🔬 Law 62 — 0νββ half-life from SPT closed-form inputs
Neutrinoless double beta decay (0νββ) is the most direct test of whether neutrinos are Majorana (their own antiparticles) or Dirac. SPT predicts Majorana from Z_2_DA flip symmetry (Law 8) — i.e., the DA(±) phase symmetry inherently mixes lepton-number-violating channels.
SPT-derived effective mass: with m_ν1 = 0 (Law 40 EXACT), PMNS angles sin²θ_12 = 4/13 + sin²θ_13 = 3/136 (Law 48), and neutrino masses m_ν2 ≈ 8.6 meV, m_ν3 ≈ 50 meV from oscillation Δm²:
- Term A = c_13²·m_ν2·s_12² ≈ 2.59 meV
- Term B = s_13²·m_ν3 ≈ 1.10 meV
- m_ββ ∈ [1.49, 3.69] meV depending on Majorana phases (constructive vs destructive)
Xe-136 half-life prediction: with G_0ν ≈ 1.46×10⁻¹⁴/yr, |M_0ν|² ≈ 4 (lattice+shell-model):
- T_1/2 ∈ [1.91×10²⁸, 1.17×10³⁰] yr
- Current KamLAND-Zen 2024 bound: T_1/2 > 2.3×10²⁶ yr — SPT well above
- nEXO 2030+ reach: 5×10²⁸ yr — within SPT band
- KZ-NEXT 2030+: 10²⁸ yr — partial coverage
Honest scope: SPT inputs (PMNS + hierarchy + Majorana) are closed-form. Majorana phases α_21, α_31 are NOT predicted by current SPT — they form the prediction band. Nuclear matrix element |M_0ν|² has ~30% systematic uncertainty (standard ChPT + lattice issue, not SPT-specific).
§1 Cách verify hoạt động (6 stages)
Stage 1 — Majorana from Law 8
Z_2_DA flip symmetry φ → −φ mixes lepton-number channels → neutrinos are Majorana (their own antiparticles).
Don't want to install Python? Paste the prompt straight into Grok / Claude / ChatGPT / Gemini — the AI fetches the public script URL below and independently verifies each assertion in ~30 s. Open grok.com or claude.ai , paste, send.
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Inputs: Bagua integers + π/√ only — no CODATA, no PDG, no calibration (Tier B). SymPy-verified as exact fractions (not floating-point). See full context at /theory/sympy-breakthrough-2026.
§3 Độ chính xác
Observable
SPT prediction
Current bound / future reach
m_ββ
[1.49, 3.69] meV
Current limit ~50-200 meV (KZ-2024); nEXO 2030+ reaches 5-20 meV
All three observables enter the experimentally-testable range in 2027-2035 window.
§4 Mô tả chi tiết
0νββ requires: (i) neutrinos are Majorana (SPT: Z_2_DA, Law 8); (ii) m_ν has a specific spectrum (SPT: m_ν1=0 + Δm², Law 25 + 40); (iii) PMNS mixing controls effective mass (SPT: closed-form, Law 48). All three ingredients are SPT-clean. The only freedom is the two Majorana phases α_21, α_31 — these enter as relative complex phases between the m_ν2 and m_ν3 contributions to m_ββ. Constructive interference gives the maximum (~3.7 meV); destructive gives the minimum (~1.5 meV). Future experiments measuring m_ββ to ~1 meV precision would pin down the Majorana phases.
§5 So sánh với học thuyết hiện đại
Framework
Predicts m_ββ?
Standard Model + Δm²
Free Majorana phases; broad band [1, 50] meV for NH
Type-I See-saw
Range depends on heavy neutrino spectrum (many parameters)
SPT Law 62
[1.49, 3.69] meV band from closed-form PMNS + m_ν1=0 EXACT
SPT narrows m_ββ band by 10× vs naive SM (Majorana phases still free, but PMNS angles closed-form removes one source of variability).
§6 Tầm quan trọng
Importance: HIGH — 0νββ is the direct test of Majorana-vs-Dirac neutrino nature. SPT predicts Majorana via Z_2_DA Law 8; this Law makes the prediction quantitative with a narrow m_ββ band. Detection at nEXO/KZ-NEXT in the SPT band confirms the framework; non-detection at T_1/2 > 10³⁰ yr by 2035 constrains SPT's NH + Z_2_DA picture.
§7 Falsifiable claim
Inverted hierarchy detected by JUNO/DUNE 2030: falsifies Law 25 NH → forces revision of Law 62 m_ββ prediction.
Dirac neutrino confirmed (no 0νββ at T_1/2 > 10³⁰ yr by 2035 combined nEXO + KZ-NEXT): constrains SPT Z_2_DA Majorana mechanism.
Σm_ν measured outside [50, 80] meV by CMB-S4 + DESI 2028 at >5σ: falsifies SPT m_ν1=0 + Δm² closure.
Comments — Law 62 — 0νββ Half-Life from PMNS + Majorana (Đợt 32 · 11/05/2026 v3.34)