Scale Factorized-Quantum Field Theory: Eliminating renormalization ambiguities in QCD and QED
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918399387369472 |
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| author | Chishtie, Farrukh A. |
| author_facet | Chishtie, Farrukh A. |
| contents | 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, $a_{\mathrm{eff}}(Q)$ evolves with scheme-independent equations, with higher-order $β$-coefficients absorbed into Wilson coefficients. For the inclusive ratio $R_{e^{+}e^{-}}$, SF-QFT gives $R^{\mathrm{SF-QFT}}(31.6\,\mathrm{GeV}) = 1.05262 \pm 0.0005$, in excellent agreement with experiment ($1.0527 \pm 0.005$) while requiring calculations orders of magnitude simpler than conventional four-loop $\overline{\mathrm{MS}}$ 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 $a_e^{\text{theory}} = 0.001\,159\,652\,180\,61(76)$, differing from experiment by only $0.15σ$. The framework enables self-consistent extraction of $α_{\text{eff}}^{-1}(m_e) = 137.036005301$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scale Factorized-Quantum Field Theory: Eliminating renormalization ambiguities in QCD and QED Chishtie, Farrukh A. High Energy Physics - Phenomenology General Relativity and Quantum Cosmology High Energy Physics - Experiment High Energy Physics - Lattice High Energy Physics - Theory 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, $a_{\mathrm{eff}}(Q)$ evolves with scheme-independent equations, with higher-order $β$-coefficients absorbed into Wilson coefficients. For the inclusive ratio $R_{e^{+}e^{-}}$, SF-QFT gives $R^{\mathrm{SF-QFT}}(31.6\,\mathrm{GeV}) = 1.05262 \pm 0.0005$, in excellent agreement with experiment ($1.0527 \pm 0.005$) while requiring calculations orders of magnitude simpler than conventional four-loop $\overline{\mathrm{MS}}$ 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 $a_e^{\text{theory}} = 0.001\,159\,652\,180\,61(76)$, differing from experiment by only $0.15σ$. The framework enables self-consistent extraction of $α_{\text{eff}}^{-1}(m_e) = 137.036005301$. 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. |
| title | Scale Factorized-Quantum Field Theory: Eliminating renormalization ambiguities in QCD and QED |
| topic | High Energy Physics - Phenomenology General Relativity and Quantum Cosmology High Energy Physics - Experiment High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.09947 |