Anomalous magnetic dipole moment

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 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 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 α 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 α3  and have been calculated up to order α5: 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, ae is known to an accuracy of around 1 part in 1 billion (109). This required measuring g to an accuracy of around 1 part in 1 trillion (1012). 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: