# Anomalous magnetic dipole moment

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 "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

:$a = frac\left\{g-2\right\}\left\{2\right\}$

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 [See section 6.3 of Michael E. Peskin and Daniel V. Schroeder, "An Introduction to Quantum Field Theory", Addison-Wesley, Reading, 1995.] and the one-loop result is:

:$a = frac\left\{alpha\right\}\left\{2 pi\right\} approx .0011614$

where $alpha$ is the fine structure constant.This result was first found by Schwinger in 1948. [J. Schwinger, "Phys. Rev." 73, 416L (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. The prediction for the value of the muon anomalous magnetic moment includes three parts: α&mu;SM = α&mu;QED + α&mu;EW + α&mu;had. The first two components represent the photon and lepton loops, and the W boson and Z boson loops, respectively, and can be calculated precisely from first principles. The third term represents hadron loops, and cannot be calculated accurately from theory alone. It is estimated from experimental measurements of the ratio of hadronic to muonic cross sections (R) in e+e- collisons. As of November 2006, the measurement disagrees with the Standard Model by 3.4 standard deviations [cite journal
last = Hagiwara
first = K.
coauthors = Martin, A. D. and Nomura, Daisuke and Teubner, T.
title = Improved predictions for g-2 of the muon and alpha(QED)(M(Z)**2)
date = 2006
url = http://arxiv.org/abs/hep-ph/0611102
format = abstract
] , 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

ee also

* anomalous electric dipole moment
* g-factor

* [http://www.g-2.bnl.gov/physics/index.html Overview of the "g-2" experiment]

Wikimedia Foundation. 2010.

### См. также в других словарях:

• Anomalous electric dipole moment — In particle physics, the anomalous electric dipole moment, or the electric dipole moment of a particle in short, is the electric dipole moment of a particle. There is a symmetry, the CP symmetry, which if exact and unbroken will predict an… …   Wikipedia

• Electron magnetic dipole moment — In atomic physics, the magnetic dipole moment of an electron is caused by its intrinsic property of spin within a magnetic field. Explanation of magnetic momentThe electron is a negatively charged particle with angular momentum. A rotating… …   Wikipedia

• Moment Magnétique — Pour les articles homonymes, voir Moment. En physique, le moment magnétique est une grandeur vectorielle qui permet de mesurer l intensité d une source magnétique. La source peut être une distribution de courant, ou bien un matériau présentant un …   Wikipédia en Français

• Moment magnetique — Moment magnétique Pour les articles homonymes, voir Moment. En physique, le moment magnétique est une grandeur vectorielle qui permet de mesurer l intensité d une source magnétique. La source peut être une distribution de courant, ou bien un… …   Wikipédia en Français

• Moment magnétique — Pour les articles homonymes, voir Moment. En physique, le moment magnétique est une grandeur vectorielle qui permet de mesurer l intensité d une source magnétique. La source peut être une distribution de courant, ou bien un matériau présentant un …   Wikipédia en Français

• Earth's magnetic field — Computer simulation of the Earth s field in a normal period between reversals.[1] The tubes represent magnetic field lines, blue when the field points towards the center and yellow when away. The rotation axis of the Earth is centered and… …   Wikipedia

• Precision tests of QED — Quantum electrodynamics (QED), a relativistic quantum field theory of electrodynamics, is among the most stringently tested theories in physics.Precision tests of QED consist of measurements of the electromagnetic fine structure constant, α, in… …   Wikipedia

• Muon — The Moon s cosmic ray shadow, as seen in secondary muons generated by cosmic rays in the atmosphere, and detected 700 meters below ground, at the Soudan II detector Composition Elementary particle Statistics …   Wikipedia

• g-factor (physics) — For the acceleration related quantity in mechanics, see g force. A g factor (also called g value or dimensionless magnetic moment) is a dimensionless quantity which characterizes the magnetic moment and gyromagnetic ratio of a particle or nucleus …   Wikipedia

• Electron — For other uses, see Electron (disambiguation). Electron Experiments with a Crookes tube first demonstrated the particle nature of electrons. In this illustration, the profile of the cross shaped target is projected against the tube face at right… …   Wikipedia

### Поделиться ссылкой на выделенное

##### Прямая ссылка:
Нажмите правой клавишей мыши и выберите «Копировать ссылку»