Electron electric dipole moment

Last updated

The electron electric dipole momentde is an intrinsic property of an electron such that the potential energy is linearly related to the strength of the electric field:

Contents

The electron's electric dipole moment (EDM) must be collinear with the direction of the electron's magnetic moment (spin). [1] Within the Standard Model of elementary particle physics, such a dipole is predicted to be non-zero but very small, at most 10−38e⋅cm, [2] 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. [3] [4]

Implications for Standard Model and extensions

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. [2] [lower-alpha 1]

If neutrinos are Majorana particles, a larger EDM (around 10−33 e⋅cm) is possible in the Standard Model. [2]

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. [5] Some supersymmetric models predict that |de| > 10−26 e⋅cm [6] 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, [7] would place further limits on which theory takes precedence. [8]

Historical record of electron electric dipole moment measurements in leptonic systems. Electron EDM limits.png
Historical record of electron electric dipole moment measurements in leptonic systems.

Formal definition

As the electron has a net charge, the definition of its electric dipole moment is ambiguous in that

depends 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. [9]

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 [10]

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. [3]

Experimental measurements

Electron EDMs are usually not measured on free electrons, but instead on bound, unpaired valence electrons inside atoms and molecules. In these, one can observe the effect of as a slight shift of spectral lines. The sensitivity to scales approximately with the nuclear charge cubed. [11] For this reason, electron EDM searches almost always are conducted on systems involving heavy elements. [6]

To date, no experiment has found a non-zero electron EDM. As of 2020 the Particle Data Group publishes its value as |de| < 0.11×10−28 e⋅cm. Here is a list of some electron EDM experiments after 2000 with published results:

List of Electron EDM Experiments
YearLocationPrincipal InvestigatorsMethodSpeciesExperimental upper limit on |de|
2002 University of California, Berkeley Eugene Commins, David DeMille Atomic beam Tl 1.6×10−27 e⋅cm [12]
2011 Imperial College London Edward Hinds, Ben Sauer Molecular beam Yb F 1.1×10−27 e⋅cm [13]
2014 Harvard-Yale
(ACME I experiment)		 David DeMille, John Doyle, Gerald Gabrielse Molecular beam Th O 8.7×10−29 e⋅cm [14]
2017 JILA Eric Cornell, Jun Ye Ion trap Hf F+1.3×10−28 e⋅cm [15]
2018 Harvard-Yale
(ACME II experiment)		 David DeMille, John Doyle, Gerald Gabrielse Molecular beam Th O 1.1×10−29 e⋅cm [16]
2022 JILA Eric Cornell, Jun Ye Ion trap Hf F+4.1×10−30 e⋅cm [17] [18]

The ACME collaboration is, as of 2020, developing a further version of the ACME experiment series. The latest experiment is called Advanced ACME or ACME III and it aims to improve the limit on electron EDM by one to two orders of magnitude. [19] [20]

Future proposed experiments

Besides the above groups, electron EDM experiments are being pursued or proposed by the following groups:

See also

Footnotes

  1. ↑ More precisely, a non-zero EDM does not arise until the level of four-loop Feynman diagrams and higher. [2]

Related Research Articles

<span class="mw-page-title-main">Hyperfine structure</span> Small shifts and splittings in the energy levels of atoms, molecules and ions

In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate electronic energy levels and the resulting splittings in those electronic energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucleus and electron clouds.

<span class="mw-page-title-main">Magnetic moment</span> Magnetic strength and orientation of an object that produces a magnetic field

In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude of torque the object experiences in a given magnetic field. When the same magnetic field is applied, objects with larger magnetic moments experience larger torques. The strength of this torque depends not only on the magnitude of the magnetic moment but also on its orientation relative to the direction of the magnetic field. Its direction points from the south pole to north pole of the magnet.

In solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor when pushed or pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility.

In physics, the gyromagnetic ratio of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol γ, gamma. Its SI unit is the radian per second per tesla (rad⋅s−1⋅T−1) or, equivalently, the coulomb per kilogram (C⋅kg−1).

The Kerr–Newman metric describes the spacetime geometry around a mass which is electrically charged and rotating. It is a vacuum solution which generalizes the Kerr metric by additionally taking into account the energy of an electromagnetic field, making it the most general asymptotically flat and stationary solution of the Einstein–Maxwell equations in general relativity. As an electrovacuum solution, it only includes those charges associated with the magnetic field; it does not include any free electric charges.

In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magnetic moment is −9.2847646917(29)×10−24 J⋅T−1. In units of the Bohr magneton (μB), it is −1.00115965218059(13) μB, a value that was measured with a relative accuracy of 1.3×10−13.

