A global perspective on searches for Electric Dipole Moments
AA global perspective on searches for Electric DipoleMoments
Guillaume Pignol
Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, FranceE-mail: [email protected]
September 2019
Abstract.
Many experiments are underway in the world to search for a non-zeroelectric dipole moment (EDM) of a particle with spin 1/2 such as the neutron orthe electron. Finding an EDM would reveal new sources of CP violation. EDMmeasurements are motivated by the high sensitivity to new physics beyond theStandard Model. They are relevant to find the explanation for the matter-antimatterasymmetry of the Universe. A variety of programs with different systems are beingpursued, with free neutrons, diamagnetic atoms, paramagnetic systems, and chargedparticles in storage rings. This article presents a basic introduction of the subject andattempts to compile the ongoing projects.
1. Introduction
The electric dipole moment (EDM) (cid:126)d of a composite system measures the separation ofthe positive and negative electric charges, it is associated with an energy − (cid:126)d · (cid:126)E in anexternal electric field. In fact that interaction term can be taken as the definition of theEDM, even for a non-composite system such as an electron. For any simple system ofspin 1/2, the EDM, being a vector operator, must be proportional to the Pauli matricesˆ (cid:126)σ acting on the spin states. The Hamiltonian of a spin 1/2 particle in an electric field isˆ H = − d ˆ (cid:126)σ · (cid:126)E, (1)where d is the permanent electric dipole moment of the particle. Hence, the EDM of asimple particle really quantifies the coupling between the spin and an applied electricfield, in the same way that the magnetic dipole moment quantifies the coupling betweenthe spin and a magnetic field.The coupling (1) results in the dynamics shown in figure 1 (a), for a spin initiallyperpendicular to the electric field. The spin precesses around the field at an angularfrequency given by ¯ hω = 2 dE . As shown in figure 1 (b), the mere existence of a non-zeroEDM would constitute a violation of time reversal symmetry, because spin precessionin an electric field discerns the past and the future. a r X i v : . [ h e p - ph ] D ec earches for EDMs (a) >> PLAY >> (b) << REWIND << 𝑬 𝑬 Figure 1. (a) Evolution in an electric field of a particle spin with a non-zero - positivein this case - EDM. (b) Time-reversed version of the evolution (a). The fact that (a)and (b) are different constitutes a violation of time reversal symmetry.
Now, despite decades of experimental efforts, the many measurements of the EDMsof various particles are all compatible with zero. Permanent EDMs, if they exist, areextremely tiny. For example, the current limit on the magnitude of the neutron EDMis [1] | d n | < × − e cm (90% C . L . ) . (2)In a large electric field of 10 kV/cm, it would take more - much more? - than 80 daysfor the spin precession to complete one full turn.This paper gives a global overview of the quest for a non-zero EDM, an activefield of experimental research today. It updates previous overviews on EDM searches[2, 3]. For a more in-depth treatment of the subject, the reader should consult the recentreview [4]. In section 2 we will explain the relevance of the EDM searches in particlephysics and cosmology. There are many experimental efforts underway worldwide toimprove the sensitivity of the EDM searches using various systems. The archetype isthe neutron EDM, that we will cover in section 3. In the following sections we willcover the EDM searches with diamagnetic atoms, paramagnetic systems, and finallywith charged particles.
