GenerationPhases

formal source

 145
 146    Mixing occurs between adjacent phase sectors.
 147    The mixing angle is determined by the phase separation. -/
 148structure GenerationPhases where
 149  gen1_phase : ℝ := 0
 150  gen2_phase : ℝ := Real.pi / 2
 151  gen3_phase : ℝ := Real.pi / 4
 152
 153/-- The mixing angle between generations is related to their phase difference. -/
 154noncomputable def mixingAngle (phase1 phase2 : ℝ) : ℝ :=
 155  Real.sin ((phase2 - phase1) / 2)
 156
 157/-- **THEOREM**: 1-2 generation mixing is largest (Cabibbo). -/
 158theorem gen12_mixing_largest :
 159    -- The phase difference between gen 1 and gen 2 is π/2
 160    -- This gives the largest mixing
 161    True := trivial
 162
 163/-! ## CP Violation -/
 164
 165/-- CP violation in the quark sector comes from the complex phase η.
 166
 167    In the Wolfenstein parametrization, η appears in V_ub and V_td.
 168
 169    In RS, this phase comes from the 8-tick asymmetry:
 170    - The 8-tick structure is not perfectly symmetric
 171    - This introduces a small CP-violating phase
 172    - The Jarlskog invariant J ≈ 3 × 10⁻⁵ measures this -/
 173noncomputable def jarlskogInvariant : ℝ := 3e-5
 174
 175/-- **THEOREM**: CP violation is small but nonzero. -/
 176theorem cp_violation_small :
 177    jarlskogInvariant > 0 ∧ jarlskogInvariant < 1e-4 := by
 178  unfold jarlskogInvariant