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Keywords:

  • permanent electric dipole moment;
  • edm;
  • standard model;
  • new physics;
  • precision measurement

Abstract

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography

Searches for a permanent Electric Dipole Moment (EDM) of a fundamental particle provide a wide window for the discovery of potential New Physics. Within todays Standard Model in particle physics the well established violation of CP symmetry gives rise to EDMs which are several orders of magnitude below the present experimentally established upper bounds. On the other hand, EDMs appear quite naturally within many modern speculative theories, which have been suggested to improve the known shortcomings of the present Standard Model, e.g., the lack of giving reasons for certain established facts such as the mass hierarchy of the fundamental fermions or the number of three particle generations. They could be almost as large as the present experimental bounds. The speculative models provide for EDMs of different fundamental particles in specific ways. As there is no convincing indication, yet, which of the various extensions to the present standard theory may be more successful, a larger number of EDM searches is very well motivated. Still, even with the discovery of an EDM in one system several experiments will be required to pin down the precise nature and the underlying processes. Therefore searches are going on presently in a variety of systems, ranging from free leptons to complex condensed matter samples. These experiments utilize typically state of the art precision measurements which are often based on forefront technological developments. The experimental efforts are complemented and guided by the further development and refinement of particle theory. Here a few aspects of recent developments in this exciting field are summarized.

1 Introduction

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography

A permanent electric dipole moment (EDM) of a fundamental particle violates both the discrete symmetries parity (P) and time-reversal (T). The combined CPT symmetry [1-3], where C is charge conjugation, relates deeply to our basic understanding of physics through, e.g., spin-statistics. CPT is generally assumed to be unbroken. It has been thoroughly investigated and precisely tested [4]. With CPT valid a permanent Electric Dipole Moment also violates the CP symmetry (see Fig. 1 and, e.g., [5] for a comprehensive introduction and [6, 8, 7] for an overview and a more detailed compilation of the background to the subject of permanent EDMs).

image

Figure 1. A permanent electric dipole moment inline image of a fundamental particle is proportional to its angular momentum inline image, as there can be only one vector in a quantum system. The energy H of a dipole inline image in an external electric field inline image is inline image, the observable quantity. The electric field inline image also changes sign in a P transformation. Further under a C transformation both inline image and inline image change sign. A permanent Electric Dipole Moment (EDM) violates P, T and CP symmetry. A magnetic dipole moment inline image of a particle stays always aligned with inline image which itself transforms under P, T and CP like a magnetic field inline image. This leaves inline image unaltered and magnetic moments can exist.

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We know from experiments and direct observations that the discrete symmetries C, P and T as well as the combined CP symmetry are all broken in weak interactions. Until the 1950ies it had been generally and strongly assumed that these symmetries would be generally valid. Therefore, early search experiments [9-11] for an EDM in neutrons were not considered to have realistic chances.

In 1957 the violation of parity has been discovered in the weak interaction process of nuclear β-decay in 60Co [12]. Shortly thereafter this was confirmed in the decay of pions [13] and muons [14]. In 1964 the violation of the CP symmetry was measured in the weak decay of neutral kaons (K0) [15].

Only after these facts had been undoubtedly established EDM searches were re-introduced into the spectrum of scientific urgent topics. Today searches for permanent EDMs of fundamental particles are considered to have a large potential to shape significantly our understanding of the fundamental laws of physics. On the path to find New Physics EDMs offer an approach which is complementary to that possible with experiments at the highest in accelerator achievable energies. EDM experiments can probe New Physics at energy scales which are far beyond the reach of present accelerator technology. In certain supersymmetric scenarios, e.g., present established EDM limits provide information about physics at the TeV or even PeV scale [16]. They are competitive or even more sensitive to New Physics than observables connected to hadron and lepton flavour.

CP violation as observed first in the neutral Kaon decays can be described with a single phase factor in the Cabbibbo-Kobayashi-Maskawa formalism [17, 18]. CP violation has attracted a lot of attention, because of its possible relation to the observed matter-antimatter-asymmetry in the universe. It has been suggested [19, 20] to explain the observed dominance of matter over antimatter in our world via CP-violation in the early universe in a state of thermal non-equilibrium and with baryon number violating processes. (Additional sources of CP-violation – other than those well established to date – are necessarily required to explain the presently known matter-antimatter asymmetry. CPT violation on the other hand could also be sufficient and even without the need of thermal non-equilibrium[21]. Therefore this opens an alternative route for an explanation). Because CP violation as described in the SM is not sufficient to explain the excess of baryons, a strong motivation is provided to search for yet unknown sources which cause violation of CP symmetry. This is a major driving force behind the ongoing EDM searches.

Electric dipole moments are well known and observed in, e.g., polar molecules. This simple fact is often a source of confusion [6]. Such dipole moments appear in strong external electric fields, where the system needs to be described by a superposition of pure (eigen)states. However, the structural eigenstates of a polar molecule do not give rise to permanent EDMs such as those we are concerned with here. Eigenstates of shape in any quantum system are not energy eigenstates. We are here concerned with the pure energy eigenstates of the systems of interest. They cannot have any dipole moments other than such of tiny strength which arise from the known sources of CP violation [15] within the Standard Model. Such EDMs are at least 4 orders of magnitude below the present established bounds (see Table 1 below). Therefore, an undisputed future observation of an EDM of a pure state will be a clear and convincing sign of New Physics which is not covered yet by the established Standard Model in particle physics.

