What question did this study set out to answer?

To propose a unified theory that resolves mass singularities and sheds light on dark matter phenomenology.

March 3, 2026Open Access

Dynamic Modulation of Relativistic Color-Dipole Fields: A Unified Theory for Mass Singularity Resolution and Dark Matter Phenomenology

Key Points

To propose a unified theory that resolves mass singularities and sheds light on dark matter phenomenology.
Developed a Dynamic Modulation Equation (DME) to describe relativistic mass behavior.
Introduced a Saturation Operator (ф) to replace the Lorentz factor in calculations.
Conducted numerical simulations to validate the proposed model and its effects at ultra-relativistic speeds.
Eliminated energy singularity at high velocities, introducing a finite Saturation Scale (Qs).
Explained galactic-scale gravitational anomalies as evidence of field stiffness linked to orbital velocities.
Demonstrated the 'Plateau Effect' in numerical simulations and provided a mathematical resolution for the 'Ridge Effect' observed in LHC collisions.

Abstract

MANUSCRIPT FOR THEORETICAL PHYSICS Title: Dynamic Modulation of Relativistic Color-Dipole Fields: A Unified Theory for Mass Singularity Resolution and Dark Matter Phenomenology AUTHOR:Volkan Çelik, Chemist / Research InitiativeTheoretical Physics Division / Independent Researcher Subject: High Energy Physics - Phenomenology / Quantum Chromodynamics / Cosmology DATE OF SUBMISSION: March 1, 2026 STATUS: Peer-Review Pending / Theoretical Framework AuthenticatedVERSION: 1.0.4 (Unified Field Edition ABSTRACT: We propose a novel unified framework that redefines the interaction between relativistic particle velocity and the Quantum Chromodynamic (QCD) vacuum. Traditionally, mass-energy equivalence leads to a Lorentz singularity as ν → c. By introducing the Dynamic Modulation Equation (DME), we demonstrate that the relativistic increase in mass is a manifestation of color-dipole field saturation. Our model successfully eliminates the energy singularity, replacing it with a finite Saturation Scale (Qs) This manuscript introduces a groundbreaking unified framework, Dynamic Modulation Theory (DMT), which posits that the relativistic increase in particle mass is a manifestation of the quantum vacuum's color-dipole field impedance. By replacing the traditional Lorentz factor with a velocity-dependent Saturation Operator (ф) we demonstrate the elimination of the energy singularity (E → ∞) as ν → c, replacing it with a finite Saturation Scale (Qs). Furthermore, the theory provides a parsimonious solution to the Dark Matter problem by identifying galactic-scale gravitational anomalies as a macroscopic manifestation of field stiffness induced by orbital velocities. We present numerical simulations validating the "Plateau Effect" at ultra-relativistic speeds and offer a mathematical resolution to the "Ridge Effect" observed in LHC high-multiplicity collisions. KEYWORDS: QCD (Quantum Chromodynamics) Color-Dipole Model (CDM) Relativistic Saturation Singularity Resolution Non-Particle Dark Matter Dynamic Modulation Equation (DME) CLASSIFICATION (PACS/JCS): 12.38.-t (Quantum Chromodynamics) 12.39.Mk (Glueball and Nonstandard Mesons) 95.35.+d (Dark Matter) 03.30.+p (Special Relativity)

Dynamic Modulation of Relativistic Color-Dipole Fields: A Unified Theory for Mass Singularity Resolution and Dark Matter Phenomenology

Key Points

Abstract

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