What question did this study set out to answer?

This research aims to establish a connection between the muon g−2 anomaly and FCNC processes using Granular Entropic Physics.

April 5, 2026Open Access

Universal Operator Scaling from Critical Spacetime: Linking Muon g−2 and FCNC in Granular Entropic Physics

Key Points

This research aims to establish a connection between the muon g−2 anomaly and FCNC processes using Granular Entropic Physics.
Developed a scaling framework based on Granular Entropic Physics (GEP).
Derived the fluctuation exponent α and the universal operator scaling dimension Δ_O.
Analyzed the dipole and four-fermion operators with regard to their anomalous dimensions and network stiffness.
Predicted the relationships between FCNC and muon g−2 based on critical network structures.
Established a parameter-free relation linking FCNC anomalies to the muon g−2 anomaly.
Demonstrated that the scaling dimensions yield results consistent with experimental anomalies without introducing new particles.
Identified an enhancement factor that predicts increased rates of FCNC transitions.

Abstract

We present a unified scaling framework within Granular Entropic Physics (GEP) that connects two persistent anomalies in particle physics — the muon anomalous magnetic moment deviation and the excess in the ultra-rare kaon decay K+ → π+νν̄ reported by NA62 — as distinct projections of a single critical network structure. Starting from the fluctuation exponent α = 8/3, derived independently from the requirement that the cosmological constant be scale-independent, we obtain a universal operator scaling dimension ΔO = α/2 = 4/3 and an operator-dependent network stiffness κₑff (O) ~ ξ^ΔO, where ξ is the correlation length near the critical point Kcrit. The dipole operator governing g−2 carries anomalous dimension ΔD ≈ 3, arising from a topological chirality flip in the Möbius defect picture with energy cost E ~ 1/L. The FCNC four-fermion operator carries ΔF ≈ 1, requiring no chirality flip. This hierarchy naturally yields κₑff (dipole) ~ 10⁶–10⁷ and κₑff (FCNC) ~ 10–100, reproducing δa_μ ~ 10⁻⁹ and δBR/BR ~ 10–20% without new particles. An enhancement factor Z₃ × Z₂ × log ξ ~ 50 for FCNC transitions is derived from the three inequivalent classes of edge-based loops in the tetrahedral network and the Möbius twist degeneracy — not fitted to data. The central result is a parameter-free master relation: δFCNC ~ (δa_μ) ^1/3, linking the kaon anomaly to the muon g−2 through a single critical exponent. This prediction is testable at Belle II, KOTO, and future precision experiments.

Universal Operator Scaling from Critical Spacetime: Linking Muon g−2 and FCNC in Granular Entropic Physics

Key Points

Abstract

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