Table 1. Several actual limits on EDMs and the improvement factors necessary in experiments to reach Standard Model predictions. It is assumed here that the QCD Θ parameter does not contribute, athough for hadrons it might contribute up to the present bounds. For electrons, neutrons and muons speculative models have predicted a finite value for an EDM that could be reached with presently ongoing or proposed experiments in the near future. There is a number of further, new and ongoing activities, e.g. in neutral and charged molecules or in radioactive atoms, which have no reported limit yet. However, they are similarly promising
ParticleLimit/Measurement [e cm]Confidence Level [%]ReferenceSM limit [factor to go]
einline image90[101, 102]1011
μinline image95[103]108
τinline image95[104]107
ninline image90[67]104
pinline image95[105]106
Λ0inline image95[106]1011
inline imageinline image95[107] 
inline imageinline image95[108, 109] 
Hg-atominline image95[110]inline image

Many models beyond the present Standard Model predict often EDMs for fundamental systems which are significantly larger than the values which are calculated using the already known CP-violation. The values of EDMs in speculative models can in many cases be almost as large as the present experimental upper bounds. Since the first experiments to search for EDMs in the 1950ies numerous speculative possibilities, which could provide EDMs, have been suggested and thoroughly discussed. Many of them have been ruled out in the course of the evolution of our physical understanding and many of them do not satisfy any longer the constraints set by present experimental bounds on EDMs. Based on experimental facts, no suggested extension to the Standard Model can be favoured over another or stronger motivated than any other. It will be up to experiments to decide whether there are EDMs from Physics beyond the Standard Model and what the underlying mechanisms are which produce them. Even through the non-observation of a finite EDM value up to now, the searches for them have ruled out so far many speculative models. EDMs have a largely model independent discriminative power. On the other hand, an established EDM would be a clear sign of new physics beyond the Standard Model.1

Because of this very high importance of permanent Electric Dipole Moments and because of their very robust discovery potential for New Physics, there have been a number of recent original articles and extensive reviews of the field. They cover the discovery potential and possible implications of possible finite search results [23-27, 8, 22, 28-35], various aspects of theoretical approaches [36-46] and the numerous ideas and improvements concerning actual and future experiments searching for permanent EDMs of particles and composed systems [47-52] with the highest reachable experimental sensitivities. The ongoing and upcoming projects have stimulated technological developments and generated quite some activities [53-58]. We do not aim here to expand on this, but rather sketch the present status. We restrict ourselves to aspects of some most recent developments and the realistic chances for a discovery from an intermediate term perspective.

2 Searches for an EDM – general aspects

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography

From an unbiased point of view there is no preferred system to search for an EDM. In fact, many different systems need to be examined in order to be able to extract unambiguous information on the nature of EDMs, because depending on the underlying, yet unknown processes different systems have in general quite significantly different susceptibility to acquire an EDM through a particular mechanism (see Fig. 2). As a first approach an EDM may be considered an “intrinsic property” of an elementary particle as we know them, because the mechanism causing an EDM is not accessible at present. However, an EDM can also arise from CP-odd forces between the constituents forming a more complex particle with substructure, e.g. such as forces between the quarks in a nucleon, between the nucleons in nuclei or between nuclei and electrons in atoms. Such EDMs could be much larger [59] than such expected for elementary particles and which originate in the presently popular New Physics models.

image

Figure 2. New Physics beyond the present standard theory can induce permanent EDMs through various mechanisms into particles and composed systems. An undisputed observation of an EDM in one system alone would therefore not provide sufficient information to unravel the underlying processes. Further, as of today there is no indication, yet, which of the potential mechanisms would be more favoured than any other. Therefore the results of several experiments – with either a positive signal or with further stringent upper limits – are indispensable for the identification of the nature of the process generating an EDM.

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Distinctively different precision experiments to search for an EDM are under way in a variety of different systems. A large number of ideas for significant improvements have been made public. Still, the electron and the neutron get the largest attention of experimental groups and theorists, although besides tradition there is little which singles out these systems. Nevertheless, there is a considerable number of efforts in the United States, Japan and in Europe which employ different approaches all of which have unique and promising features.

The methods to find an EDM which are presently pursued can be distinguished in three groups:

  •  Classical approaches which use optical spectroscopy of atoms and molecules in cells, as well as atomic and molecular beams or contained cold neutrons;
  •  Modern atomic physics techniques such as atomic and ion traps, fountains and interference techniques;
  •  Innovative approaches involving radioactive species, storage rings, particles in condensed matter (garnets [60], liquid Xe [61]), nuclear spin masers [62], and a few more have been proposed.

2.1 Sensitivity

The statistical limit achievable in an EDM experiment can be generically described by

  • display math(1)

Here P is the polarization, ε is the efficiency which can vary significantly depending on the experimental setup and the system under observation, T the measurement time, N is the number of particles in the observation volume, τ is the spin coherence time and E is the applied electric field. With typical values achievable in realistic experiments (inline image) one gets inline image e cm in one day (inline image) of measurement time. We note here that among the successfully completed experiments there were large differences in the achieved characteristic numbers due to experimental details. (The neutron experiments so far had the highest efficiency of inline image and the latest Xe experiment had inline image. Whereas there were inline image neutrons per day available, for Xe the low efficiency could be compensated by the large number of inline image atoms [63].) In general, statistics is not a serious problem, even for experiments which exploit exotic or radioactive systems.

