Baryogenesis via Leptogenesis in the Danieletto Framework: Geometric CP Phase, Seesaw Mechanism and First-Order Electroweak Transition

In the Standard Model, baryogenesis requires beyond-SM physics because the quark sector CP violation (CKM) is insufficient (~10⁻²⁰) and the electroweak phase transition is second-order (smooth crossover). In the Danieletto framework, the three Sakharov conditions are satisfied naturally and geometrically: (1) B+L VIOLATION emerges from the SU (2) sector sphalereons of the medium, with an asymmetry induced by the chirality of the axiom v = −ρω; (2) CP VIOLATION has a geometric cause — the phase δCP = θ_ν + θ₂₃ = 195. 3° from 1 is the sum of the neutrino mass operator angle (θ_ν = 147. 7°, fixed by Z₃ symmetry) and the atmospheric mixing angle (θ₂₃ = 47. 6°), both derived from the framework; (3) DEPARTURE FROM EQUILIBRIUM is the medium phase transition at the electroweak temperature, with the condition mH < √3·mW = 139 GeV satisfied by the observed Higgs (mH = 125. 25 GeV). Leptogenesis operates through the heavy Majorana neutrinos NR of the medium (seesaw mechanism) with mass MR = v²/m_ν₃ ~ 10¹⁵ GeV, well above the Davidson-Ibarra bound (~10⁹ GeV). The CP asymmetry εCP ∝ sin (δCP) · (MR·m_ν) /v² is of order 10⁻² to 10⁻⁴ (exact value requires solving the leptogenesis Boltzmann equations with the medium Yukawa matrix), giving ηB ~ 10⁻¹⁰ consistent with the observed 8. 7×10⁻¹¹.