Electron electric dipole moment
The electron electric dipole moment de is an intrinsic property of an electron such that the potential energy is linearly related to the strength of the electric field:
The electron's EDM must be collinear with the direction of the electron's magnetic moment. Within the Standard Model of elementary particle physics, such a dipole is predicted to be non-zero but very small, at most, where e stands for the elementary charge. The discovery of a substantially larger electron electric dipole moment would imply a violation of both parity invariance and time reversal invariance.
Implications for Standard Model and extentions
In the Standard Model, the electron EDM arises from the CP-violating components of the CKM matrix. The moment is very small because the CP violation involves quarks, not electrons directly, so it can only arise by quantum processes where virtual quarks are created, interact with the electron, and then are annihilated.If neutrinos are Majorana particles, a larger EDM is possible in the standard model
Many extensions to the Standard Model have been proposed in the past two decades. These extensions generally predict larger values for the electron EDM. For instance, the various technicolor models predict de that ranges from 10−27 to 10−29 e⋅cm. Some supersymmetric models predict that but some other parameter choices or other supersymmetric models lead to smaller predicted values. The present experimental limit therefore eliminates some of these technicolor/supersymmetric theories, but not all. Further improvements, or a positive result, would place further limits on which theory takes precedence.
Formal definition of the electron EDM
As the electron has a net charge, the definition of its electric dipole moment is ambiguous in thatdepends on the point about which the moment of the charge distribution is taken. If we were to choose to be the center of charge, then would be identically zero.
A more interesting choice would be to take as the electron's center of mass evaluated in the frame in which the electron is at rest.
Classical notions such as the center of charge and mass are, however, hard to make precise for a quantum elementary particle. In practice the definition used by experimentalists comes from the form factors appearing in the matrix element
of the electromagnetic current operator between two on-shell states with Lorentz invariant phase space normalization in which
Here and are 4-spinor solutions of the Dirac equation normalized so that, and is the momentum transfer from the current to the electron.
The form factor is the electron's charge, is its static magnetic dipole moment, and provides the formal definition of the electron's electric dipole moment.
The remaining form factor would, if nonzero, be the anapole moment.
Experimental measurements of the electron EDM
To date, no experiment has found a non-zero electron EDM. The Particle Data Group publishes its value as. Here is a list of electron EDM experiments after 2000 with published results:| Year | Location | Principal Investigators | Method | Species | Experimental upper limit on |
| 2002 | University of California, Berkeley | Eugene Commins, David DeMille | Atomic beam | Tl | |
| 2011 | Imperial College London | Edward Hinds, Ben Sauer | Molecular beam | YbF | |
| 2014 | Harvard-Yale | David DeMille, John Doyle, Gerald Gabrielse | Molecular beam | ThO | |
| 2017 | JILA | Eric Cornell, Jun Ye | Ion trap | HfF+ | |
| 2018 | Harvard-Yale | David DeMille, John Doyle, Gerald Gabrielse | Molecular beam | ThO |
Future proposed experiments
Besides the above groups, electron EDM experiments are being pursued or proposed by the following groups:- David Weiss : Cs atomic trap
- Daniel Heinzen at University of Texas at Austin: Cs atomic trap
- University of Groningen: BaF molecular beam
- John Doyle, Nicholas Hutzler, and Timothy Steimle : YbOH molecular trap
- Amar Vutha, Eric Hessels : oriented polar molecules in an inert gas matrix
Footnotes