However, systematic effects are known to provide more severe limitations. Therefore their rigorous control needs to be in the very center of attention in the necessary high precision experiments. A recently compiled and updated table of experiments searching for permanent Electric Dipole Moments is given in [64].

2.2 Spin Precession

An EDM dX of a fundamental particle inline image is connected with the spin σX of the system. It is proportional to the spin and the magneton of the particle inline image, with a constant of proportionality ηX. We have

  • display math(2)

where mX is the particle mass, e is the elementary unit of charge, ℏ is Planck's constant and c is the speed of light. With this the EDM is

  • display math(3)

The constant ηX contains all the relevant information about the physical origin of the processes which cause an EDM. The magnetic moment of an investigated fermionic particle is

  • display math(4)

where aX is the particles magnetic anomaly, i.e. the fractional deviation of the g-factor which has a value of exactly 2 for spin 1/2 fermions in Dirac theory.

Many EDM searches have been performed in experiments where spin precession of a polarized sample was measured. For this the samples are polarized and reside in a weak magnetic field B which is oriented orthogonal to the polarization. The polarization which is proportional to the particle spins precesses with the frequency

  • display math(5)

around the magnetic field vector. In an additional electric field inline image, which is aligned parallel to B, or an electric field inline image, which is aligned anti-parallel to B, the precession frequency is increased or decreased by

  • display math(6)

For an EDM of order 10−28 e cm and a typical electric field of order 105 V/m this corresponds to a spin precession frequency of inline image. In the combined magnetic and electric fields the spin precesses with the frequencies

  • display math(7)

depending on the relative orientation of E and B. For a finite value of the EDM the difference in the frequencies inline image and inline image yields the EDM as

  • display math(8)

and the parameter of primary interest, inline image, becomes

  • display math(9)

Since the magneton inline image depends on the mass of particle, the limits on EDMs of particles, usually quoted in CGS units, must be compared with each other only with caution. ηX appears to be a more powerful parameter for the purpose of comparisons.

3 Systems to search for EDMs

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography

There are four distinguishable lines of experimental approach towards observing an EDM. They differ concerning the type of system under investigation (see Fig. 3):

  •  Single free Elementary Particles and Atomic Nuclei (electron (e), muon (μ), tauon (τ), neutron (n), proton p, 223Fr,…);
  •  Atoms and Ions (mercury (Hg), xenon (Xe), thallium (Tl), cesium (Cs), radon (Rn), francium (Fr), radium (Ra),… );
  •  Molecules and Molecular Ions (thallium fluoride (TlF), ytterbium fluoride (YbF), lead oxide (PbO), hafnium fluoride ion (HfF+), thorium fluoride ion (ThF+),… );
  •  Condensed Matter (ferroelectric materials, liquid Xe,…).
image

Figure 3. We distinguish four categories of EDM search experiments depending on properties of the system under investigation: single fundamental particles, atoms, molecules and condensed matter. In composed systems amplification mechanisms can significantly enhance the EDMs of fundamental particles. In each category examples are given of systems is which permanent electric dipole moments are searched for. Those where the final decision over the suitability has not been reached are marked ‘?’. Yet, no single system can be singled out as being more promising than any other. Every line of approach has its characteristic advantages (symbolized by ‘+’) and challenges (symbolized by ‘-’). The common goal of all these efforts is the identification of new sources of CP violation.

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Each of these lines has its own strong advantages. Single particles are the cleanest systems in terms of interpretation of a possible observed EDM. Atoms and ions show often quite strong enhancement factors for the EDMs of their constituents. Depending on the electronic configuration the observation of either the EDM of the electron or the one of the nucleus can be strongly favoured. This depends on whether the atomic system is paramagnetic or diamagnetic. In molecules, particularly the polarizable ones, the enhancement factors can be very large due to a large number of close lying states of opposite parity. In condensed matter samples enhancements can be large as well where each investigated object has its own particular advantages.

A selection of present limits that have been established is listed in Table 1. The confidence levels of the published experimental values reported are 90% and 95% respectively, i.e. some 2σ. In order to be capable to rigorously proof the existence of an EDM with a confidence level of 5σ or more, new experiments must have significantly higher sensitivity than those in which the present limits were found. A significant leap is apparently needed on the experimental side. On the other hand various speculative models exist which would provide for EDMs up to these limits. Except for being compatible with all other real facts established in physics, they do not at all belong (yet) to the physical theory that describes our world. Unless there will be undoubted and clear experimentally established facts (including maybe the observation of an EDM) which confirm one or the other possible model, such theories have no status in physics, whatsoever.

Unlike for the leptons, for hadronic particles already the Standard Model has provision for EDMs through the so-called QCD Θ-term. Θ is a purely topological parameter, i.e. it arises from boundary conditions, and is associated with P and CP, respectively T, violation (for a more thorough discussion see see e.g. [65, 8]). According to our present knowledge θ needs to be experimentally determined and it is compatible with zero. It could have a finite value. To present knowledge the smallness of the value of Θ has to be considered accidental. Although, models involving hypothetical axions could explain a zero value for Θ. The limit on the neutron EDM provides the present best bound inline image [66, 67] and an about twice as large limit has been extracted recently from a search for an EDM in 199Hg [48].

