A Curvature-Induced Log-Periodic Deformation of C9(q 2): Wave Confinement Theory and the LHCb B 0 → K ∗0µ+µ− Anomaly

A Curvature-Induced Log-Periodic Deformation of C9(q 2): Wave Confinement Theory and the LHCb B 0 → K ∗0µ+µ− Anomaly
Richard J. Reyes - April 22, 2026

Overview

This work introduces a curvature-driven deformation of the Wilson coefficient C₉(q²) in the b → s ℓ⁺ℓ⁻ sector, motivated by Wave Confinement Theory (WCT). The deformation takes the form of a log-periodic modulation arising from curvature-induced spectral structure in a confined wavefield.

The framework proposes that the observed deviations in B⁰ → K*⁰ μ⁺μ⁻ angular observables, particularly P′₅(q²), can be modeled as a structured, scale-dependent perturbation of C₉(q²), rather than a constant shift.

Core Result

The effective Wilson coefficient is modified as:

C₉^eff(q²) = C₉^SM + δC₉(q²)

with a curvature-induced deformation:

δC₉(q²) = A · cos(ω · log(q² / Λ²) + φ)

where:

• A — modulation amplitude
• ω — log-frequency
• Λ — curvature-defined scale
• φ — phase offset

This form produces localized deviations across q² consistent with LHCb measurements while preserving the global structure of the Standard Model.

Key Structure

The construction follows the chain:

wavefield dynamics
→ curvature feedback
→ spectral band selection
→ discrete scale structure
→ log-periodic modulation
→ deformation of C₉(q²)
→ angular observable deviations

The log-periodicity arises from discrete scale invariance induced by curvature locking across spectral shells.

Physical Interpretation

Within this framework:

• C₉(q²) encodes the effective response of a curvature-regulated field
• deviations are interpreted as spectral interference effects rather than new particle exchange
• the anomaly reflects structured modulation in the underlying wavefield rather than a constant offset

No additional degrees of freedom are introduced; the effect emerges from internal geometric dynamics.

Scope and Limitations

This work does not claim:

• a full global fit across all flavor observables
• resolution of all anomalies in the b → s ℓ⁺ℓ⁻ sector
• a complete embedding within the Standard Model effective field theory

The deformation is presented as a minimal, structured ansatz motivated by curvature dynamics.

Open problems include:

• global fit validation across all Wilson coefficients
• correlation with other decay channels
• derivation of parameters (A, ω, Λ, φ) from first principles

Significance

If supported by further analysis, this framework suggests:

• anomalies in flavor physics may arise from geometric spectral structure
• log-periodic modulations provide a new class of signatures beyond constant Wilson shifts
• curvature-based field dynamics can produce observable effects at collider scales

More broadly, the work proposes that certain deviations from Standard Model predictions may reflect underlying spectral structure rather than new particle content.

Keywords

flavor physics; LHCb; Wilson coefficient; C₉(q²); B⁰ → K*⁰ μ⁺μ⁻; angular anomaly; log-periodic modulation; discrete scale invariance; spectral structure; wave confinement theory

Author & Contact

Author: Richard J. Reyes
ORCID iD: 0009-0005-5975-8718
Email: reyes.ricky30@gmail.com