In quantum physics, the spin–orbit interaction is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin–orbit interaction leading to shifts in an electron's atomic energy levels, due to electromagnetic interaction between the electron's magnetic dipole, its orbital motion, and the electrostatic field of the positively charged nucleus. This phenomenon is detectable as a splitting of spectral lines, which can be thought of as a Zeeman effect product of two relativistic effects: the apparent magnetic field seen from the electron perspective and the magnetic moment of the electron associated with its intrinsic spin. A similar effect, due to the relationship between angular momentum and the strong nuclear force, occurs for protons and neutrons moving inside the nucleus, leading to a shift in their energy levels in the nucleus shell model. In the field of spintronics, spin–orbit effects for electrons in semiconductors and other materials are explored for technological applications. The spin–orbit interaction is at the origin of magnetocrystalline anisotropy and the spin Hall effect.

The Breit equation, or Dirac–Coulomb–Breit equation, is a relativistic wave equation derived by Gregory Breit in 1929 based on the Dirac equation, which formally describes two or more massive spin-1/2 particles interacting electromagnetically to the first order in perturbation theory. It accounts for magnetic interactions and retardation effects to the order of 1/c2. When other quantum electrodynamic effects are negligible, this equation has been shown to give results in good agreement with experiment. It was originally derived from the Darwin Lagrangian but later vindicated by the Wheeler–Feynman absorber theory and eventually quantum electrodynamics.

<span class="mw-page-title-main">Mathematical formulation of the Standard Model</span> Mathematics of a particle physics model

This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.

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 magnetic moment, also called magnetic dipole moment, is a measure of the strength of a magnetic source.

In physics, the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is

In physics, charge conservation is the principle, of experimental nature, that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved. Charge conservation, considered as a physical conservation law, implies that the change in the amount of electric charge in any volume of space is exactly equal to the amount of charge flowing into the volume minus the amount of charge flowing out of the volume. In essence, charge conservation is an accounting relationship between the amount of charge in a region and the flow of charge into and out of that region, given by a continuity equation between charge density and current density .

In the physics of electromagnetism, the Abraham–Lorentz force is the reaction force on an accelerating charged particle caused by the particle emitting electromagnetic radiation by self-interaction. It is also called the radiation reaction force, the radiation damping force, or the self-force. It is named after the physicists Max Abraham and Hendrik Lorentz.

A g-factor 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 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 in the definition. The two definitions coincide for the proton.

In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them also work with special relativity.

The Bohr–Van Leeuwen theorem states that when statistical mechanics and classical mechanics are applied consistently, the thermal average of the magnetization is always zero. This makes magnetism in solids solely a quantum mechanical effect and means that classical physics cannot account for paramagnetism, diamagnetism and ferromagnetism. Inability of classical physics to explain triboelectricity also stems from the Bohr–Van Leeuwen theorem.

In quantum mechanics, orbital magnetization, Morb, refers to the magnetization induced by orbital motion of charged particles, usually electrons in solids. The term "orbital" distinguishes it from the contribution of spin degrees of freedom, Mspin, to the total magnetization. A nonzero orbital magnetization requires broken time-reversal symmetry, which can occur spontaneously in ferromagnetic and ferrimagnetic materials, or can be induced in a non-magnetic material by an applied magnetic field.

The Aharonov–Casher effect is a quantum mechanical phenomenon predicted in 1984 by Yakir Aharonov and Aharon Casher, in which a traveling magnetic dipole is affected by an electric field. It is dual to the Aharonov–Bohm effect, in which the quantum phase of a charged particle depends upon which side of a magnetic flux tube it comes through. In the Aharonov–Casher effect, the particle has a magnetic moment and the tubes are charged instead. It was observed in a gravitational neutron interferometer in 1989 and later by fluxon interference of magnetic vortices in Josephson junctions. It has also been seen with electrons and atoms.

Electric dipole spin resonance (EDSR) is a method to control the magnetic moments inside a material using quantum mechanical effects like the spin–orbit interaction. Mainly, EDSR allows to flip the orientation of the magnetic moments through the use of electromagnetic radiation at resonant frequencies. EDSR was first proposed by Emmanuel Rashba.

<span class="mw-page-title-main">Dual graviton</span> Hypothetical particle found in supergravity

In theoretical physics, the dual graviton is a hypothetical elementary particle that is a dual of the graviton under electric-magnetic duality, as an S-duality, predicted by some formulations of eleven-dimensional supergravity.