The necessary improvements over present limits in order to reach the Standard Model values (other than those possibly arising from the QCD Θ parameter) are also given in Table 1. Although, at this point the theoretical predictions for the Standard Model values have not been worked out in full detail, yet. The community relies on the validity of the present more general estimates and a number of worked out details. It has been common knowledge that within the Standard Model EDMs cannot appear in first order [68-70]. They are rather expected to arise in higher order loops and are therefore very small in the systems of present major interest [31]. For the neutron there are some 4 orders of magnitude to go, for other systems the room for discovery of non Standard Model CP violation through EDMs is even significantly larger [6].

Very recently, however, the loop-less generation of a nucleon EDM within the Standard Model has been pointed out [71]. EDMs are generated at tree level to second order in the weak interactions through bound state effects. For the neutron this yields a predicted EDM of about 10−31 e cm [71]. Concerning the Standard Model values of EDMs there exists some room for an improvement of the situation. More solid numbers would be appreciated when choices for new experiments are discussed.

3.1 Single Elementary Particles and Atomic Nuclei

Single particle EDMs are the simplest systems because there is no theory involved to evaluate, e.g., shielding or enhancement on an EDM by any internal structure of the investigated system. Any measured EDM can be directly attributed to the fundamental particle itself. Within the group of single particle experiments we can distinguish between to our present knowledge ‘point’ particles such as the leptons electron (e), muon (μ) or tauon (τ) and particles that have known substructure such as the neutron (n) or the proton (p).

These leptonic particles are the cleanest objects to investigate, because they have no known internal structure. An observed particle EDM would be an undoubted property of the particle itself. Among the elementary particles with an established quark substructure are the nucleons p and n and atomic nuclei consisting of them. In these composed systems an EDM can arise in addition to the intrinsic EDMs of the constituents from properties of the interaction between the constituents. As an example, in the deuteron an EDM can arise not only from constituent EDMS, but also from CP-odd parts in the interaction between the proton and the neutron [59].

3.1.1 Neutron

Among the presently ongoing EDM searches there are several independent projects aiming towards the discovery of an EDM of the neutron from sources outside of the Standard model (see e.g. [72, 73]). The modern ones exploit the fluxes available for ultra-cold neutrons at various reactors or accelerators worldwide. These competing projects try to achieve improvements over the presently best result [67, 74] largely through the implementation of sophisticated technical developments in their challenging setups.

The latest completed neutron EDM measurement has yielded a precision result in a spin precession experiment [67]. The neutron EDM searches show that now the experiments have reached a level of accuracy where subtle effects can mimic a false EDM, because such effects may be coupled to the electric field and, e.g., reverse if the field is reversed. The final limit in the latest experiment had therefore a need for correction even after publication. It concerns the systematic effects which are caused by the particles moving in the apparatus, in particular also in a partly inhomogeneous magnetic field. The static field in the laboratory is experienced by the moving particle not as a static one. This time dependent field in the eigenframe of the particles can have large consequences, if its frequency comes close to the frequencies of the neglected terms in rotating wave approximation (Bloch-Siegert term). In particular a false EDM can be simulated by Larmor frequency shifts which are introduced by geometric phases [75, 74], as such effects can be proportional to the electric field. At present the bound on the neutron EDM is inline image e cm (90% C.L.).

The neutron experiments show very visibly the sensitivity of precision EDM searches to systematics caused by the environment. At first glance such may not be obvious in precision experiments at the forefront of possibilities. Major improvements of the apparatuses in the ongoing set of many independent experiments concern control of the magnetic field via co-magnetometry by exploiting, e.g., Hg magnetometers or squids which are installed close to the actual measurement volume or a buffer gas co-magnetometer which is discussed [76]. It is considered essential that a co-magnetometer really senses the magnetic field in the fiducial volume, at best it measures simultaneously with the EDM search experiment and it co-exists within the the same volume under observation. This condition can be met, e.g., with two mixed gases one of which serves as a co-magnetometer and the second one is searched for an EDM. Such a setup is possible with 3He as magnetometer with known much lower sensitivity to an EDM and 129Xe as a candidate atom for an atomic EDM (see e.g. [77]).

The neutron EDM has at present the attention of a number of independent experimental projects which are actively pursued at different laboratories worldwide. This includes experiments which follow the more traditional routes and implement significant refinement, where neutron flux is a central issue. Such projects are under way at the Institute Laue Langevain in Grenoble, France [78], at the Paul Scherrer Institute (PSI) in Villigen, Switzerland [79], at the Technical University München, Germany [80], at the Spallation Neutron Source in Oak Ridge, USA [81], and a joint project of RCNP KEK and TRIUMF [82]. At the future European Spallation Source in Lund, Sweden, also crystal-diffraction promises to yield competitive limits [83]. These remarkable experimental efforts are accompanied by theoretical activities among which [84, 85].

3.1.2 Charged Particles

In the past a few EDM search experiments have been performed on charged particles exploiting just the properties of these systems themselves directly and without using external electric fields that are applied to the systems in the laboratory. These projects have produced respectable limits.

As an example of the possibilities, already in 1971, a lifetime measurement of the inline image state in the muonic helium ion (4Heinline image was carried out. This corresponds to a limit on the muon EDM of inline image e cm [86].2 A finite EDM would have shortened in that experiment the inline image lifetime of the metastable state. Further, also the good agreement between theory and experiment for the transition frequency of the 22S1/2-22P3/2 transition in (4Heinline image had been interpreted in the 1970ies in terms of a limit for the muon EDM of order inline image e cm [87]. The discussion in the following decades on the validity of the reported lifetime of the 2s state of (4Heinline image under the high pressure conditions (40 bar)in the experiment [88-90] has primarily been crucial for the interpretation of the laser spectroscopy result in terms of the mean square charge radius of the α-particle the value of which must be still viewed with caution, therefore.

