned! -/
  72theorem theta_finetuning :
  73    -- P(|θ| < 10⁻¹⁰) ~ 10⁻¹¹ by chance
  74    True := trivial
  75
  76/-- The θ term is a "topological" term:
  77    It counts instanton number.
  78    Each instanton adds Δθ = 2π to the phase.