RFT Solution to the Strong CP Problem

Scalaron-twistor axion dynamics driving θ̄ → 0 and baryogenesis

1. The Strong CP Problem: A 50-Year Puzzle NEW

In 1973, physicists discovered that quantum chromodynamics (QCD) permits a CP-violating term that should make the neutron electric dipole moment roughly 1010 times larger than experimental limits allow. This "strong CP problem" asks: why is nature so precisely fine-tuned to cancel this effect?

The Problem

QCD permits a CP-violating term in the Lagrangian:

$\mathcal{L}_{\text{QCD}}\;\supset\;\frac{\bar\theta\,g_s^{\,2}}{32\pi^{2}}\;G_{\mu\nu}\tilde G^{\mu\nu}$

where \bar{\theta} = \theta_{\text{QCD}} + \arg(\det M_q) combines the bare θ angle with phases from quark masses. This term would induce a neutron electric dipole moment:

$d_n\simeq3\times10^{-16}\,\bar\theta\;e\;\text{cm}$

Current bounds require |d_n| < 1.8 \times 10^{-26} e·cm, implying |\bar{\theta}| < 10^{-10}. Without a mechanism to suppress θ̄, this represents an unnatural fine-tuning of 10 decimal places.

How RFT Solves It

RFT's scalaron-twistor structure naturally generates a Peccei–Quinn symmetry that dynamically drives θ̄ → 0 through an emergent axion field, eliminating the fine-tuning without adding new fundamental scales or fields beyond those already required for inflation and neutrino masses.

2. Twistor U(1)T → Peccei–Quinn

The RFT Resolution

  • Twistor Symmetry: RFT's recursive structure includes a U(1)T twistor symmetry that emerges from the spinor field dynamics.
  • Peccei–Quinn Identification: This U(1)T acts as a Peccei–Quinn symmetry at low energies, with the scalaron field Φ carrying PQ charge.
  • Axion Emergence: When ⟨Φ⟩ ≠ 0 (at the inflation scale), U(1)PQ breaks spontaneously, giving rise to the axion a as the Goldstone boson.
  • θ Relaxation: The axion potential V(a) develops a minimum at a = -θ̄fa, dynamically canceling the CP-violating phase.
  • Baryogenesis Link: The same scalaron dynamics responsible for θ → 0 also generate the observed baryon asymmetry YB ≈ 9 × 10-11.
📐 Show detailed derivation

Starting from the RFT action with twistor fields ξA:

The effective low-energy theory inherits a U(1)PQ symmetry:

After scalaron condensation at ⟨Φ⟩ ≈ 1013 GeV:

The axion couples to QCD through the anomaly:

This generates an effective potential that dynamically sets θ̄eff = 0, solving the strong CP problem.

RFT's dynamical theta angle potential showing how scalaron interactions naturally drive the strong CP angle to zero without requiring axions or fine-tuning

Figure 1: The axion potential shifts θeff → 0

3. Key Predictions

RFT makes specific, testable predictions for the axion properties and related observables:

  • Axion decay constant: fa ≈ 1–2 × 1013 GeV
  • Axion mass: ma ≈ (5–8) × 10-7 eV
  • Axion-photon coupling: gaγγ ≈ 10-13 GeV-1
  • Neutron EDM: |dn| < 1.8 × 10-26 e·cm ✓
  • Baryon asymmetry: YB ≈ 9 × 10-11 ✓

🧮 Interactive Axion Calculator

Combined axion-scalaron energy landscape showing the coupled potential with minimum at theta equals zero

Figure 2: The coupled axion-scalaron potential landscape

4. Full Paper

For complete derivations, numerical analysis, and experimental implications:

📄 Download PDF 📝 DOCX Source

5. Related Topics

Explore how the strong CP solution connects to other aspects of RFT:

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