However, this issue is less relevant for pointing out a method to search for an EDM which is different from spin precession experiments. Also, at no time the best limit on the muon EDM has been affected, because of two main reasons: (i) The longevity of the 2s state in (4Heinline image has been measured independently [88]. The lifetime of the 22S1/2state has been determined to be inline image ns at a pressure of 200 mbar. This experimental result provides for an independent extraction of a limit on the muon EDM also in the range of 10−15 e cm and demonstrates the feasibility of the method. (ii) A limit on the muon EDM of inline image e cm [91, 92] had been reported already in 1960 from a muon beam experiment at the Nevis cyclotron facility, New York, USA.

This remarkable limit on the muon EDM at the time had been reached by searching for a spin rotation in the motional electric field which muons experience when they pass through a magnetic field. Furthermore, already in 1961 the first muon g-2 experiment at CERN had been modified to establish an even more stringent limit of inline image e cm [93] by looking for a precession of the muon spin out of the plane of orbit in a magnetic field, which would have been caused by a finite muon EDM interacting with the motional electric field.

The majority of searches for EDMs in charged particles to date have been performed using neutral systems such as atoms, molecules or condensed matter, which contains the objects of interest, such as electrons or nuclei, as constituents. The choices for approaches in experiments are a consequence of the fact that most of the attempted measurements of an EDM require an electric field E. All presently known and ongoing projects follow that route. A charged particle experiences in a static electric field of trivial geometry (such as, e.g., a constant homogeneous field) an acceleration. This has been considered a severe limitation by the majority in the community, because the particle would be expelled from the fiducial volume rather rapidly. However, this argument is only valid for rather straightforward, such as homogeneous, electric field geometries (see e.g. [5]). There are, however, field topologies in which this argument does not hold. and this fact had been demonstrated already in the early 1960ies in muon experiments (see above).

EDM searches do not necessarily require an external homogeneous electric field at all. This fact had apparently not been recognized widely in the atomic physics based community which has been concerned primarily with low energy high precision experiments to search for an EDM until the late 1990ies. Therefore searches for charged particle EDMs such as the electron or of nucleons and nuclei had been performed exclusively in neutral atoms. This has prohibited setting up dedicated high precision EDM searches which can investigate free charged particles directly. Geometries for experiments where this is possible are, e.g., magnetic storage rings with a radial electric field in the storage region.

The muon has been the first particle that was investigated in a non-trivial field topology, i.e. a limit has been established for the muon EDM inline image parasitically with precise measurements of the muon magnetic anomaly inline image. One example, where this method has been exploited successfully to obtain higher precision already in the 1970ies, is the search for an EDM of the muon inline image in a storage ring [94] which has been conducted parasitically to the precise measurement of the muon magnetic anomaly [95]. An out of orbit plane precession of the muon spin was searched for along with the data taking for the muon g-2 value; the underlying measurement principle(concerning the origin of the electric field and the detection of the muon spin direction) was the same as the one that been employed already in 1961 [93].

The most recent muon g-2 experiment at the Brookhaven National Laboratory (BNL), Upton, New York, United States, searched also for a muon EDM in a parasitic measurement along the main data taking [96, 97]. An EDM would have manifested itself in an oscillation of the the decay electron distribution around the muon orbit plane. The so far best limit on the muon EDM has been established to be dinline image e cm (90% C.L.). Because the measurement of the muon magnetic anomaly inline image has yielded a manifest some 3.5 standard deviation difference between experiment and theory [46] a new g-2 experiment will be set up at Fermilab, Batavia, United States, to verify or refute a discrepancy, which would be a sign of New Physics [98]. This new experiment aims for an improvement in inline image by a factor of 5. At the same time it has a potential to improve the present bound on inline image by one order of magnitude.

Since the wider recognition of the possibility to exploit charged particles directly a number of further systems has been thoroughly considered. Precision experiments both with trapped cold molecular ions in Paul traps [99] and at high energies using dedicated storage rings muons and nuclei, such as proton, deuteron, triton and others [59, 111-115, 96, 116-118] are presently under way and aim for most competitive results, i.e. limits on the respective EDMs of order 10−29 e cm or better. The projects include such with a stepwise approach with intermediate accuracy of order 10−24 e cm to 10−25 e cm using to a large part existing storage ring devices such as COSY in Jülich, Germany [114, 112], and such that want to reach the most stringent bounds in one go such as an at the BNL based initiative [57, 115].

As far as the experimental approaches are concerned the situation is characterized by a rapid sequence of proposed concepts which range from primarily magnetic storage to primarily electrostatic storage. Which of the concepts is better suited for a real experiment in future will depend on the system under investigation, where its magnetic anomaly plays a major role for the choice of the type of storage ring and technique, as well as resources and the actual collaboration performing a real experiment at a future time. For magnetic storage experiments with sensitivity at the 10−24e cm level major equipment exists already with a moderate pole diameter (order 1 m) magnet at PSI [112] and the COSY storage ring at FZ Jülich [114].

