New Value of theα3Electron Anomalous Magnetic Moment

Abstract

Highly accurate numerical evaluation of the sixth-order term of the electron anomalous magnetic moment a, has detected an error in the analytic value of a fourth-order infrared-divergent integral, which is needed to obtain the best estimate of the n term as a combination of analytic values of 67 Feynman diagrams and numerical values of 5 diagrams for which no analytic results are known. Correction of this error leads to a small but significant revision of the u term. As a consequence the fine structure constant n determined from theory and experiment of a, is reduced by 55 && 10 PACS numbers: 12.20.Ds, 06.20.Jr, 12.20.Fv, 13.40.Em The anomalous magnetic moment of the electron a, is one of the simplest quantities precisely calculable from first principles. Furthermore, it has been measured very accurately [1]: a, (expt) = 1159652188. 4(4.3) X 10 ' .(1) Thus it plays a crucial role in testing the validity of QED, or, more generally, the standard model. An even more rigorous test will become feasible when the forthcoming experiments are completed [2]. To make such a test meaningful, however, it is necessary to improve the sixthorder (n ) and eighth-order (n") terms of a, . This paper reports the result of a new numerical evaluation of the n3 term. All 72 Feynman diagrams contributing to the n3 term have been evaluated numerically [3], and all but 5 are now known analytically [4 -6]. The new calculation confirms the analytic results to a much higher degree, and reduces the uncertainty in the remaining 5 diagrams by an order of magnitude. More importantly, however, improved precision of the calculation has led to the discovery of a small error in the analytic value of a fourth-order infrared-divergent (IR-divergent) integral, which is needed to obtain the best estimate of the n3 term as a "hybrid" of analytic values of 67 Feynman diagrams and numerical values of the remaining 5 diagrams. Correction of this error leads to a small (0.44%) but significant revision of the a term. This has the effect of reducing the fine structure constant n determined from theory and experiment of a, by 55 X 10The QED part of the contribution can be expressed as a, = At + A2(m, /m~) + A2(m, /m, ) At = At (n/vr) + At (a/n) (2) (4) + A, (n/~) + A, (n/~) +3 (8) representing 1, 7, 72, and 891 Feynman diagrams, respectively, have been evaluated. Previously reported values of these coefficients are [3] Ai = 05, (2) 0.328 478 965. . . , At = 1.176 11(42), AI = -1.434(138) . (4) Ai and A~are known analytically. The value of A~is (2) (4) (~) . determined by purely numerical means using the Monte Carlo integration routine vEGAs [7]. On the other hand, the value of At quoted in (4) is a "hybrid" obtained by (6) combining the analytic results for 51 diagrams and the best numerical values of 21 diagrams for which no exact values were available. (Of the latter, 16 have since been evaluated analytically [5]. ) 22 of the diagrams contributing to A~contain closed (6) electron loops of vacuum-polarization or light-light scattering type. Numerical and an...

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