Electron electric dipole moment explained
The electron electric dipole moment 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 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,[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]
If neutrinos are Majorana particles, a larger EDM (around) 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 that ranges from 10−27 to 10−29 e⋅cm. Some supersymmetric models predict that [5] 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,[6] would place further limits on which theory takes precedence.
Formal definition
As the electron has a net charge, the definition of its electric dipole moment is ambiguous in that
d\rm=\int({r}-{r}0)\rho({r})d3{r}
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.
appearing in the matrix element
[7] \langle
\rangle=\baru(pf)\left\{
\gamma\mu+
q\nu
\mu\nu\rho\sigma\sigma\rho\sigmaq\nu
}\left(q^\mu-\frac \gamma^\mu \right)\gamma_5 F_4(q^2) \right\} u(p_i) of the electromagnetic current operator between two on-shell states with Lorentz invariant phase space normalization in which
\langlepf\vertpi\rangle=2E(2\pi)3\delta3({\bfp}f-{\bfpi}).
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,
\mu=\tfrac{F1(0) + F2(0)}{2m\rm
} 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
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.
[8] For this reason, electron EDM searches almost always are conducted on systems involving heavy elements.
To date, no experiment has found a non-zero electron EDM. As of 2020 the Particle Data Group publishes its value as .[9] Here is a list of some electron EDM experiments after 2000 with published results:
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.[16] [17]
Future proposed experiments
Besides the above groups, electron EDM experiments are being pursued or proposed by the following groups:
See also
Notes and References
- 10.1103/PhysRevLett.109.193003 . 23215379 . Limit on the electron electric dipole moment using paramagnetic ferroelectric Eu0.5Ba0.5TiO3 . Physical Review Letters . 109 . 19 . 193003 . 2012 . Eckel . S. . Sushkov . A.O. . Lamoreaux . S.K. . 1208.4420. 2012PhRvL.109s3003E . 35411253 .
- Pospelov . M. . Ritz . A. . 10.1016/j.aop.2005.04.002 . Electric dipole moments as probes of new physics . Annals of Physics . 318 . 1 . 119–169 . 2005 . hep-ph/0504231 . 2005AnPhy.318..119P. 13827759 .
- Book: Khriplovich . I.B. . Lamoreaux . S.K. . 1997 . CP violation without strangeness: Electric dipole moments of particles, atoms, and molecules . Springer-Verlag.
- P. R. Bunker and P. Jensen (2005), Fundamentals of Molecular Symmetry (CRC Press) https://www.routledge.com/Fundamentals-of-Molecular-Symmetry/Bunker-Jensen/p/book/9780750309417 Chapter 15
- Arnowitt . R. . Dutta . B. . Santoso . Y. . 2001 . Supersymmetric phases, the electron electric dipole moment and the muon magnetic moment . . 64 . 11 . 113010 . 10.1103/PhysRevD.64.113010 . hep-ph/0106089 . 2001PhRvD..64k3010A. 17341766 .
- Web site: Ultracold Atomic Physics Group . Physics . U. Texas . 2015-11-13 . dmy-all.
- Nowakowski . M. . Paschos . E.A. . Rodriguez . J.M. . 10.1088/0143-0807/26/4/001 . All electromagnetic form factors . European Journal of Physics . 26 . 4 . 545–560 . 2005 . physics/0402058. 2005EJPh...26..545N . 119097762 .
- 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 . hep-ph . 2203.08103 .
- Web site: Electron listing . Particle Data Group . Lawrence Berkeley Laboratory . 2020.
- Regan . B.C. . Commins . Eugene D. . Schmidt . Christian J.. DeMille . David . 2002-02-01 . New Limit on the Electron Electric Dipole Moment . Physical Review Letters . 88 . 7 . 071805 . 10.1103/PhysRevLett.88.071805 . 11863886 . 2002PhRvL..88g1805R . 32396668 . dmy-all.
- 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 . . 473 . 7348 . 493–496 . 2011Natur.473..493H . 10.1038/nature10104 . 21614077 . 10044/1/19405. 205224996 . free .
- The ACME Collaboration . January 2014 . Order of Magnitude Smaller Limit on the Electric Dipole Moment of the Electron . . 343 . 6168 . 269–272 . 1310.7534 . 2014Sci...343..269B . 10.1126/science.1248213 . 24356114 . 564518 . 2014-06-24 . https://web.archive.org/web/20150427085647/http://laserstorm.harvard.edu/wiki/images/1/1a/Order_of_Magnitude_Smaller_Limit_on_the_Electric_Dipole_Moment_of_the_Electron._-_Baron_et_al._-_2014.pdf . 2015-04-27 . dead .
- 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 . 10.1103/PhysRevLett.119.153001 . 29077451 . 1704.07928 . 2017PhRvL.119o3001C . 44043558 .
- The ACME Collaboration . October 2018 . Improved Limit on the Electric Dipole Moment of the Electron . . 562 . 7727 . 355–360 . 10.1038/s41586-018-0599-8. 30333583 . 2018Natur.562..355A . 52985540 .
- 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 . 10.1126/science.adg4084 . 2212.11841. 2023Sci...381...46R .
- Web site: ACME Electron EDM.
- 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 . 10.1103/PhysRevA.106.022808. 2204.05904 .
- 1804.10012 . 10.1140/epjd/e2018-90192-9 . Measuring the electric dipole moment of the electron in BaF . The European Physical Journal D . 72 . 11 . 2018 . 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. 96439955 .
- 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 . 10.1103/PhysRevLett.119.133002 . 29341669 . 1705.11020 . 2017PhRvL.119m3002K . 33254969 .
- 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 . en . 6 . 1 . 3 . 1710.08785 . 2018Atoms...6....3V . 10.3390/atoms6010003 . 3349485 . free .
- Web site: EDMcubed . 2023-10-31 . www.yorku.ca.
- Web site: Search for the Electron EDM Using Cs and Rb in Optical Lattice Traps . 2022-09-09 . Penn State . en.
- Web site: Report Summary TRIUMF : Canada's National Laboratory for Particle and Nuclear Physics . 2022-09-09 . mis.triumf.ca.
- Web site: Moment dipolaire électrique des électrons à l'aide de Cs en matrice cryogénique - LAC . 2022-09-09 . www.lac.universite-paris-saclay.fr.