The "Dirac" magnetic moment, corresponding to tree-level Feynman diagrams, can be calculated from the Dirac equation. It is usually expressed in terms of the g-factor; the Dirac equation predicts $g\; =\; 2$. For particles such as the electron, this classical result differs from the observed value by a small fraction of a percent. The difference is the anomalous magnetic moment, denoted $a$ and defined as

$a\; =\; frac\{g-2\}\{2\}$

The one-loop contribution to the anomalous magnetic moment of the electron is found by calculating the vertex function shown in the diagram on the right. The calculation is relatively straightforward and the one-loop result is:

$a\; =\; frac\{alpha\}\{2\; pi\}\; approx\; .0011614$

where $alpha$ is the fine structure constant. This result was first found by Schwinger in 1948. As of 1997, the coefficients of the QED formula for the anomalous magnetic moment of the electron have been calculated through order $alpha^4$. The QED prediction agrees with the experimentally measured value to more than 10 significant figures, making the magnetic moment of the electron the most accurately verified prediction in the history of physics. (See precision tests of QED for details.)

The anomalous magnetic moment of the muon is calculated in a similar way; its measurement provides a precision test of the Standard Model. As of November 2006, the measurement disagrees with the Standard Model by 3.4 standard deviations, suggesting beyond the Standard Model physics may be having an effect.

Composite particles often have a huge anomalous magnetic moment. This is true for the proton, which is made up of charged quarks, and the neutron, which has a magnetic moment even though it is electrically neutral.

Notes