V2.126 - BSM Exclusion Bounds — What R = Ω_Λ Rules Out
V2.126: BSM Exclusion Bounds — What R = Ω_Λ Rules Out
Status: COMPLETE
Motivation
V2.125 showed the SM gauge group and 3 generations are predicted by R = Ω_Λ. Since SM + graviton (f_g = 0.293) matches Ω_Λ exactly, ANY new physics shifts R and creates a gap. This means the framework constrains all BSM scenarios.
The key mechanism: every new field adds both |δ| (numerator) and α (denominator) to R = |δ|/(6α), but different field types contribute asymmetrically. Vectors push R up (high |δ|/dof), fermions push R down (low |δ|/dof), and scalars push R down slightly. Since the SM already sits at R = Ω_Λ with f_g = 0.293, any addition disrupts the balance.
Method
- Scan 13 named BSM scenarios (MSSM, dark matter candidates, neutrino mass models, etc.)
- For each: compute R bare, R with graviton (f_g = 0.293), and required f_g for R = Ω_Λ
- Classify as EXCLUDED (no f_g works), DISFAVORED (needs f_g > 0.5), VIABLE, or PREFERRED
- Additional scans: QCD color number, maximum field budget, neutrino mass mechanisms, SUSY variants
Results
Phase 1: Named BSM Scenario Scan
| Scenario | R (bare) | Gap | R (w/grav) | Gap | f_g needed |
|---|---|---|---|---|---|
| SM (baseline) | 0.665 | -3.0% | 0.685 | -0.0% | 0.293 |
| SM + 1 sterile ν | 0.657 | -4.1% | 0.677 | -1.1% | 0.407 |
| SM + axion | 0.660 | -3.7% | 0.680 | -0.7% | 0.367 |
| SM + scalar DM | 0.660 | -3.7% | 0.680 | -0.7% | 0.367 |
| SM + fermion DM | 0.657 | -4.1% | 0.677 | -1.1% | 0.407 |
| SM + Z’ (extra U(1)) | 0.671 | -2.0% | 0.691 | +0.8% | 0.208 |
| SM + dark photon | 0.694 | +1.3% | 0.714 | +4.3% | EXCLUDED |
| SM + 3 ν_R (Dirac) | 0.643 | -6.2% | 0.662 | -3.3% | 0.634 |
| SM + 2HDM | 0.645 | -5.8% | 0.665 | -2.9% | 0.587 |
| SM + scalar triplet | 0.636 | -7.1% | 0.656 | -4.3% | 0.735 |
| MSSM | 0.448 | -34.6% | 0.461 | -32.7% | EXCLUDED |
| NMSSM | 0.442 | -35.4% | 0.455 | -33.6% | EXCLUDED |
| Split SUSY | 0.569 | -16.9% | 0.586 | -14.5% | EXCLUDED |
Key finding: 4 scenarios are outright excluded (no graviton fraction can save them), 3 more are disfavored (need f_g > 0.5, meaning gravity is more than half emergent).
Phase 2: QCD Color Number Prediction
| N_c | n_v | n_w | R (w/grav) | Gap |
|---|---|---|---|---|
| 2 | 7 | 33 | 0.610 | -10.9% |
| 3 | 12 | 45 | 0.685 | -0.0% |
| 4 | 19 | 57 | 0.770 | +12.4% |
| 5 | 28 | 69 | 0.855 | +24.8% |
| 6 | 39 | 81 | 0.935 | +36.5% |
N_c = 3 is uniquely selected, confirming V2.125. The spacing between N_c = 2 and N_c = 4 is >20 percentage points, far exceeding any residual uncertainty.
Phase 3: Maximum BSM Field Budget
| Field type | Max extra fields | Notes |
|---|---|---|
| Weyl fermions | 6 | With f_g pushed to ~1.0 |
| Real scalars | 9 | With f_g pushed to ~1.0 |
| Vector bosons | 0 | Even 1 extra vector overshoots |
Vectors are the most constrained: adding even a single vector boson (dark photon) pushes R above Ω_Λ with no way back, because vectors contribute 11.3× more |δ| per dof than Weyls. For fermions and scalars, the budget exists but requires trading off against f_g — every extra field demands a higher graviton fraction.
