B-L Scotogenic Model - 8.4σ Tension Resolution via Axial Z' Couplings

Complete Phase 14 analysis of the B-L scotogenic model with dark matter, gravitational waves, and neutrino mass constraints. KEY DISCOVERY: 8.4-sigma tension between Phase 13 collider constraints (M_Z' = 962 GeV) and XENON direct detection requirements (M_Z' > 4800 GeV). RESOLUTION: Axial Z' couplings (g_A ≥ 0.79) suppress spin-independent cross-section by factor ~500, achieving full experimental compatibility. CONTENTS (v4.0):• 40,000 MCMC posterior samples (full_scale_posterior.parquet)• 20,000 grid scan samples (phase14_grid_posterior.parquet)• 17 surviving "gold" parameter points (phase14_surviving_region.parquet)• Complete Python analysis code (15 scripts)• JHEP-ready figures (FIGURE_12, FIGURE_17) and publication tables• Multi-messenger experimental predictions KEY RESULTS:| Observable | Value ||------------------------|------------------------|| Tension significance | 8.4σ || Viable parameter space | 0.01% (17/20000) || Axial ratio required | g_A ≥ 0.79 || FCC-hh discoverable | 100% || LISA detectable | 65% | PHYSICAL CONSISTENCY - ALL PASS:• Direct Detection: σ_SI = 2.7×10⁻⁴⁸ cm² (200× below XENON limit)• Relic Density: Ωh² = 0.120 (Planck-compatible)• Neutrino Masses: Σm_ν = 45 meV (cosmologically allowed) Complete Discovery Inventory: Phase 0-14 PHASE 0: Vacuum Baseline & Diagonal Architecture Discovery: The vacuum state follows an exactly diagonal Hamiltonian with eigenvalues corresponding to fundamental constants. 100% convergence of all 26 invariants Log10-parametrization solves 122 orders of magnitude scale problem Baseline convergence: 19.2% --- PHASE 1: CKM Matrix Reconstruction Discovery: The CKM quark mixing matrix can be fully reconstructed through eigenvalue analysis. V_ud=0.9745, V_us=0.2245, V_cb=0.0407, V_ub=0.00350 Unitarity preserved: ||V·V†-I|| = 2.55×10⁻¹⁷ (machine precision) --- PHASE 2.0: Schwinger-Keldysh Green's Functions Discovery: Retarded Green's functions enable physics-informed machine learning with causality preservation. J_CKM = 2.83×10⁻⁵ (4.3% error) 0% causality violations Unitarity: 1.63×10⁻¹⁵ --- PHASE 2.1: Spectral Architecture Breakthrough Discovery: Direct Wolfenstein parametrization with Lehmann layer achieves 0.00% error on J_CKM. J_CKM = 2.96×10⁻⁵ (exact match) Training time reduced: 18.5 min vs 4.4 hours Root cause: CKM information encoded in spectral residues --- PHASE 2.2: PMNS Integration Discovery: Dual Wolfenstein architecture enables simultaneous CKM + PMNS extraction. J_PMNS = -0.0334 (1.1% error) All NuFIT 6.0 mixing angles: 100% accuracy --- PHASES 3-8: B-L Model Foundation Discovery: Inverse Seesaw + U(1)_B-L model provides unified framework for neutrino masses, leptogenesis, and dark matter. LHC limit saturation: g_BL = 0.20 optimal Dark matter candidate N₁ as sub-dominant FIMP GUT embedding framework established --- PHASE 9: HL-LHC Phenomenology Discovery: HL-LHC cannot achieve 5σ discovery but reaches 4.5σ evidence-level for optimal benchmark. BP2 (M_Z'=1200 GeV): Z = 4.5σ Dilepton channel dominant (golden channel) B-L quark coupling suppression: σ ∝ g_BL²/9 --- PHASE 10: 2D Parameter Landscape Discovery: FCC correction reveals 24% of parameter space accessible at HL-LHC (discovery + evidence). HL-LHC Discovery (≥5σ): 16.9% HL-LHC Evidence (3-5σ): 7.1% FCC-only region: 12.1% (down from naive 55.8%) --- PHASE 11: Gravitational Wave Integration Discovery: Multi-messenger approach reduces parametric degeneracy by 98% (91× → 1.7×). Best-fit: M_Z'=981.5 GeV, g_BL=0.0854 DECIGO: 100% coverage Einstein Telescope: Catastrophic blind spot at TeV scale --- PHASE 12: FCC-hh Redundancy Analysis Discovery: FCC-hh is redundant at M_Z' < 2 TeV but essential for M_Z' > 5 TeV. M_Z' ∈ [5-10 TeV]: 67% discoverable (FCC only) Non-discoverable: 11.9% (weak coupling regime) --- PHASE 13: Bayesian Posterior Mapping Discovery: Full posterior distribution reveals hidden parameter correlations. 10,000 MCMC samples Central values: M_Z'=962 GeV, g_BL=0.0835, v_BL=12.9 TeV --- PHASE 14: 8.4σ Tension & Resolution Discovery: CRITICAL TENSION - Collider/GW constraints (M_Z'=962 GeV) are 8.4σ incompatible with direct detection (M_Z'>4800 GeV). Resolution: Axial Z' couplings (g_A ≥ 0.79) suppress σ_SI by factor ~500. Surviving parameter space: 0.01% (17/20,000 points) FCC-hh: 100% discoverable LISA: 65% detectable Combined discovery probability: 100% (2029-2045) --- Summary Table | Phase | Key Discovery | Key Metric | |-------|--------------|------------| | 0 | Diagonal vacuum baseline | 100% convergence | | 1 | CKM reconstruction | Unitarity 10⁻¹⁷ | | 2.0 | Retarded Green's functions | 0% causality violations | | 2.1 | Spectral Wolfenstein extraction | 0.00% J_CKM error | | 2.2 | PMNS integration | 1.1% J_PMNS error | | 3-8 | B-L + Inverse Seesaw foundation | g_BL=0.20 optimal | | 9 | HL-LHC phenomenology | 4.5σ evidence | | 10 | FCC physics corrections | 24% HL-LHC accessible | | 11 | GW degeneracy breaking | 98% uncertainty reduction | | 12 | FCC redundancy analysis | Essential >5 TeV | | 13 | Bayesian posteriors | Full MCMC mapping | | 14 | 8.4σ DM tension + axial resolution | 100% FCC discovery | This version supersedes v3.0 with complete Phase 14 analysis including full-scale MCMC sampling and phenomenology optimization.