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Theory of the Anomalous Magnetic Moment of the Electron

Theory Center, IPNS, KEK, Tsukuba 305-0801, Japan
Nishina Center, RIKEN, Wako 351-0198, Japan
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602, Japan
Laboratory for Elementary Particle Physics, Cornell University, Ithaca, NY 14853, USA
Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusetts, Amherst, MA 01003, USA
Department of Physics, Saitama University, Saitama 338-8570, Japan
Author to whom correspondence should be addressed.
Atoms 2019, 7(1), 28;
Received: 27 November 2018 / Revised: 3 February 2019 / Accepted: 12 February 2019 / Published: 22 February 2019
(This article belongs to the Special Issue High Precision Measurements of Fundamental Constants)
PDF [564 KB, uploaded 25 February 2019]


The anomalous magnetic moment of the electron a e measured in a Penning trap occupies a unique position among high precision measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant α , with an effective parameter α / π . Both numerical and analytic evaluations of a e up to ( α / π ) 4 are firmly established. The coefficient of ( α / π ) 5 has been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been estimated. The sum of all these terms leads to a e ( theory ) = 1 159 652 181.606 ( 11 ) ( 12 ) ( 229 ) × 10 12 , where the first two uncertainties are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current best value of the fine-structure constant derived from the cesium recoil measurement: α 1 ( Cs ) = 137.035 999 046 ( 27 ) . The discrepancy between a e ( theory ) and a e ( ( experiment ) ) is 2.4 σ . Assuming that the standard model is valid so that a e (theory) = a e (experiment) holds, we obtain α 1 ( a e ) = 137.035 999 1496 ( 13 ) ( 14 ) ( 330 ) , which is nearly as accurate as α 1 ( Cs ) . The uncertainties are from the tenth-order QED term, hadronic term, and the best measurement of a e , in this order. View Full-Text
Keywords: electron anomalous magnetic moment; QED; perturbation theory electron anomalous magnetic moment; QED; perturbation theory

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Aoyama, T.; Kinoshita, T.; Nio, M. Theory of the Anomalous Magnetic Moment of the Electron. Atoms 2019, 7, 28.

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