References

  1. ↑ Eckel, S.; Sushkov, A.O.; Lamoreaux, S.K. (2012). "Limit on the electron electric dipole moment using paramagnetic ferroelectric Eu0.5Ba0.5TiO3". Physical Review Letters. 109 (19): 193003. arXiv: 1208.4420 . Bibcode:2012PhRvL.109s3003E. doi:10.1103/PhysRevLett.109.193003. PMID   23215379. S2CID   35411253.
  2. 1 2 3 4 Pospelov, M.; Ritz, A. (2005). "Electric dipole moments as probes of new physics". Annals of Physics. 318 (1): 119–169. arXiv: hep-ph/0504231 . Bibcode:2005AnPhy.318..119P. doi:10.1016/j.aop.2005.04.002. S2CID   13827759.
  3. 1 2 Khriplovich, I.B.; Lamoreaux, S.K. (1997). CP violation without strangeness: Electric dipole moments of particles, atoms, and molecules. Springer-Verlag.
  4. ↑ P. R. Bunker and P. Jensen (2005), Fundamentals of Molecular Symmetry (CRC Press) ISBN   0-7503-0941-5 Chapter 15
  5. ↑ Roussy, Tanya S.; Caldwell, Luke; Wright, Trevor; Cairncross, William B.; Shagam, Yuval; Ng, Kia Boon; Schlossberger, Noah; Park, Sun Yool; Wang, Anzhou; Ye, Jun; Cornell, Eric A. (2023-07-07). "An improved bound on the electron's electric dipole moment". Science. 381 (6653): 46–50. arXiv: 2212.11841 . Bibcode:2023Sci...381...46R. doi:10.1126/science.adg4084. ISSN   0036-8075. PMID   37410848.
  6. 1 2 Arnowitt, R.; Dutta, B.; Santoso, Y. (2001). "Supersymmetric phases, the electron electric dipole moment and the muon magnetic moment". Physical Review D . 64 (11): 113010. arXiv: hep-ph/0106089 . Bibcode:2001PhRvD..64k3010A. doi:10.1103/PhysRevD.64.113010. S2CID   17341766.
  7. ↑ "Ultracold Atomic Physics Group". Physics. U. Texas. Retrieved 13 November 2015.
  8. ↑ Andreev, V.; Ang, D. G.; DeMille, D.; Doyle, J. M.; Gabrielse, G.; Haefner, J.; Hutzler, N. R.; Lasner, Z.; Meisenhelder, C.; O’Leary, B. R.; Panda, C. D.; West, A. D.; West, E. P.; Wu, X.; ACME Collaboration (October 2018). "Improved limit on the electric dipole moment of the electron" . Nature. 562 (7727): 355–360. Bibcode:2018Natur.562..355A. doi:10.1038/s41586-018-0599-8. ISSN   1476-4687. PMID   30333583.
  9. ↑ Verma, Mohit; Jayich, Andrew M.; Vutha, Amar C. (2020-10-08). "Electron Electric Dipole Moment Searches Using Clock Transitions in Ultracold Molecules". Physical Review Letters. 125 (15): 153201. arXiv: 1909.02650 . doi:10.1103/PhysRevLett.125.153201. ISSN   0031-9007. PMID   33095600.
  10. ↑ Nowakowski, M.; Paschos, E.A.; Rodriguez, J.M. (2005). "All electromagnetic form factors". European Journal of Physics. 26 (4): 545–560. arXiv: physics/0402058 . Bibcode:2005EJPh...26..545N. doi:10.1088/0143-0807/26/4/001. S2CID   119097762.
  11. ↑ Alarcon, Ricardo; Alexander, Jim; Anastassopoulos, Vassilis; Aoki, Takatoshi; Baartman, Rick; Baeßler, Stefan; Bartoszek, Larry; Beck, Douglas H.; Bedeschi, Franco; Berger, Robert; Berz, Martin; Bethlem, Hendrick L.; Bhattacharya, Tanmoy; Blaskiewicz, Michael; Blum, Thomas (2022-04-04). "Electric dipole moments and the search for new physics". arXiv: 2203.08103 [hep-ph].
  12. ↑ Regan, B.C.; Commins, Eugene D.; Schmidt, Christian J.; DeMille, David (1 February 2002). "New Limit on the Electron Electric Dipole Moment" (PDF). Physical Review Letters. 88 (7): 071805. Bibcode:2002PhRvL..88g1805R. doi:10.1103/PhysRevLett.88.071805. PMID   11863886. S2CID   32396668.
  13. ↑ Hudson, J.J.; Kara, D.M.; Smallman, I.J.; Sauer, B.E.; Tarbutt, M.R.; Hinds, E.A. (2011). "Improved measurement of the shape of the electron" (PDF). Nature . 473 (7348): 493–496. Bibcode:2011Natur.473..493H. doi:10.1038/nature10104. hdl: 10044/1/19405 . PMID   21614077. S2CID   205224996.
