In
quantum electrodynamicsQuantum electrodynamics is a relativistic quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s. It basically describes how light and matter interact. More specifically it deals with the interactions between electrons, positrons and photons...
, the
anomalous magnetic moment of a particle is a contribution of effects of
quantum mechanicsQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
, expressed by
Feynman diagramIn quantum field theory a Feynman diagram is an intuitive graphical representation of a contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory....
s with loops, to the
magnetic momentThe magnetic moment of a system is a measure of the strength and the direction of its magnetism. More technically , the term magnetic moment of a system usually refers to its magnetic dipole moment, and quantifies the contribution...
of that particle. (The "
magnetic momentThe magnetic moment of a system is a measure of the strength and the direction of its magnetism. More technically , the term magnetic moment of a system usually refers to its magnetic dipole moment, and quantifies the contribution...
", also called "magnetic dipole moment", is a measure of the strength of a magnetic source.)
The "Dirac"
magnetic momentThe magnetic moment of a system is a measure of the strength and the direction of its magnetism. More technically , the term magnetic moment of a system usually refers to its magnetic dipole moment, and quantifies the contribution...
, corresponding to tree-level Feynman diagrams, can be calculated from the
Dirac equationIn physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 which provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special...
. It is usually expressed in terms of the
g-factorA g-factor is a dimensionless quantity which characterizes the magnetic moment and gyromagnetic ratio of a particle or nucleus...
; the Dirac equation predicts .
In
quantum electrodynamicsQuantum electrodynamics is a relativistic quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s. It basically describes how light and matter interact. More specifically it deals with the interactions between electrons, positrons and photons...
, the
anomalous magnetic moment of a particle is a contribution of effects of
quantum mechanicsQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
, expressed by
Feynman diagramIn quantum field theory a Feynman diagram is an intuitive graphical representation of a contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory....
s with loops, to the
magnetic momentThe magnetic moment of a system is a measure of the strength and the direction of its magnetism. More technically , the term magnetic moment of a system usually refers to its magnetic dipole moment, and quantifies the contribution...
of that particle. (The "
magnetic momentThe magnetic moment of a system is a measure of the strength and the direction of its magnetism. More technically , the term magnetic moment of a system usually refers to its magnetic dipole moment, and quantifies the contribution...
", also called "magnetic dipole moment", is a measure of the strength of a magnetic source.)
The "Dirac"
magnetic momentThe magnetic moment of a system is a measure of the strength and the direction of its magnetism. More technically , the term magnetic moment of a system usually refers to its magnetic dipole moment, and quantifies the contribution...
, corresponding to tree-level Feynman diagrams, can be calculated from the
Dirac equationIn physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 which provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special...
. It is usually expressed in terms of the
g-factorA g-factor is a dimensionless quantity which characterizes the magnetic moment and gyromagnetic ratio of a particle or nucleus...
; the Dirac equation predicts . For particles such as the
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
, 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
Anomalous magnetic moment of Electron
The one-loop contribution to the anomalous magnetic moment of the electron is found by calculating the
vertex functionIn quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory...
shown in the diagram on the right. The calculation is relatively straightforward and the one-loop result is:
where is the fine structure constant.
This result was first found by
SchwingerJulian Seymour Schwinger was an American theoretical physicist. He is best known for his work on the theory of quantum electrodynamics, in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order.Schwinger is recognized as one of the...
in 1948. As of 1997, the coefficients of the QED formula for the anomalous magnetic moment of the electron have been calculated through 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
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
. (See
precision tests of QEDQuantum electrodynamics , a relativistic quantum field theory of electrodynamics, is among the most stringently tested theories in physics....
for details.)
Anomalous magnetic moment of Muon
The anomalous magnetic moment of the
muonThe muon is an elementary particle similar to the electron, with negative electric charge and a spin of . Together with the electron, the tauon, and the three neutrinos, it is classified as a lepton. It is the unstable subatomic particle with the second longest mean lifetime , behind the neutron...
is calculated in a similar way; its measurement provides a precision test of the
Standard ModelThe Standard Model of particle physics is a theory of three of the four known fundamental interactions and the elementary particles that take part in these interactions. These particles make up all visible matter in the universe...
. The prediction for the value of the muon anomalous magnetic moment includes three parts: α
μSM = α
μQED + α
μEW + α
μhad. 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 (
RR is the ratio of the hadronic cross section to the muon cross section in electron-positron collisions:where the superscript indicates that the cross section has been corrected for initial state radiation....
) in e
+e
- collisions. As of November 2006, the measurement disagrees with the Standard Model by 3.4
standard deviationIn probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though...
s, suggesting
beyond the Standard ModelIn physics, the Standard Model of particle physics is currently the best description of all experimental data.Nevertheless, there are reasons to think that there are phenomena that are not accurately described by this theory and...
physics may be having an effect.
Anomalous magnetic moment of Composite particle
Composite particles often have a huge anomalous magnetic moment. This is true for the
protonThe proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H
+...
, which is made up of charged
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never found in...
s, and the
neutronThe neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutron are usually found in atomic nuclei. The nuclei of most atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of protons in a...
, which has a magnetic moment even though it is electrically neutral.
Alternatively, the formula
provides a value to the limit of experimental error.
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