Phase 4: Neutrino Mass Mechanism Predictions
| Mechanism | f_g needed | Status |
|---|---|---|
| Majorana (SM as-is) | 0.293 | PREFERRED |
| Dirac (3 ν_R) | 0.634 | Disfavored |
| Type-I seesaw (3 ν_R) | 0.634 | Disfavored |
| Type-II seesaw (scalar triplet) | 0.735 | Disfavored |
| Type-III seesaw (fermion triplet) | 0.975 | Strongly disfavored |
| Inverse seesaw (3+3) | 0.975 | Strongly disfavored |
| Scotogenic (inert doublet + 3 ν_R) | 0.929 | Strongly disfavored |
The framework predicts Majorana neutrinos. The SM as-is (with dimension-5 Weinberg operator generating Majorana masses) is the unique preferred option. All Dirac and seesaw mechanisms add enough new fields to require f_g > 0.5, pushing into the disfavored regime. Type-III seesaw and scotogenic models need f_g ≈ 0.97, essentially ruling them out.
Phase 5: SUSY Exclusion
| SUSY variant | N_eff | R (bare) | Gap | f_g needed |
|---|---|---|---|---|
| MSSM | 199 | 0.448 | -34.6% | EXCLUDED |
| NMSSM | 203 | 0.442 | -35.4% | EXCLUDED |
| Split SUSY (all) | 150 | 0.569 | -16.9% | EXCLUDED |
| Split SUSY (gauginos) | 126 | 0.636 | -7.1% | 0.748 |
| SUSY heavy 3rd gen | 175 | 0.493 | -28.1% | EXCLUDED |
All conventional SUSY is excluded. The MSSM nearly doubles the effective dof count (N_eff: 118 → 199), dropping R by 35%. Even split SUSY with only fermionic partners remaining is excluded because it still adds 32 effective dofs. The only SUSY variant not outright excluded is one where only gauginos survive (bino + wino + gluino), but even that needs f_g = 0.75.
Phase 6: Dark Matter Candidates
| DM candidate | R (w/grav) | Gap | f_g needed |
|---|---|---|---|
| No particle DM | 0.685 | -0.0% | 0.293 |
| Real scalar singlet | 0.680 | -0.7% | 0.367 |
| Majorana fermion | 0.677 | -1.1% | 0.407 |
| Complex scalar | 0.675 | -1.5% | 0.440 |
| Scalar + Majorana | 0.672 | -1.9% | 0.480 |
| Dirac fermion | 0.670 | -2.2% | 0.521 |
| Inert doublet | 0.665 | -2.9% | 0.587 |
| Dark photon | 0.714 | +4.3% | EXCLUDED |
| Dark photon + Higgs | 0.709 | +3.5% | EXCLUDED |
Vector dark matter is excluded. Any dark photon scenario overshoots R. Scalar and fermionic DM candidates are viable but push f_g upward. A single real scalar singlet is the most economical particle DM option (f_g = 0.37), while Majorana fermion DM is nearly as good (f_g = 0.41). The framework slightly favors DM scenarios that don’t introduce a new particle (e.g., primordial black holes, axion-like particles counted as the SM axion).
Phase 7: Exclusion Classification Summary
| Category | Count | Examples |
|---|---|---|
| EXCLUDED | 4 | MSSM, NMSSM, Split SUSY, dark photon |
| DISFAVORED (f_g > 0.5) | 3 | Dirac neutrinos, 2HDM, scalar triplet |
| VIABLE (0 < f_g < 0.5) | 5 | Axion, sterile ν, scalar DM, fermion DM, Z’ |
| PREFERRED (f_g ≈ 0.29) | 1 | SM (baseline) |
Key Conclusions
-
SUSY is excluded: The MSSM, NMSSM, and all split SUSY variants with full fermionic partners are incompatible with R = Ω_Λ. The doubling of dof count cannot be compensated by any graviton fraction.
-
Vectors are maximally constrained: Adding even one vector boson overshoots R. This excludes dark photon models and strongly constrains extra gauge symmetries (Z’ with anomaly-canceling fermions is viable only because the fermions compensate).
-
Majorana neutrinos predicted: The SM as-is (dimension-5 Weinberg operator) is the unique preferred neutrino mass mechanism. Dirac neutrinos require f_g = 0.63, seesaw mechanisms even more.
-
N_c = 3 confirmed: QCD with 3 colors is the unique integer giving R ≈ Ω_Λ, with >10% spacing to N_c = 2 and N_c = 4.
-
Minimal DM favored: No-particle DM (primordial BHs, axions) or at most a single scalar/Majorana singlet is preferred. Multi-field dark sectors are disfavored.
-
Total BSM budget: At most 6 extra Weyl fermions or 9 extra scalars, with each addition demanding higher f_g. Zero extra vectors allowed.
Falsifiability
This is a genuinely falsifiable prediction:
- If SUSY partners are discovered at any mass scale → framework is wrong
- If a dark photon is discovered → framework is wrong
- If neutrinos are Dirac (0νββ non-observation) → framework disfavored at f_g > 0.5
- If only a single scalar or Majorana DM particle exists → framework accommodated with modest f_g increase
Runtime
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