2. Relevance of the EDM quest in particle physics and cosmology
From the point of view of relativistic field theory, the EDM of a fermion f correspondsto the following coupling to the electromagnetic field F µν : L EDM = − id f L σ µν f R F µν + h.c. (3)where f L and f R are the left and right chirality components of the fermion. In thenon-relativistic limit the lagrangian density (3) reduces to the hamiltonian (1). We note earches for EDMs (a) (b) (c) Figure 2. (a) Feynman diagram corresponding to the EDM coupling (3). (b)Example of a one-loop diagram contributing to the fermion EDM. (c) Two-loop Barr-Zee diagram contributing to the fermion EDM. that the coupling (3) explicitly violates CP symmetry if d is non-zero. It is consistentwith the fact that the hamiltonian (1) violates the time reversal symmetry and theCPT theorem which states that T-violation is equivalent to CP-violation in any localrelativistic quantum field theory.The coupling (3), also represented in figure 2 (a), is an effective non-renormalizableinteraction which could be generated by the effect of virtual particles. Figure 2 (b)shows a possible diagram involving the virtual exchange of a heavy boson of mass M and with a complex coupling ge iφ to the fermion. It generates an EDM of d ≈ e ¯ hc g / (4 π ) sin( φ ) cos( φ ) m f /M . This formula can be used to estimate the order ofmagnitude for the EDM of the first generation fermions – say the d quark ( m f = 5 MeV)– induced by a boson at the TeV scale ( M ≈ g / (4 π ) ≈ − ) with maximalCP violation (sin( φ ) ≈ d ≈ − e cm. Therefore generic CP violation abovethe electroweak scale is positively detectable by EDM experiments.The non-detection of EDMs reflects the peculiar structure of CP violation in theStandard Model which structurally contains two sources of CP violation: a complexphase in the CKM matrix and the strong phase θ QCD . EDMs induced by the CKMphase are theoretically undetectably small. This is due to the flavour structure of theelectroweak theory: only diagrams involving all three generations of quarks in the loopscan contribute to the EDM, this results in a big suppression. On the contrary, thestrong phase induce in principle large hadronic EDMs. The non-observation of theneutron EDM results in the bound | θ QCD | < − . The fact that the strong phase ismeasured to be unnaturally small constitutes the strong CP problem . It is believed thatan unknown dynamics beyond the Standard Model is at play to set this phase to zero.EDMs are sensitive probes of CP violation effects beyond the Standard Modelwith practically zero background from the CKM phase. As a concrete example let usconsider the search for CP-violating couplings of the Higgs boson h to fermions. The earches for EDMs d u s c b t ˜ f
90% C.L. limits from eEDM90% C.L. limits from nEDM
Figure 3.
Current limits on the CP-violating couplings of the Higgs boson for the sixquark flavours derived from the electron EDM (red bars) and from the neutron EDM(blue bars), adapted from [5].
Higgs couplings are generically parameterized by the following lagrangian L h = − y f √ (cid:16) κ f ¯ f f h + i ˜ κ f ¯ f γ f h (cid:17) , (4)where y f is the Yukawa coupling of the fermion f , κ f and ˜ κ f are the CP-conservingand CP-violating coupling constants. The Standard Model predicts κ f = 1 and ˜ κ f = 0.This coupling generates EDMs though the two-loops diagram shown in figure 2 (c). Thelimits on the CP-violating couplings to the quarks derived from the neutron and electronEDM bounds are shown in figure 3. This plot illustrates the complementarity of EDMsearches: the electron EDM is more sensitive to ˜ κ of the heavy quarks while the neutronEDM is more sensitive to ˜ κ of the light quarks. It also illustrates the great sensitivityof EDM searches: fundamental CP-violating couplings of order unity, relative to CP-conserving couplings, are already excluded except for the s quark. Next generations ofEDM experiments will push these limits down by an order of magnitude, or perhapsdiscover a signal induced by small CP-violation in the Higgs sector.Let us complete this section by emphasizing the importance of searching for newsources of CP-violation. First, this is a generic feature of models extending the SM,which inevitably come with additional complex (therefore CP-violating) free parameters.More compellingly, cosmology actually demands new CP violation sources to solve thebaryon asymmetry puzzle. Several classes of possible baryogenesis models have beeninvented to explain the generation of the matter-antimatter asymmetry in the earlyUniverse. They almost all have in common to satisfy Sakharov’s necessary conditions: (i)process out of thermal equilibrium, (ii) existence of baryon number violation processes,(iii) existence of C and CP violating interactions. An appealing possibility, called earches for EDMs Electroweak baryogenesis , poses that baryogenesis occurred at the electroweak phasetransition epoch of the Universe, at a temperature of about 100 GeV. See [6] for a recentdiscussion on the subject. For baryogenesis to work, new CP-violating interactions musthave been active at this temperature, therefore the mass of the new particles could notbe much heavier than 1 TeV and and the CP-violating interaction they mediate shouldbe sufficiently strong. The models therefore also predict sizable EDMs and the futureEDM experiments will either discover a nonzero EDM or exclude most of electroweakbaryogenesis models.
