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Anomalous g values of the electron and muon

Historically, the spin magnetic moment of the electron µ e or its gvalue g e has played a central role in modern physics, dating from its discovery in atomic optical spectroscopy and its subsequent incorporation in the Dirac theory of the electron, which predicted the value g e = 2 The experimental discovery in atomic microwave spectroscopy that g e was larger than 2 by a multiplicative factor of about 1 part in 103, g e =2.00238(10), together with the discovery of the Lamb shift in hydrogen (S=22 S 1/2 − 22 P 1/2), led to the development of modern quantum electrodynamics with its renormalization procedure. The theory enables us to calculate these effects precisely as finite radiative corrections. By now the experimental value of g e -2has been measured to about 4 ppb, and the theoretical value, which is expressed as a power series in the fine-structure constant a, has been evaluated to better than 1 ppb, assuming the value of α is known.