Stochastic computation of $g-2$ in QED

TL;DR

This paper introduces a stochastic numerical method on the lattice to compute the electron's anomalous magnetic moment in QED, providing an independent check of traditional Feynman diagram calculations up to third order.

Contribution

Develops a lattice-based stochastic perturbation approach to calculate $g-2$ in QED without Feynman diagrams, enabling higher order estimations.

Findings

Successfully computed $g-2$ up to $ ext{order }\alpha^3$

Validated the method against known results

Offers a new independent computational approach

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.