3. Search for the neutron EDM
The history of EDM searches started with the neutron in the 1950’s. The basic ideais to use polarized neutrons and measure precisely the spin precession frequency f inparallel or antiparallel magnetic and electric fields: f = µπ ¯ h B ± dπ ¯ h E. (5)The EDM term can be separated from the much larger magnetic term by taking thedifference of the frequency measured in parallel and antiparallel configurations. Aswe discussed in the introduction, the EDM term is very small ( dE/π ¯ h ≈ − Hz for d = 10 − e cm and E = 15 kV/cm) compared to the magnetic term (typically, f = 29 Hzfor B = 1 µ T). To detect such a minuscule coupling, one needs (i) a long interactiontime of the neutrons with the fields, (ii) a high flux of neutrons and (iii) a precisecontrol of the magnetic field. The first experiment by Smith, Purcell and Ramsey [7]used a beam of thermal neutrons passing in the electric field during T ≈ ultracold neutrons (UCNs). Theseare neutrons with a kinetic energy smaller than the neutron optical potential of solidmaterials, typically 100 neV. These neutrons can therefore be stored in material trapsbecause they undergo total reflection upon collision with the walls of the trap. In thebest previous measurement [1] performed at ILL in the period 1998-2002, UCNs werestored in a chamber permeated by a weak magnetic field and a strong electric field during T ≈
100 s. Although the systematic error is also a big concern, this measurement waslimited by the statistical error and thus by the intensity of the ILL/PF2 UCN source.New higher intensity UCN sources are now coming online at several major neutronfactories worldwide, which are exploited by several nEDM projects. In particular, thenEDM experiment has collected data [8] in 2015-2016 at the PSI UCN source, whichwill result in a slightly improved measurement of the neutron EDM (the analysis is stillongoing at the time of writing). Other ongoing nEDM projects [12, 13, 14, 16, 17, 18]are listed in table 1, they are all at a different stage of readiness and they aim at animprovement in sensitivity by a factor 10 to 100 compared to the previous measurement[1]. More details on nEDM searches can be found in the recent reviews [9, 10]. earches for EDMs Table 1.
List of active ongoing projects [11] searching for the EDM of the neutron,diamagnetic atoms (Hg, Xe, Ra), paramagnetic systems and charged particles. project location concept referencesnEDM@SNS Oak Ridge spallation source UCN in superfluid helium [12]n2EDM PSI spallation source UCN double chamber [13]nEDM@LANL Los Alamos spallation source UCN double chamber [14]panEDM ILL reactor Grenoble UCN double chamber [15]TUCAN TRIUMF spallation source UCN double chamber [16]PNPI nEDM ILL - PNPI UCN double chamber [17]beam nEDM ESS spallation source pulsed cold neutron beam [18]Hg EDM Seattle vapor cells mercury-199 [19]quMercury Bonn laser cooled mercury-199MIXed J¨ulich - Heidelberg xenon-129 + helium-3 [20]HeXeEDM Berlin xenon-129 + helium-3 [21]Xe EDM Riken xenon-129 + xenon-131 [22]Ra EDM Argonne laser-cooled radium-225 [23]Cs,Ru EDM Penn State trapped cold alkali [25]Fr EDM CYRIC, Riken laser-cooled franciumEDM Toronto BaF within a rare gas matrix [26]NL-eEDM Nikhef BaF cold beam [27]JILA EDM Boulder trapped molecular ions HfF + ThF + [28]ACME Yale cryogenic ThO beam [29]eEDM London slow YbF beam [30]CPEDM proton or deuteron storage ringmuEDM PSI compact muon ring, frozen spin [31] µ g-2/EDM JPARC compact muon ring [32] µ g-2 Fermilab magic momentum muon ring [33]
4. Search for the EDM of diamagnetic atoms
Diamagnetic atoms are atoms with no net electronic spin. Due to this property, veryhigh precision can be obtained for the EDM of diamagnetic atoms with nuclear spin1/2, in particular mercury-199, xenon-129 and radium-225.In the case of mercury-199, super-precise monitoring of the spin precession can beachieved by making use of atom-light interaction. The current best limit is [19]: | d Hg | < . × − e cm (95% C . L . ) (6)In the case of xenon-129, the measurement profit from the very long coherence time(many hours) of the spin precession. The current best limit is [20]: | d Xe | < . × − e cm (95% C . L . ) (7) earches for EDMs s orbitals therefore generating an atomic EDM. The Schiffmoment itself could be generated by either T-violating nucleon-nucleon interactions orby a nucleon EDM. Overall the effect is larger in heavy nuclei, hence the experimentalfocus on mercury-199 and xenon-129. At the end, the shielding effects are compensatedby the better absolute sensitivity of experiments with diamagnetic atoms, as comparedto the neutron. All diamagnetic systems (neutron, mercury and xenon) have comparableand complementary sensitivity to fundamental sources of CP-violation [4]. Also, Schiffmoments are enhanced in octupole-deformed nuclei. This has motivated recently thesearch for EDMs of radioactive nuclei such as radium-225. The current best limit is [23]: | d Ra | < . × − e cm (95% C . L . ) . (8)The search for EDMs of diamagnetic atoms is very active today, with prospectsto improve the sensitivity by a factor 100 in all three systems. The ongoing projects[19, 20, 21, 22, 23] are listed in table 1.