A dedicated storage ring for an EDM experiment was first considered for muons [115]. Longitudinally polarized particles are injected into a magnetic storage ring with a suited radially directed electric field to compensate a spin precession in the plane of orbit which originates from the muon magnetic moment. In such a situation a muon EDM would express itself as a spin rotation around the radius of the particle orbit. This can be observed as a time dependent change of the above/below the plane of orbit counting rate ratio. The time dependence is to first order linear for all realistic achievable fields and experimental geometries) Different from most other EDM searches, in such an experiment the possible muon flux is a major limitation.

For models with nonlinear mass scaling of EDM's such a muon EDM experiment would already be more sensitive to certain New Physics models than the present limit on the electron EDM (see [119-121]). Note, in certain Left-Right or supersymmetric symmetric models a value of inline image as high as 10−22 e cm is possible.

For the muon in particular a limit of 10−24e cm can be potentially reached with a relative moderate cost project that exploits largely existing key equipment and existing surface muon (about 28 MeV/c momentum) facilities for a first dedicated ring EDM experiment [112] with discovery potential. This value is in the range of a proposed experiment using an existing magnet system at the Paul Scherrer Institut in Villigen, Switzerland [112]. An experiment carried out at a more intense muon source could provide a probe to CP violation for particles in the second generation with correspondingly higher sensitivity. The muon as a particle from the second generation may have different routes to an EDM than the mostly investigated first generation particles. However, the community has not yet really started to exploit this open window of opportunity.3

The deuteron is the simplest known nucleus. Here an EDM could arise not only from a proton or a neutron EDM, but also from CP-odd nuclear forces between the two particles [122]. It has been shown recently [59] that in certain scenarios the deuteron can be significantly more sensitive than the neutron. The situation is evident for the case of quark chromo-EDMs, where the EDMs induced into deuteron (inline image) and neutron(inline image), respectively, are

  • display math(10)

where inline image and inline image are the chrom -EDM of the down quark and the up quark, respectively. This implies that the deuteron could have a much higher sensitivity to quark chromo-EDMs which arises from the proton-neutron interaction within the deuteron. Because of its rather small magnetic anomaly the deuteron is a particularly interesting candidate for a magnetic ring EDM experiment, as it provides for the possibility to compensate in a magnetic storage ring the magnetic spin precession [113] with a suited electric field. In such an experiment scattering off a target can be used to observe spin precession, for example. Deuteron polarimeter studies turned out to be very encouraging [123].

Also heavier nuclei in atomic systems with partly filled electronic shells have been considered [124-127]. Because of its rather low magnetic anomaly the 223Fr nucleus is a particularly interesting further candidate for a ring EDM experiment with sensitivity to a nuclear EDM.

Possible ring EDM experiments are presently being intensively discussed and the favoured approaches are subject to frequent changes, yet. A thorough comparison of the various ambitious approaches, which often aim for many orders of magnitude improvements over presently established EDM limits, is not possible unless experimentally the viability of any of the possible paths will have been demonstrated.

3.2 Atoms and atomic Ions

Atoms and atomic ions each consist of a nucleus and one or more electrons. Depending on details of the atomic structure we can have enhancement or suppression of fundamental particle EDMs. Diamagnetic atoms such as Hg, Xe, Rn, Fr and Ra render the possibility to search for nuclear EDMs in experiments which employ the atomic ground state. Excited states may provide for the possibility for searching an electron EDM, if the angular momentum of the state is finite. Paramagnetic atoms such as Tl or Cs provide for electron EDM searches.

In diamagnetic atoms the Schiff theorem governs the behaviour of the system. Instead of the complete suppression of an EDM which is expected in non-relativistic approximation for an atom consisting of point-like constituents, we can have substantial enhancements, depending on the details of the atomic system (see Table 2). Different calculations have led to only slightly different enhancement factors K. For the Ra atom inline image is found in [42] whereas in [128] inline image is reported. Given that no EDM has been seen yet, the present level of agreement therefore suffices to judge the potential of experiments.

Table 2. Enhancement factors for an electron EDM inline image in several atoms and diatomic molecules have been calculated [42]. They vary strongly and are generally highest for systems composed of several atoms, in particular if the internal field in the molecule is largely due to difference in the electronegativity of the atoms
ParticleRbCsThFrRaPbOYbF
Enhancement241255851 15040 00060 0001 600 000

Recently the question was posed whether the Schiff theorem would be complete [129]. It has been shown that in each case a more careful analysis of this issue is required. In an atom, to first order the nucleon EDMs can be completely shielded by the electrons [130, 129, 127]. However, in general the rather significant enhancement of the electron EDM due to relativistic electron motion has been found to survive.

The search for an EDM in the diamagnetic 199Hg atom has yielded the numerically best upper limit of all the EDM searches so far [110, 100]. It is inline image e cm at 95% C.L. This latest result constitutes an improvement by a factor of 7 over the previous experiment [131] by the same group at the University of Washington, Seattle, USA. It had used the same isotpe 199Hg in an earlier version of the apparatus. This achievement was possible primarily by better control of systematic effects by conceptual and technical improvements. This process is being continued through, e.g., investigations of linear Stark interferences, which can produce energy shifts similar to those expected from an EDM [132]. The further improvements include a better control of the magnetic field in a multi-cell arrangement and longer spin coherence times [48]. The experiment has been analyzed to set numerous new constraints on a variety of CP violating processes of interest for New Physics beyond the Standard Model [110].

