Improved α4 term of the electron anomalous magnetic moment -: art. no. 013003

We report a new value of electron g-2, or a(e), from 891 Feynman diagrams of order alpha(4). The FORTRAN codes of 373 diagrams containing closed electron loops have been verified by at least two independent formulations. For the remaining 518 diagrams, which have no closed lepton loop, verification by a second formulation is not yet attempted because of the enormous amount of additional work required. However, these integrals have structures that allow extensive cross-checking as well as detailed comparison with lower-order diagrams through the renormalization procedure. No algebraic error has been uncovered for them. The numerical evaluation of the entire alpha(4) term by the integration routine VEGAS gives -1.7283(35)(alpha/pi)(4), where the uncertainty is obtained by careful examination of error estimates by VEGAS. This leads to a(e) = 1 159 652 175.86(0.10)(0.26)(8.48) x 10(-12), where the uncertainties come from the alpha(4) term, the estimated uncertainty of alpha(5) term, and the inverse fine structure constant, alpha(-1) = 137.036 000 3(10), measured by atom interferometry combined with a frequency comb technique, respectively. The inverse fine structure constant alpha(-1)(a(e)) derived from the theory and the Seattle measurement of a(e) is 137.035 998 83(51).