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Concept
Anomalous magnetic dipole moment
Summary
In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. (The magnetic moment, also called magnetic dipole moment, is a measure of the strength of a magnetic source.)
The "Dirac" magnetic moment, corresponding to tree-level Feynman diagrams (which can be thought of as the classical result), can be calculated from the Dirac equation. It is usually expressed in terms of the g-factor; the Dirac equation predicts . 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 and defined as
The one-loop contribution to the anomalous magnetic moment—corresponding to the first and largest quantum mechanical correction—of the electron is found by calculating the vertex function shown in the adjacent diagram. The calculation is relatively straightforward and the one-loop result is:
where is the fine-structure constant. This result was first found by Julian Schwinger in 1948 and is engraved on his tombstone. As of 2016, the coefficients of the QED formula for the anomalous magnetic moment of the electron are known analytically up to and have been calculated up to order :
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 current experimental value and uncertainty is:
According to this value, is known to an accuracy of around 1 part in 10 billion (1010). This required measuring to an accuracy of around 1 part in 10 trillion (1013).
The anomalous magnetic moment of the muon is calculated in a similar way to the electron. The prediction for the value of the muon anomalous magnetic moment includes three parts:
Of the first two components, represents the photon and lepton loops, and the W boson, Higgs boson and Z boson loops; both can be calculated precisely from first principles.
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