NEUTRAL-MESON MIXING AND CP VIOLATION (XII v6)

Abstract

Within the FCD-RBv6 pregeometric framework, CP violation is not a primitive phase complex inserted ad hoc in the Cabibbo-Kobayashi-Maskawa (CKM) matrix, but the low-energy projection of an emergent holonomic geometric phase (Berry Phase) at the tri-coordinated junction of the 5D Y-gate. While baryons are protected against unbraiding by the non-abelian braid lock Δ² = (σ₁ σ₂)³ of the Artin group B₃, neutral mesons (such as the neutral kaon, K⁰ = d s̄) are represented as two-strand configurations of the abelian braid group B₂ ≅ ℤ, which explains their intrinsic instability and flavor-mixing oscillations. In this revision v6, this topological phase slip is shown to be strictly unitary and adiabatic (dS = 0) in the quantum phase space of the non-traversable ER bridge, regularized at the Morris-Thorne centrifugal Compton floor R₀ ≈ 0.6308 fm. The periodic oscillation K⁰ ↔ K̄⁰ is modeled as a continuous helicoidal phase shift of π radians (180°) at the Y-gate junction, where the tiny mass difference Δm_K ≈ 3.484 × 10⁻¹² eV reflects the differential elastic impedance of the bulk. CP violation emerges naturally when the geometric misalignment of the Y-gate’s bulk-facing mouth (Mouth C) breaks the reciprocal symmetry between direct (A → B) and reverse (B → A) transitions, resulting in an asymmetry parameter Re(ε_K) ≈ 2.228 × 10⁻³ (0.22%). We integrate this mechanism with the global orientation parameter Ω = ±1, unifying CP violation, flavor oscillations, and the topological asymmetry of the vacuum into a single, cohesive pregeometric ontology.