Phase Differential Theory
Phase Differential
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QM III

QM III: Scalar Spectrum and Experimental Signatures

Graham Fincham, Daniel Hilton

Reader summary

A theory is only physics if it can be wrong. QM III makes PDT wrong-able. It takes the defect picture from QM II, computes the spectrum of small wobbles around the defect, and reads off concrete numbers experiments can check. The lowest wobble looks like the Higgs at 125 GeV. The next two land around 290 and 510 GeV, with more in the 1 to 2 TeV range. Higgs couplings should drift from Standard Model values by one to five percent. Electroweak precision should shift by about a part in a thousand. Gravitational waves should pick up a tiny dispersion, and interferometers should see a faint coherence noise. If none of those show up, the framework is in serious trouble, and the paper says so.

Abstract

Phase Differential Theory (PDT) predicts that particle physics and spacetime structure emerge from a dynamical phase manifold. This paper develops the experimental consequences of this framework by analysing scalar excitations arising from fluctuations around topological defect solutions of the phase manifold. A discrete scalar bound-state spectrum is obtained from the linearised fluctuation operator, with the lowest mode able to be associated with the observed 125 GeV Higgs boson and additional scalar states arising naturally within the EFT spectrum in the 300 GeV–2 TeV range. Mixing between defect-localised and internal bundle modes leads to percent-level deviations in Higgs couplings. Associated precision-electroweak corrections, modifications to gravitational-wave dispersion, and interferometric signatures of phase-manifold fluctuations are derived. All predictions follow from a controlled effective-field-theory analysis and a well-defined numerical pipeline. Explicit parameter scans and higher-order corrections are deferred to subsequent work.

Falsifiable predictions

  1. 01
    Additional scalar bound states exist with masses m₂ ≈ 290 GeV, m₃ ≈ 510 GeV, m₄ ≈ 1–2 TeV. PDT is falsified if no such scalars exist below ∼1 TeV.
  2. 02
    Higgs couplings deviate from Standard Model values at the 1–5 % level. Couplings matching the SM at the 0.1 % level falsify the mixing prediction.
  3. 03
    Electroweak precision parameter Δρ ∼ 10⁻³. Tighter agreement with the SM falsifies the custodial-breaking estimate.
  4. 04
    Gravitational waves show dispersion Δv/v ∼ 10⁻¹⁵ to 10⁻¹². Interferometric coherence noise ΔL/L ∼ 10⁻²¹ to 10⁻¹⁸.

Full paper

1. Introduction

The discovery of the Higgs boson confirms the existence of a scalar sector responsible for electroweak symmetry breaking, yet the microscopic origin of this sector remains unclear. In the Standard Model, the Higgs field is introduced as a fundamental scalar, leaving its mass stability and structural origin unexplained.

PDT offers an alternative perspective: scalar fields arise not as fundamental degrees of freedom, but as dynamically generated bound excitations of a topological defect embedded in a deeper phase manifold. In this picture, the Higgs boson corresponds to the lowest scalar bound state of the defect, while heavier scalar excitations represent additional, testable predictions.

All numerical values presented here should be interpreted as representative EFT-scale estimates rather than precision predictions.

Assumptions

- **A1.** The phase manifold admits stable, finite-energy topological defects. - **A2.** Scalar excitations are treated within the linearised fluctuation operator. - **A3.** Only leading-order terms in the derivative expansion are retained. - **A4.** The defect profile and fluctuation spectrum admit stable numerical solutions. - **A5.** Mixing and coupling deviations are computed within a low-energy EFT regime.

2–5. Defect profile, fluctuation operator, spectrum pipeline

A static, spherically symmetric defect satisfies a radial profile equation with boundary conditions F(0)=π, F(∞)=0. The shooting method gives a profile with characteristic mass M₀ ≈ 1/R₀. Small fluctuations F(r,t) = F(r) + δ(r,t) separate into eigenmodes of −d²u/dr² + V_eff(r) u = m² u, with V_eff built from the defect profile. The pipeline solves the profile, builds V_eff, and solves the eigenvalue problem.

6. Scalar spectrum

Representative eigenvalue ratios m₂/m₁ ≈ 2.3 and m₃/m₁ ≈ 4.1. Fixing m₁ = 125 GeV gives m₂ ≈ 290 GeV, m₃ ≈ 510 GeV, m₄ ≈ 1–2 TeV. These should be read as order-of-magnitude estimates.

7. Higgs identification and mixing

Mixing between defect and bundle sectors gives a 2×2 mass matrix with eigenvalues m_± and angle θ. Coupling modifications scale as g_h = g_SM cos θ.

8–10. Collider and precision predictions

Production σ(pp → h₂) ≈ cos² θ σ_SM(m₂), giving σ(h₂) ≈ 0.01–0.1 × σ_SM. Dominant decays h₂ → ZZ, WW, hh. Δρ ≈ ε² m_h² ∼ 10⁻³. Higgs coupling deviations δg/g ≈ θ² ∼ 1–5 %.

11–12. Gravitational waves and interferometry

Dispersion ω² = k²(1 + α k/Λ_Φ²) gives Δv/v ∼ 10⁻¹⁵ to 10⁻¹². Phase-manifold fluctuations induce interferometric noise ΔL/L ∼ 10⁻²¹ to 10⁻¹⁸.

13. Falsifiable predictions

PDT is falsified if no additional scalars exist below ∼1 TeV, Higgs couplings match the SM at the 0.1 % level, no electroweak deviations at Δρ ∼ 10⁻³ appear, or no gravitational-wave dispersion is seen at the predicted scales.

14–15. Limitations and conclusion

The analysis is restricted to linearised fluctuations, spherically symmetric defects, and leading-order EFT. The framework is quantitatively defined and experimentally falsifiable.

BibTeX

@article{fincham_hilton_qm_iii,
  author  = {Fincham, Graham and Hilton, Daniel},
  title   = {Phase Differential Theory: Experimental Signatures of the Phase Manifold},
  journal = {Phase Differential Theory Series, QM III},
  year    = {2025}
}