Stochastic computation of $g-2$ in QED

Abstract

We perform a numerical computation of the anomalous magnetic moment ($g-2$) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of $g-2$ without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the ${\alpha }^3$ order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

35 pages, 5 figures, 2 tables, the version to appear in JHEP

References in corpus (5)

• QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons
• Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops
• Eighth-Order Vacuum-Polarization Function Formed by Two Light-by-Light-Scattering Diagrams and its Contribution to the Tenth-Order Electron g-2
• Tenth-Order Lepton Anomalous Magnetic Moment -- Second-Order Vertex Containing Two Vacuum Polarization Subdiagrams, One Within the Other
• Tenth-order lepton g-2: Contribution of some fourth-order radiative corrections to the sixth-order g-2 containing light-by-light-scattering subdiagrams

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