Scale Factorized-Quantum Field Theory: Eliminating renormalization ambiguities in QCD and QED

Abstract We introduce Scale Factorized-Quantum Field Theory (SF-QFT), a framework performing path-integral factorization of ultraviolet and infrared momentum modes at a physical scale Q* before perturbative expansion through Effective Dynamical Renormalization (EDR) with Principle of Observable Effective Matching (POEM) constraints. This yields completely scale and scheme invariant observables. Because the two-loop β-function is universal, aeff (Q) evolves with scheme-independent equations, with higher-order β-coefficients absorbed into Wilson coefficients. For the inclusive ratio R₄^+e^{-}, SF-QFT gives RSF-QFT (31. 6 GeV) = 1. 05262 ± 0. 0005, in excellent agreement with experiment (1. 0527 ± 0. 005) while requiring calculations orders of magnitude simpler than conventional four-loop MS approaches. SF-QFT generates universal algebraic recursion relations producing all higher-order contributions without additional Feynman diagrams. For QED, the formalism yields scheme-independent predictions for the electron anomalous magnetic moment with aₑ^theory = 0. 001\, 159\, 652\, 180\, 61 (76), differing from experiment by only 0. 15σ. The framework enables self-consistent extraction of ₄₅₅^-1 (mₑ) = 137. 036005301. SF-QFT represents a paradigm shift, replacing pursuit of ever-higher loop orders with a unified framework eliminating renormalization ambiguities through systematic EDR and POEM implementation.