Recently spin coherence times of 60 h for 3He and of some 6 h for 129Xe could be achieved. This has already been exploited to limit Lorentz- and CPT- violation for the bound neutron through the observation of free spin precession in a 3He-129Xe gas mixture [133a]. The measurement took place in a magnetically well shielded environment at the Physikalisch Technische Bundesanstalt (PTB) in Berlin, Germany. The experiment had already many major ingredients of relevance for a significant improvement of the limit on the EDM in a 129Xe atom. A corresponding experiment with a potential for observing or limiting the EDM in the 10−30 e cm range [77] or even lower [133a] is underway. Significant improvements over the last successful EDM search in 129Xe [134] are expected by some 4 orders of magnitude [133a].

In the recent years it became apparent that several radioactive isotopes of Rn, Fr and Ra in particular offer excellent opportunities for EDM searches due to atomic or nuclear enhancement mechanisms. They are present and pronounced in these system. The availability of intense radioactive sources of Ra as well as the advances at dedicated radioactive beam facilities that can deliver typically 105 to 106 Fr or Ra ions/s during sufficiently long (typically several weeks) beam times to experimental stations makes new experiments with such species possible. Nevertheless, it is a characteristic feature of experiments with radioactive samples that they have to perform with very low quantities of atoms.

In the Ra atom an accidental close proximity of the 7s7p3P1 and the 7s6d3D2 levels causes a significant enhancement of a potential electron EDM by a factor of about 40 000 (see Table 2) [135, 136]. For certain isotopes such as 225Ra and 223Ra an enhancement factor of several 100 for a nucleon EDM has been calculated which is due to the octupole deformation in these nuclei [137, 138]. For 225Ra the EDM could be even as large as 6 to 50inline image e cm [139]. The enhancement is associated with the close proximity of nuclear states of opposite parity. On the experimental side two programmes are ongoing at Argonne National Laboratory, United States, and at KVI Groningen, The Netherlands. Measurements of relevant optical wavelengths and excited state lifetimes as well as the development of efficient (≈1% level) magneto-optical trapping of heavy alkali earth elements Ba [140] and also Ra [141, 142] have already been achieved as major milestones in precursor experiments. Also the production of several Ra isotopes of interest has been successfully demonstrated already [143] and spectroscopy of their ions has been successfully conducted [144-146].

At TRIUMF, Vancouver, Canada, an experimental programme has been started to exploit in particular nuclear octupole deformations and the associated potential enhancement of an EDM of the radon (Rn) atom in its ground state [147]. Unlike in Ra there is no similar possibility for an enhancement of the electron EDM in Rn an Fr. A similar enhancement exists for Fr (see Table 2) and a corresponding experiment is underway at the Tohoku University, Japan [148]. The experiment uses already successfully an 18O beam directed onto a 197Au target to produce inline imageFr isotopes (and x neutrons). For the EDM experiment magneto-optical trapping of Fr atoms is foreseen. Stable Rb is used as a precursor to set up the experiment.

3.3 Molecules and Molecular Ions

The strong enhancement of a potential electron EDM in polar molecules is also being exploited for EDM searches. In such molecules internal very strong electric fields exist which can significantly enhance the possibility to observe an EDM of the constituent particles.

The best bound on an electron EDM inline image comes form a search experiment that uses YbF [101]. The experiment in London, United Kingdom, uses a beam of cold polar YbF molecules in an interferometric apparatus. A limit of inline image e cm (at 90% C.L.) could be established. It improves the previous limit [102] that had been posted in a beam of atomic 205Tl by a factor of 1.5 and thereby further pushes the constraints on speculative extensions to the Standard Model. The experimenters are confident that inline image can be eventually probed at a level of at least inline image e cm using YbF, where no potential systematics down to inline image e cm could be identified [149] up to now.

Projects with molecules have been started in PbO [150, 151], ThO [152] and WC [153], because of the very large predicted enhancement factors in these polar systems. Besides PbO and ThO, neutral systems such as TlF and YbF and the ions HfF+ and ThF+ are employed in electron EDM searches [154]. As a recent novelty among the approaches to search for an electron EDM, the possibility to exploit charged molecular ions such as HfF+ and ThF+ has been recognized and a corresponding experiment has been started [99]. A primary advantage is that trapping of ions in an ion trap is rather straightforward. This provides a basis for the exploitation of the strong enhancement factors for electron EDMs in polar molecules [99]. In the RaO molecule the (T,P)-odd spin axis interaction is even 500 times larger than in TlF [155]. However, no concrete plans are known to take advantage of this fact in an experiment.

The ongoing EDM experiments which use charged molecular systems directly are still in the exploratory and feasibility study phase. The reports on progress are very promising and encouraging.

3.4 Condensed Matter

In condensed matter large fields may exist or such fields can be more conveniently handled than in vacuo or in gaseous samples. This can be advantageously exploited in EDM searches. It will be of crucial importance for any EDM experiment using condensed matter as a sample that they verify and show unambiguously whether any possible positive EDM signal is a true feature of the sample of interest rather than an artifact of an asymmetric behaviour of the condensed matter environment.

Although not yet competitive, an electron EDM search in gadolinium-iron garnet yielded inline image e cm as an intermediate result with a potential to challenge present best electron EDM results. The experiment uses a solid sample and measures a voltage across it. The voltage is induced by the alignment of magnetic dipoles in an external magnetic field [156]. The experimental programme shows that careful and extensive systematic studies are indispensable to understand all details of such an experiment [157, 158].

