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The current status of the experimental and theoretical knowledge of the anomalous magnetic moment of the electron is reviewed, and a progress report of the precise numerical evaluation of the 4 loop contribution in perturbative QED is given. [Copyright &y& Elsevier]

In this Letter we calculate at high-precision the Laurent expansions in ϵ=(4−D)/2 of the 17 master integrals which appeared in the analytical calculation of 3-loop QED contribution to the electron g–2, using difference and differential equations. The coefficients of the expansions so obtained are in perfect agreement with all the analytical expressions already known. The values of coefficients not previously known will be used in the high-precision calculation of the 4-loop QED contribution to the electron g–2.

The contribution to the g−2 of the electron from the light-light graphs aixth order (three loops) in QED perturbation theory has been evaluated in closed analytical form. The analytic value is in excellent agreement with the most precise numerical evaluation existing in the literature.