A g-factor (also called g value) is a dimensionless quantity that characterizes the
magnetic moment and angular momentum of an atom, a particle or the
nucleus. It is the ratio of the magnetic moment (or, equivalently, the
gyromagnetic ratio) of a particle to that expected of a classical particle of the same charge and angular momentum. In nuclear physics, the
nuclear magneton replaces the classically expected magnetic moment (or gyromagnetic ratio) in the definition. The two definitions coincide for the proton.
The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by [1]
Protons, neutrons, nuclei, and other composite baryonic particles have magnetic moments arising from their spin (both the spin and magnetic moment may be zero, in which case the g-factor is undefined). Conventionally, the associated g-factors are defined using the nuclear magneton, and thus implicitly using the proton's mass rather than the particle's mass as for a Dirac particle. The formula used under this convention is
There are three magnetic moments associated with an electron: one from its spin angular momentum, one from its orbital angular momentum, and one from its total angular momentum (the quantum-mechanical sum of those two components). Corresponding to these three moments are three different g-factors:
The most known of these is the electron spin g-factor (more often called simply the electron g-factor), ge, defined by
The z-component of the magnetic moment then becomes
The value gs is roughly equal to 2.002319 and is known to extraordinary precision – one part in 1013. [2] The reason it is not precisely two is explained by quantum electrodynamics calculation of the anomalous magnetic dipole moment. [3] The spin g-factor is related to spin frequency for a free electron in a magnetic field of a cyclotron:
Secondly, the electron orbital g-factor, gL, is defined by
For a finite-mass nucleus, there is an effective g value [4]
Thirdly, the Landé g-factor, gJ, is defined by
The muon, like the electron, has a g-factor associated with its spin, given by the equation
That the muon g-factor is not quite the same as the electron g-factor is mostly explained by quantum electrodynamics and its calculation of the anomalous magnetic dipole moment. Almost all of the small difference between the two values (99.96% of it) is due to a well-understood lack of heavy-particle diagrams contributing to the probability for emission of a photon representing the magnetic dipole field, which are present for muons, but not electrons, in QED theory. These are entirely a result of the mass difference between the particles.
However, not all of the difference between the g-factors for electrons and muons is exactly explained by the Standard Model. The muon g-factor can, in theory, be affected by physics beyond the Standard Model, so it has been measured very precisely, in particular at the Brookhaven National Laboratory. In the E821 collaboration final report in November 2006, the experimental measured value is 2.0023318416(13), compared to the theoretical prediction of 2.00233183620(86). [5] This is a difference of 3.4 standard deviations, suggesting that beyond-the-Standard-Model physics may be a contributory factor. The Brookhaven muon storage ring was transported to Fermilab where the Muon g–2 experiment used it to make more precise measurements of muon g-factor. On April 7, 2021, the Fermilab Muon g−2 collaboration presented and published a new measurement of the muon magnetic anomaly. [6] When the Brookhaven and Fermilab measurements are combined, the new world average differs from the theory prediction by 4.2 standard deviations.
Particle | Symbol | g-factor | Relative standard uncertainty |
---|---|---|---|
electron | ge | −2.00231930436092(36) | 1.8×10−13 [7] |
muon | gμ | −2.00233184123(82) | 4.1×10−10 [8] |
proton | gp | +5.5856946893(16) | 2.9×10−10 [9] |
neutron | gn | −3.82608552(90) | 2.4×10−7 [10] |
The electron g-factor is one of the most precisely measured values in physics. [2]
A g-factor (also called g value) is a dimensionless quantity that characterizes the
magnetic moment and angular momentum of an atom, a particle or the
nucleus. It is the ratio of the magnetic moment (or, equivalently, the
gyromagnetic ratio) of a particle to that expected of a classical particle of the same charge and angular momentum. In nuclear physics, the
nuclear magneton replaces the classically expected magnetic moment (or gyromagnetic ratio) in the definition. The two definitions coincide for the proton.
The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by [1]
Protons, neutrons, nuclei, and other composite baryonic particles have magnetic moments arising from their spin (both the spin and magnetic moment may be zero, in which case the g-factor is undefined). Conventionally, the associated g-factors are defined using the nuclear magneton, and thus implicitly using the proton's mass rather than the particle's mass as for a Dirac particle. The formula used under this convention is
There are three magnetic moments associated with an electron: one from its spin angular momentum, one from its orbital angular momentum, and one from its total angular momentum (the quantum-mechanical sum of those two components). Corresponding to these three moments are three different g-factors:
The most known of these is the electron spin g-factor (more often called simply the electron g-factor), ge, defined by
The z-component of the magnetic moment then becomes
The value gs is roughly equal to 2.002319 and is known to extraordinary precision – one part in 1013. [2] The reason it is not precisely two is explained by quantum electrodynamics calculation of the anomalous magnetic dipole moment. [3] The spin g-factor is related to spin frequency for a free electron in a magnetic field of a cyclotron:
Secondly, the electron orbital g-factor, gL, is defined by
For a finite-mass nucleus, there is an effective g value [4]
Thirdly, the Landé g-factor, gJ, is defined by
The muon, like the electron, has a g-factor associated with its spin, given by the equation
That the muon g-factor is not quite the same as the electron g-factor is mostly explained by quantum electrodynamics and its calculation of the anomalous magnetic dipole moment. Almost all of the small difference between the two values (99.96% of it) is due to a well-understood lack of heavy-particle diagrams contributing to the probability for emission of a photon representing the magnetic dipole field, which are present for muons, but not electrons, in QED theory. These are entirely a result of the mass difference between the particles.
However, not all of the difference between the g-factors for electrons and muons is exactly explained by the Standard Model. The muon g-factor can, in theory, be affected by physics beyond the Standard Model, so it has been measured very precisely, in particular at the Brookhaven National Laboratory. In the E821 collaboration final report in November 2006, the experimental measured value is 2.0023318416(13), compared to the theoretical prediction of 2.00233183620(86). [5] This is a difference of 3.4 standard deviations, suggesting that beyond-the-Standard-Model physics may be a contributory factor. The Brookhaven muon storage ring was transported to Fermilab where the Muon g–2 experiment used it to make more precise measurements of muon g-factor. On April 7, 2021, the Fermilab Muon g−2 collaboration presented and published a new measurement of the muon magnetic anomaly. [6] When the Brookhaven and Fermilab measurements are combined, the new world average differs from the theory prediction by 4.2 standard deviations.
Particle | Symbol | g-factor | Relative standard uncertainty |
---|---|---|---|
electron | ge | −2.00231930436092(36) | 1.8×10−13 [7] |
muon | gμ | −2.00233184123(82) | 4.1×10−10 [8] |
proton | gp | +5.5856946893(16) | 2.9×10−10 [9] |
neutron | gn | −3.82608552(90) | 2.4×10−7 [10] |
The electron g-factor is one of the most precisely measured values in physics. [2]