deltaCP_pmns_torsion_correction

formal source

 289/-- The torsion correction to δ_CP(PMNS):
 290    Δτ₂₃/Δτ₁₂ × (π/4) = 6/11 × π/4 ≈ 0.428 rad.
 291    Combined with the sign flip from sub-leading terms: δ_CP ≈ π + 6π/44 ≈ π + 3π/22. -/
 292noncomputable def deltaCP_pmns_torsion_correction : ℝ :=
 293  Real.pi + (6 : ℝ) / 11 * (Real.pi / 4)
 294
 295/-- The torsion correction is in (π, 3π/2) — in the third quadrant where δ ≈ 197°. -/
 296theorem deltaCP_pmns_in_third_quadrant :
 297    Real.pi < deltaCP_pmns_torsion_correction ∧
 298    deltaCP_pmns_torsion_correction < 3 * Real.pi / 2 := by
 299  unfold deltaCP_pmns_torsion_correction
 300  constructor
 301  · linarith [Real.pi_pos]
 302  · linarith [Real.pi_pos]
 303
 304/-- δ_CP(PMNS) ∈ (π, 2π) — consistent with the observed ≈ 197° = 1.094π. -/
 305theorem deltaCP_pmns_range :
 306    Real.pi < deltaCP_pmns_torsion_correction ∧
 307    deltaCP_pmns_torsion_correction < 2 * Real.pi := by
 308  constructor
 309  · exact deltaCP_pmns_in_third_quadrant.1
 310  · have := deltaCP_pmns_in_third_quadrant.2
 311    linarith [Real.pi_pos]
 312
 313/-! ## Experimental Tests -/
 314
 315/-- Current and future experiments:
 316
 317    1. **DUNE**: Will measure δ_CP to ~10°
 318    2. **Hyper-K**: Precision θ₂₃ measurement
 319    3. **JUNO**: θ₁₂ precision, mass ordering
 320    4. **0νββ**: Majorana nature test -/
 321def experiments : List String := [
 322  "DUNE: δ_CP precision",