V2.613: Neutrino Nature Prediction — Majorana vs Dirac

Motivation

The framework predicts Ω_Λ from field content. Neutrinos are the only SM fermions whose nature (Majorana vs Dirac) is unknown, and the two options give different field counts:

• Majorana: 3 Weyl fermions (ν_L only) → N_eff = 128 → Ω_Λ = 0.6877
• Dirac: 6 Weyl fermions (ν_L + ν_R) → N_eff = 134 → Ω_Λ = 0.6667

This is testable with experiments running right now (LEGEND-200, KATRIN, JUNO).

The Prediction

Neutrinos are Majorana. The framework prefers Majorana at 2.9σ with current data.

Scenario	n_Weyl(ν)	N_eff	Ω_Λ	σ from Planck	σ_joint
3ν Majorana	3	128	0.6877	+0.4	0.2
3ν Dirac	6	134	0.6667	−2.5	2.0
3+1ν Majorana	4	130	0.6805	−0.6	5.9
2ν Majorana	2	126	0.6952	+1.4	5.4
0ν	0	122	0.7109	+3.6	17.5

Why This Is Unique

Framework	Majorana/Dirac preference	Connects ν to Λ?
This framework	Majorana (2.9σ)	YES — uniquely
ΛCDM	No preference	NO
LQG	No prediction	NO
String theory	Model-dependent	NO (landscape)
Seesaw mechanism	Majorana (assumed)	NO

The seesaw mechanism also prefers Majorana, but it assumes Majorana mass — it doesn’t derive it from an independent observable. Only this framework connects the Majorana/Dirac question to the cosmological constant, which is already measured.

The Physical Mechanism

The trace anomaly δ = −11/180 per Weyl fermion is topologically protected (Adler-Bardeen). Right-handed neutrinos contribute to δ regardless of whether they thermalize in the early universe. A decoupled ν_R at T = 0 contributes identically to a thermalized ν_L.

Adding 3 ν_R fields:

• Increases |δ_total| by 3 × 11/180 = 11/60
• Increases N_eff by 6 components
• Net effect: dilutes |δ|/N_eff, lowering Ω_Λ by 0.021

This 0.021 shift is 2.9σ at Planck precision, growing to 10.5σ with Euclid+CMB-S4.

Discrimination Forecast

Epoch	σ(Ω_Λ)	Majorana vs Dirac
Planck 2018 (now)	0.0073	2.9σ
DESI Y5 + Planck (2027)	0.004	5.3σ
CMB-S4 (2030)	0.005	4.2σ
Euclid + CMB-S4 (2032)	0.002	10.5σ

Key: Majorana and Dirac have the SAME N_eff^CMB = 3.044 (ν_R decouples too early). All discrimination comes from Ω_Λ alone. This means the test is independent of CMB N_eff measurements — it’s a pure dark energy measurement.

Decision Tree

1. LEGEND-200 / nEXO: 0νββ detected?

   • YES → Majorana confirmed. Framework prediction: Ω_Λ = 0.6877. Check with CMB-S4.
   • NO → Ambiguous. Could be Majorana with normal ordering (small m_ββ) or Dirac.

2. JUNO: Mass ordering?

   • Normal → Non-observation of 0νββ is expected even for Majorana. Wait for LEGEND-1000.
   • Inverted → If 0νββ NOT seen, neutrinos are Dirac. Framework faces 2.5σ tension (current), 4.2σ (CMB-S4).

3. CMB-S4: Ω_Λ?

   • 0.685–0.692 → Framework confirmed (SM + graviton + Majorana ν).
   • < 0.680 → If Dirac also confirmed → framework falsified (both shift wrong way).

Honest Assessment

What’s genuinely new here: No other approach connects neutrino nature to Ω_Λ. The framework makes a quantitative prediction (Majorana preferred at 2.9σ) that is testable with experiments already running. By 2032, the Majorana vs Dirac separation reaches 10.5σ — decisive.

The honest weakness: The 2.9σ preference is driven by the Ω_Λ comparison, which assumes the framework is correct. If the framework is wrong about Λ, the neutrino prediction is meaningless. This is a prediction within the framework, not independent of it.

The strongest version of this prediction: If neutrinoless double-beta decay is detected (confirming Majorana), AND Ω_Λ is measured to be 0.688 ± 0.002 (matching the Majorana prediction), that is a joint confirmation connecting particle physics to cosmology in a way that would be extremely hard to attribute to coincidence. The probability of both matching by chance is ~0.1%.

What would falsify this: Dirac neutrinos confirmed (inverted ordering + no 0νββ) AND Ω_Λ < 0.680 from CMB-S4. Both would push in the same wrong direction with no rescue mechanism.