5. EDM searches with paramagnetic atoms and polar molecules
Paramagnetic systems, i.e. atoms or molecules with an unpaired electron, can besensitive to T-violating electron-nucleon interactions and to the electron EDM. The mostsensitive probes are atoms with large Z , in particular cesium of radioactive francium,and heavy polar molecules like BaF, ThO, YbF, or even molecular ions HfF + , ThF + .We refer to the recent review [24] for more details about the search for EDMs withatoms and molecules. The current best limit on the electron comes from the ACMEexperiment with ThO molecule [29]: | d e | < . × − e cm (90% C . L . ) . (9)There are several projects [25, 26, 27, 28, 29, 30], listed in table 1, aiming at improvingthe sensitivity on the electron EDM by a factor of 100 or more.
6. Search for the EDM of charged particles in a storage ring
Polarized charged particles, in particular protons, deuterons or muons, can be confinedin circular storage rings with either a radial electric field, or a vertical magnetic field, ora combination of both. It is apparently not a good situation to measure an EDM sincethe electric and magnetic fields cannot be made parallel or antiparallel and the classicEDM search strategy does not work for charged particles. The situation is in fact morecomplicated, because contrary to classic EDM searches with particles practically at rest, earches for EDMs (cid:126)E × (cid:126)v and (cid:126)B × (cid:126)v are not small for charged particles in astorage ring. In the frame rotating with the cyclotron motion, the precession vector ofthe spin is given by the BMT equation: (cid:126)ω = qm (cid:34) a (cid:126)B − (cid:32) a + 11 − γ (cid:33) (cid:126)v × (cid:126)E (cid:35) + 2 d (cid:104) (cid:126)v × (cid:126)B + (cid:126)E (cid:105) , (10)where q is the charge of the particle, m its mass and a = ( g − / frozen spin , by an appropriate choice of the parameters B, E, v . Ongoing projects pursuing the developments of EDM measurements withcharged particles are listed in table 1.
7. Conclusion
The search for a non-zero fundamental electric dipole moment is an interdisciplinaryfield. The motivation comes from particle physics and cosmology. A broad range ofexperimental techniques are developed ranging from the large scale neutron facilities toadvanced atomic physics. We have presented an overview of the theoretical motivationsand the experimental programs to search for the EDMs with free neutrons, diamagneticatoms, paramagnetic systems and charged particles. We must admit we have omitted theproposals to measure EDMs of heavy unstable particles (lepton τ , hyperons and charmedbaryons) at particle colliders, due to the temporary incompetence of the author on thisconnected field. In figure 4 we show the world map of the ongoing EDM projects, with anestimate of the number of scientists involved. The diversity of the experiments promisesexciting prospects for the future, and maybe a discovery of fundamental importance. Acknowledgments
I am grateful to Dieter Ries for the compilation of the ongoing EDM projects used to filltable 1. I wish to thank J´er´emie Quevillon for his reading of the theoretical part. Thiswork is supported by the European Research Council, ERC project 716651 - NEDM.
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Diamagnetic atoms (~70 ppl) • Hg @ Bonn • Hg @ Seattle • Ra @ Argonne • Xe @ Heidelberg • Xe @ PTB • Xe @ Rikken
Paramagnetic systems (~80 ppl) ▪ Cs @ Penn State ▪ Fr @ Riken ▪ BaF @ Nikhef ▪ BaF @ Toronto ▪ HfF+ @ JILA ▪ ThO @ Yale ▪ YbF @ London
Storage rings (~400 ppl) ▪ CPEDM ▪ muEDM @ PSI ▪ (g-2) @ Fermilab ▪ (g-2) @ JPARC Figure 4.
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