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

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 R_e⁺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 MS̄ 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 aₑᵗʰᵉᵒʳʸ = 0.001\, 159\, 652\, 180\, 61(76), differing from experiment by only 0.15σ. The framework enables self-consistent extraction of α eff⁻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.