High-precision calculation of the 4-loop contribution to the electron g-2 in QED

Abstract

I have evaluated up to 1100 digits of precision the contribution of the 891 4-loop Feynman diagrams contributing to the electron $g$-$2$ in QED. The total mass-independent 4-loop contribution is $a_e=-1.912245764926445574152647167439830054060873390658725345\dots {\left(\frac{\alpha }{\pi }\right)}^4$. I have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{i\pi }{3}}$, $e^{\frac{2i\pi }{3}}$, $e^{\frac{i\pi }{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits.

14 pages, 3 figures, 3 tables v2: version published in PRL (specified "mass-independent contribution", figure 2 reformatted)

References in corpus (5)

• New determination of the fine structure constant and test of the quantum electrodynamics
• Tenth-Order Electron Anomalous Magnetic Moment --- Contribution of Diagrams without Closed Lepton Loops
• Revised value of the eighth-order electron g-2
• Revised value of the eighth-order QED contribution to the anomalous magnetic moment of the electron
• Analytical expressions of 3 and 4-loop sunrise Feynman integrals and 4-dimensional lattice integrals

Cited by in corpus (97)

• The anomalous magnetic moment of the muon in the Standard Model
• Measurement of the fine-structure constant as a test of the Standard Model
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Dispersion relation for hadronic light-by-light scattering: pion pole
• Combined explanations of $(g-2{)}_{\mu ,e}$ and implications for a large muon EDM
• Revised and Improved Value of the QED Tenth-Order Electron Anomalous Magnetic Moment
• Measurement of the Electron Magnetic Moment
• Hadronic vacuum polarization: $(g-2{)}_{\mu }$ versus global electroweak fits
• The muon $g$-2 and $\Delta \alpha$ connection
• Feynman Integrals and Intersection Theory
• Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Numbers and Functions in Quantum Field Theory
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Beta decays as sensitive probes of lepton flavor universality
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• A light complex scalar for the electron and muon anomalous magnetic moments
• Resolving electron and muon $g-2$ within the 2HDM
• Analytic Structure of all Loop Banana Amplitudes
• An analytic solution for the equal-mass banana graph
• Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops
• Stringent test of QED with hydrogenlike tin
• Electron and muon $g-2$ anomalies in general flavour conserving two Higgs doublets models
• Unveiling Hidden Physics at the LHC
• Global Analysis of Leptophilic Z' Bosons
• Muon $g-2$: A review
• Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
• New physics at the MUonE experiment at CERN
• Anomalies in Particle Physics
• Two-loop binding corrections to the electron gyromagnetic factor
• Ultrahigh-precision measurement of the $n=2$ triplet P fine structure of atomic helium using frequency-offset separated oscillatory fields
• The Role of Mesons in Muon g-2
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• $(\mathbf{g}-2{)}_{\mathbf{e},\mathbf{\mu }}$ in an extended inverse type-III seesaw
• Power-aligned 2HDM: a correlative perspective on $(g-2{)}_{e,\mu }$
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• Towards testing the magnetic moment of the tau at one part per million
• Non-Perturbative Effects in $\mu \to e\gamma$
• Type-X two Higgs doublet model in light of the muon $\mathbf{g}-2$: confronting Higgs and collider data
• Muon and electron $g-2$ anomalies in a flavor conserving 2HDM with an oblique view on the CDF $M_W$ value
• Four-loop wave function renormalization in QCD and QED
• The complete set of two-loop master integrals for Higgs + jet production in QCD
• Ultralight scalars in leptonic observables
• Science Case for the new High-Intensity Muon Beams HIMB at PSI
• New method of computing the contributions of graphs without lepton loops to the electron anomalous magnetic moment in QED
• State of the art in the determination of the fine structure constant and the ratio $h/m_{\mathrm{u}}$
• Atomki anomaly in gauged $U(1{)}_R$ symmetric model
• Neutrino masses and magnetic moments of electron and muon in the Zee Model
• Hadronic vacuum polarization contributions to the muon $g$-2 in the space-like region
• Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment
• Hadronic light-by-light scattering contribution to the muon g-2 on the lattice
• Simplified leptoquark models for precision $l_i\to l_f\gamma$ experiments: two-loop structure of $O({\alpha }_S{Y}^2)$ corrections
• Large $(g-2{)}_{\mu }$ and signals of decays $e_b\to e_a\gamma$ in a 3-3-1 model with inverse seesaw neutrinos
• The three-loop QED contributions to the $g-2$ of charged leptons with two internal fermion loops and a class of Kampé de Fériet series
• Low-energy lepton physics in the MRSSM: $(g-2{)}_{\mu }$, $\mu \to e\gamma$ and $\mu \to e$ conversion
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor
• The QED four-photon amplitudes off-shell: part 2
• The QED four -- photon amplitudes off-shell: part 1
• Lambert-W solves the noncommutative ${\Phi }^4$-model
• LIght scalars with lepton number to solve the $(g-2{)}_e$ anomaly
• High-precision calculation of the 4-loop QED contribution to the slope of the Dirac form factor
• An explanation of experimental data of $(g-2{)}_{e,\mu }$ in 3-3-1 models with inverse seesaw neutrinos
• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• The interplay between SM precision, BSM physics and measurements of ${\alpha }_{\mathrm{had}}$ in $\mu$-$e$ scattering
• QCD calculations for the LHC: status and prospects
• Circumventing Detector Backaction on a Quantum Cyclotron
• Some algebraic and arithmetic properties of Feynman diagrams
• Heavy singly charged Higgs bosons and inverse seesaw neutrinos as origins of large $(g-2{)}_{e,\mu }$ in two higgs doublet models
• On Laporta's 4-loop sunrise formulae
• Matching the heavy-quark fields in QCD and HQET at four loops
• High-precision four-loop mass and wave function renormalization in QED
• DREAM, a program for arbitrary-precision computation of dimensional recurrence relations solutions, and its applications
• An Introduction to Motivic Feynman Integrals
• Five-Particle Phase-Space Integrals in QCD
• Improved bound-electron g-factor theory through complete two-loop QED calculations
• Matrix Field Theory
• Hyperlogarithms in the theory of turbulence of infinite dimension
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$: a dispersive approach
• On Borwein's conjectures for planar uniform random walks
• $\mathbb{Q}$-linear dependence of certain Bessel moments
• Relativistic Quantum Kinetic Theory: Higher order contributions in assisted Schwinger pair production
• Light stringy states and the $g-2$ of the muon
• Heavy $Z^{\prime }$ Bosons in the Secluded $U(1{)}^{\prime }$ Model at Hadron Colliders
• Low-energy multi-photon scattering at tree-level and one-loop order in a homogeneous electromagnetic field
• Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals
• New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values
• Quantum Logic Spectroscopy of an Electron and Positron for Precise Tests of the Standard Model
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Worldline Modeling of Ultra-Intense Lasers for N-photon Scattering Processes
• $(g-2{)}_{e,\mu }$ and decays $e_b\to e_a\gamma$ in a $ \mbox{SU}(4)_L \otimes \mbox{U}(1)_X$ model with inverse seesaw neutrinos
• Tamed loops: A way to obtain finite loop results without UV divergences
• Numerical calculation of 5-loop QED contributions to the electron anomalous magnetic moment
• Something is wrong in the state of QED
• Flat Bundles on Function Manifolds and Evolution Equations in Quantum Field Theories
• LFV decays in a 3-4-1 model with minimal inverse seesaw neutrinos
• Theory and phenomenology of Dirac neutrinos