Loop Dynamics Framework: Unifying Particle Mass Hierarchy, Lepton Anomalies, and the Cosmological Constant

Unifying Particle Physics and Cosmology through Loop Dynamics: A Data-Grounded, Geometric Framework

This paper presents a novel and comprehensive theoretical framework—Loop Dynamics (LD)—that reimagines fundamental particles as quantized, vibrating-rotating loops embedded in a dynamic spacetime fabric. Distinct from prior unification attempts, LD emerges not from abstract conjecture but through a rigorous inductive analysis of high-precision experimental data, which identifies deep structural regularities in the mass spectrum of leptons, mesons, and baryons.

From this empirical foundation, the author develops a deductive Lagrangian model that accounts for particle rest mass, vibrational amplitude, and internal angular dynamics using a minimal set of physically motivated constants. Specifically, LD introduces:

• A spacetime tension parameter P=4πc^4/G

• A universal loop impedance Z, and

• A momentum-based scaling constant alpha_0

which, together with integer-valued mode numbers, define all particle properties dynamically. A key innovation is the phenomenological mass index (N_{v,X}phenom) a dimensionless expression derived from empirical mass ratios that now functions as a structural input into the theory's dynamical core.

The LD model achieves several landmark results:

• 🔬 Mass Prediction Across Scales: Using a single mass hierarchy formula involving Euler’s number and integer mode structures, LD reproduces observed particle masses—including those of the muon, tau, proton, and mesons—with sub-0.5% average error, requiring no ad hoc Yukawa couplings or fine-tuning.

• 🧲 Lepton g−2 Anomalies: The model offers a geometric explanation for anomalous magnetic moments, calculating aℓa_\ellaℓ values from internal loop vibrations. Notably, it predicts the muon's g−2 with a deviation of only −0.178%, providing a potentially testable resolution to one of the most persistent anomalies in particle physics.

• 🌌 Cosmological Constant: LD proposes a new origin for the cosmological constant as a function of vacuum loop amplitude. Remarkably, for an effective vacuum mode number Nvac=3/2, the predicted Λ deviates by only −2.58% from Planck 2018 data—representing a one-hundred-twenty-orders-of-magnitude improvement over conventional quantum field theory estimates.

Conceptually, LD offers a unifying language that bridges quantum mechanics and general relativity by embedding mass, charge, and vacuum energy within a shared geometric dynamical origin. The particle Lagrangian formulated in the paper treats each particle as an oscillator-rotor system, yielding exact energy relations that reproduce relativistic rest energy from internal vibration modes.

This framework distinguishes itself by maintaining full dimensional consistency, deriving all quantities from first principles using only two calibrated constants, and requiring no speculative extra dimensions or new particles. It also resonates philosophically with modern emergent gravity ideas, yet retains calculational precision grounded in conventional physics.

In uniting mass generation, electromagnetic anomalies, and cosmological tension under a single, dynamically consistent model, Loop Dynamics stands as a compelling and parsimonious candidate for a next-generation unified theory.