QM III: Scalar Spectrum and Experimental Signatures

Daniel Hilton

Earlier research paper

This paper remains available as part of the development of Phase Differential Theory. The R00–R13 foundational suite provides the current formulation of the theory. Read this paper in its original model and publication context.

Current foundations Research history

Current foundational treatment

Specific claim correctedPrincipal topic: Interactions, matter and refinement.

A scalar spectrum in a calibrated effective model relates to matter models in R09.

Specific qualification: Model-dependent mass estimates.

R09: Interactions matter and refinement

A topic connection does not mean that every claim in this paper is retained or that a current paper reproduces its proof.

Context for this earlier argument

Model-dependent mass estimates

The mass estimates in this paper come from a calibrated effective model. They are model-dependent illustrations, not reproducible predictions of the current foundations, and a null search for them would bear on that model only, not on the programme as a whole.

Current context

A present-day website summary. It is not part of the original manuscript.

QM III takes the defect picture from QM II and computes the spectrum of small fluctuations around the defect within a calibrated effective model. The resulting mass estimates illustrate that model; they are not programme-wide predictions of PDT.

Original abstract

Preserved from the original manuscript.

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.

Claims stated in the original paper

01
Additional scalar bound states exist with masses m₂ $\approx$ 290 GeV, m₃ $\approx$ 510 GeV, m₄ $\approx$ 1–2 TeV. Absence of such scalars below ∼1 TeV would bear on this effective model only.
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.
03
Electroweak precision parameter $\Delta\rho$ ∼ 10⁻³. Tighter agreement with the SM falsifies the custodial-breaking estimate.
04
Gravitational waves show dispersion $\Delta$ v/v ∼ 10⁻¹⁵ to 10⁻¹². Interferometric coherence noise $\Delta$ L/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)=

\pi

, F(∞)=0. The shooting method gives a profile with characteristic mass M₀

\approx

1/R₀. Small fluctuations F(r,t) = F(r) +

\delta

(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

\approx

2.3 and m₃/m₁

\approx

4.1. Fixing m₁ = 125 GeV gives m₂

\approx

290 GeV, m₃

\approx

510 GeV, m₄

\approx

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

\times

2 mass matrix with eigenvalues m_

\pm

and angle

\theta

. Coupling modifications scale as

g_{h}

=

g_{SM}

cos

\theta

.

8–10. Collider and precision predictions

Production

\sigma

(pp

\to

h₂)

\approx

cos²

\theta \sigma

_SM(m₂), giving

\sigma

(h₂)

\approx

0.01–0.1

\times \sigma

_SM. Dominant decays h₂

\to

ZZ, WW, hh.

\Delta\rho \approx \epsilon

²

m_{h}

² ∼ 10⁻³. Higgs coupling deviations

\delta

g/g

\approx \theta

² ∼ 1–5 %.

11–12. Gravitational waves and interferometry

Dispersion

\omega

² = k²(1 +

\alpha

k/

\Lambda

_

\Phi

²) gives

\Delta

v/v ∼ 10⁻¹⁵ to 10⁻¹². Phase-manifold fluctuations induce interferometric noise

\Delta

L/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

\Delta\rho

∼ 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.

Suggested citation

Graham Fincham, Daniel Hilton. “QM III: Scalar Spectrum and Experimental Signatures.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-iii

@misc{pdt_qm_iii,
  title = {QM III: Scalar Spectrum and Experimental Signatures},
  author = {Graham Fincham and Daniel Hilton},
  url = {https://www.phasedifferentialtheory.com/papers/qm-iii}
}

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