  14. ↑ The ACME Collaboration (January 2014). "Order of Magnitude Smaller Limit on the Electric Dipole Moment of the Electron" (PDF). Science . 343 (6168): 269–272. arXiv: 1310.7534 . Bibcode:2014Sci...343..269B. doi:10.1126/science.1248213. PMID   24356114. S2CID   564518. Archived from the original (PDF) on 2015-04-27. Retrieved 2014-06-24.
  15. ↑ Cairncross, William B.; Gresh, Daniel N.; Grau, Matt; Cossel, Kevin C.; Roussy, Tanya S.; Ni, Yiqi; Zhou, Yan; Ye, Jun; Cornell, Eric A. (2017-10-09). "Precision Measurement of the Electron's Electric Dipole Moment Using Trapped Molecular Ions". Physical Review Letters. 119 (15): 153001. arXiv: 1704.07928 . Bibcode:2017PhRvL.119o3001C. doi:10.1103/PhysRevLett.119.153001. PMID   29077451. S2CID   44043558.
  16. ↑ The ACME Collaboration (October 2018). "Improved Limit on the Electric Dipole Moment of the Electron" (PDF). Nature . 562 (7727): 355–360. Bibcode:2018Natur.562..355A. doi:10.1038/s41586-018-0599-8. PMID   30333583. S2CID   52985540.
  17. ↑ Roussy, Tanya S.; Caldwell, Luke; Wright, Trevor; Cairncross, William B.; Shagam, Yuval; Ng, Kia Boon; Schlossberger, Noah; Park, Sun Yool; Wang, Anzhou; Ye, Jun; Cornell, Eric A. (2023). "An improved bound on the electron's electric dipole moment". Science. 381 (6653): 46–50. arXiv: 2212.11841 . Bibcode:2023Sci...381...46R. doi:10.1126/science.adg4084. PMID   37410848.
  18. ↑ Roussy, Tanya S.; Caldwell, Luke; Wright, Trevor; Cairncross, William B.; Shagam, Yuval; Ng, Kia Boon; Schlossberger, Noah; Park, Sun Yool; Wang, Anzhou; Ye, Jun; Cornell, Eric A. (2023-07-06), "A new bound on the electron's electric dipole moment", Science, 381 (6653): 46–50, arXiv: 2212.11841 , Bibcode:2023Sci...381...46R, doi:10.1126/science.adg4084
  19. ↑ "ACME Electron EDM".
  20. ↑ Ang, D. G.; Meisenhelder, C.; Panda, C. D.; Wu, X.; DeMille, D.; Doyle, J. M.; Gabrielse, G. (2022-08-15). "Measurement of the $H^3\Delta_1$ radiative lifetime in ThO". Physical Review A. 106 (2): 022808. arXiv: 2204.05904 . doi:10.1103/PhysRevA.106.022808.
  21. ↑ Aggarwal, Parul; Bethlem, Hendrick L.; Borschevsky, Anastasia; Denis, Malika; Esajas, Kevin; Haase, Pi A.B.; Hao, Yongliang; Hoekstra, Steven; Jungmann, Klaus; Meijknecht, Thomas B.; Mooij, Maarten C.; Timmermans, Rob G.E.; Ubachs, Wim; Willmann, Lorenz; Zapara, Artem (2018). "Measuring the electric dipole moment of the electron in BaF". The European Physical Journal D. 72 (11). arXiv: 1804.10012 . doi:10.1140/epjd/e2018-90192-9. S2CID   96439955.
  22. ↑ Kozyryev, Ivan; Hutzler, Nicholas R. (2017-09-28). "Precision Measurement of Time-Reversal Symmetry Violation with Laser-Cooled Polyatomic Molecules". Physical Review Letters. 119 (13): 133002. arXiv: 1705.11020 . Bibcode:2017PhRvL.119m3002K. doi:10.1103/PhysRevLett.119.133002. PMID   29341669. S2CID   33254969.
  23. ↑ Vutha, A.C.; Horbatsch, M.; Hessels, E.A. (2018-01-05). "Oriented polar molecules in a solid inert-gas matrix: A proposed method for measuring the electric dipole moment of the electron". Atoms. 6 (1): 3. arXiv: 1710.08785 . Bibcode:2018Atoms...6....3V. doi: 10.3390/atoms6010003 . S2CID   3349485.
  24. ↑ "EDMcubed". www.yorku.ca. Retrieved 2023-10-31.
  25. ↑ "Search for the Electron EDM Using Cs and Rb in Optical Lattice Traps". Penn State. Retrieved 2022-09-09.
  26. ↑ "Report Summary | TRIUMF : Canada's National Laboratory for Particle and Nuclear Physics". mis.triumf.ca. Retrieved 2022-09-09.
  27. ↑ "Moment dipolaire électrique des électrons à l'aide de Cs en matrice cryogénique - LAC". www.lac.universite-paris-saclay.fr. Retrieved 2022-09-09.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.