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. Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Motivation and history When calculating Scattering cross sections in Particle physics, the interaction between particles can be described In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current

One-loop correction to the fermion's magnetic dipole moment.

The "Dirac" magnetic moment, corresponding to tree-level Feynman diagrams, can be calculated from the Dirac equation. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current In Physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides It is usually expressed in terms of the g-factor; the Dirac equation predicts g = 2. For the acceleration-related quantity in mechanics see ''g''-force. For particles such as the electron, this classical result differs from the observed value by a small fraction of a percent. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The difference is the anomalous magnetic moment, denoted a and defined as

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. In Quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory. The calculation is relatively straightforward^[1] and the one-loop result is:

where α is the fine structure constant. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing This result was first found by Schwinger in 1948. Julian Seymour Schwinger ( February 12, 1918 &ndash July 16, 1994) was an American Theoretical physicist. ^[2] As of 1997, the coefficients of the QED formula for the anomalous magnetic moment of the electron have been calculated through order α⁴. 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. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. (See precision tests of QED for details. Quantum electrodynamics ( QED) a relativistic quantum field theory of electrodynamics is among the most stringently tested theories in Physics. )

The anomalous magnetic moment of the muon is calculated in a similar way; its measurement provides a precision test of the Standard Model. The muon (from the letter mu (μ--used to represent it is an Elementary particle with negative Electric charge and a spin of 1/2 The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles The prediction for the value of the muon anomalous magnetic moment includes three parts: α_μ^SM = α_μ^QED + α_μ^EW + α_μ^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. R is the ratio of the Hadronic cross section to the Muon cross section in Electron - Positron collisions R = As of November 2006, the measurement disagrees with the Standard Model by 3. 4 standard deviations^[3], suggesting beyond the Standard Model physics may be having an effect. In Probability and Statistics, the standard deviation is a measure of the dispersion of a collection of values In Physics, the Standard Model of Particle physics is currently the best description of all experimental data

One-loop MSSM corrections to the muon g-2 involving a neutralino and a smuon, and a chargino and a muon sneutrino respectively. In Particle physics, the neutralino is a hypothetical particle part of the doubling of the menagerie of particles predicted by supersymmetric theories In Particle physics, a sfermion is any of the class of spin -0 Superpartners of ordinary Fermions appearing in supersymmetric extensions The chargino is a hypothetical Supersymmetric particle. It refers to the mass Eigenstates of a charged Superpartner, i In Particle physics, a sfermion is any of the class of spin -0 Superpartners of ordinary Fermions appearing in supersymmetric extensions

Composite particles often have a huge anomalous magnetic moment. In Physics, a bound state is a composite of two or more building blocks ( particles or bodies) that behaves as a single object 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. The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive In Physics, a quark (kwɔrk kwɑːk or kwɑːrk is a type of Subatomic particle. This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron.

Notes

1. ^ See section 6. 3 of Michael E. Peskin and Daniel V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley, Reading, 1995.
2. ^ J. Schwinger, Phys. Rev. 73, 416L (1948)
3. ^ Hagiwara, K. ; Martin, A. D. and Nomura, Daisuke and Teubner, T. (2006). "Improved predictions for g-2 of the muon and alpha(QED)(M(Z)**2)" (abstract).  

See also

• anomalous electric dipole moment
• g-factor

External links

• Overview of the g-2 experiment