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 δ_CP = 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 m_H < √3·m_W = 139 GeV satisfied by the observed Higgs (m_H = 125.25 GeV). Leptogenesis operates through the heavy Majorana neutrinos N_R of the medium (seesaw mechanism) with mass M_R = v²/m_ν₃ ~ 10¹⁵ GeV, well above the Davidson-Ibarra bound (~10⁹ GeV). The CP asymmetry ε_CP ∝ sin(δ_CP)·(M_R·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 η_B ~ 10⁻¹⁰ consistent with the observed 8.7×10⁻¹¹.