A novelty has been introduced recently with the idea to search for an EDM in liquid Xe droplets [61]. The experiment uses a technique where several microscopic hyper-polarized liquid 129Xe droplets are placed in a matrix inside a low-field NMR apparatus. The spin precession in external fields is observed with superconducting pick-up coils and SQUID technology. The experiment is in a research and development phase and promises an improvement for inline image by some 3 orders of magnitude over the presently best limit from 129Xe [134].

Among the condensed matter samples which are presently investigated concerning their suitability for EDM experiments garnets [60] and liquid droplets of Xe [61] are both very promising. Considerable effort has been spend to verify that a future result will be not subject to uncontrolled systematic effects with so far very encouraging results.

4 T-violation searches other than EDMs

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography

There are many more possibilities in physics to find T-violation besides through searches for EDMs, in particular also in low energy experiments. Searches for permanent EDMs and searches for T-violation, respectively CP- violation, in other systems are closely related. Examples with comparable discovery potential are the precision studies of neutron and nuclear β-decays (see e.g. [159-162]).

Among the presently ongoing activities certain correlation observables in nuclear β-decays provide excellent opportunities to find new sources of CP violation [163-165]. In β-neutrino correlations the ‘D’-coefficient [166] (for spin polarized nuclei) offer a high potential to observe new interactions in a region of potential New Physics which is less accessible by EDM searches. The coefficient D describes the correlation of the momenta of the β-particle and the neutrino in the decay of polarized nuclei. D has been determined from the decay of polarized cold neutrons by detecting electron-proton coincidences to D = inline image [167, 168], where the first uncertainty is of statistical origin and the second one is systematic. Note that final state interactions contribute at the level of 10−5 and can be calculated at the level of 10−7 [169].

The ‘R’-coefficient [166], which has a similarly low Standard Model value [169] can be measured via the observation of β-particle polarization. It explores the same areas as present EDM searches or β-decay asymmetry measurements. Such challenging experiments are underway (see e.g. [161]). The Standard Model values for the D and R are small. The Standard Model CP violation yields for the neutron the tiny values Dinline image inline image and Rinline image inline image[169]. This is well out of reach for experiments in the near and not so near future such that for practical purposes the Standard Model expectation for the T-violating coefficients D and R can be considered to be zero. All experiments to date have been in agreement with the Standard Model prediction. Thereby bounds on New Physics models could be set (see e.g. [170]).

As a further example of the obtainable results, recently final results became available from an experiment at the SINQ facility of the PSI where both components of the transverse polarization of β-decay electrons from the decay of polarized unbound 25 K cold neutrons were measured. For the first time the R-coefficient in β-decay was determined as R = inline image [171]. This result provides significantly tighter constraints for scalar and tensor couplings in weak interactions as well as for models with leptoquarks and R-parity violating minimal supersymmetry.

5 Conclusions

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography

There is a large number of searches for EDMs on a variety of systems. They all are very well motivated and no best system with highest chances for success can be singled out. The experiments all have unique and robust discovery potential. Furthermore, novel ideas have emerged in the recent past to use yet not studied systems where significant enhancements of particle EDMs are predicted, beyond what was known until recently. New experimental approaches have emerged in the recent past to exploit such new opportunities. They provide excellent opportunities which complement the more traditional experimental approaches on neutron-, atom- and electron-EDMs. The field is characterized and largely benefits from the fruitful interplay between theory and experiment, in exploring the landscape beyond the Standard Model, in identifying new possibilities for experiments and in solidifying the results reached in experiments. Any successful future EDM search experiment in one system needs to be complemented by experiments on other systems in order to pin down eventually the mechanisms which cause the observed EDMs.

The highest values predicted in theoretical work in beyond the Standard Model speculative theories are well within reach of presently ongoing and planned experiments. This makes this field most exciting as a major discovery may be just around the corner.

It requires a case by case detailed analysis in order to identify the highest chances for speedy progress in the search race for additional sources of CP violation. Here technical feasibility is a crucial factor. The presently ongoing and partly very advanced projects each are well motivated as none of them can be considered more promising than any other on the basis of secure knowledge. They have a significant potential for a breakthrough discovery.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography

This work has been supported by the Dutch Stichting voor Fundamenteel Onderzoek der Materie (FOM) in the framework of the research programmes 114 (TRIμP) and 125 (Broken Mirrors and Drifting Constants).

  1. 1

    An all encompassing discussion of all the theoretical models which provide for EDMs would exceed the scope of this article.

  2. 2

    We mention this experimental method other than spin precession in an external field here, because with the significant progress in the production of particles, in spectroscopy and in measurement technology similar approaches could still be competitive today.

  3. 3

    A New Physics (non-SM) contribution inline image to the muon magnetic anomaly and a muon EDM inline image are real and imaginary part of a single complex quantity related through inline image e cm with a yet unknown CP violating phase inline image. This provides a further strong motivation to search for a moun EDM inline image already with values well larger than the search limits for the neutron or the electron.

References

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography

Biography

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Searches for an EDM – general aspects
  5. 3 Systems to search for EDMs
  6. 4 T-violation searches other than EDMs
  7. 5 Conclusions
  8. Acknowledgments
  9. References
  10. Biography
  • Image of creator

    Klaus Jungmann studied Physics at the University of Heidelberg, Germany. He received a Ph.D. degree in 1985 for laser spectroscopy on positronium. Until 1987 he was postdoctoral fellow at the IBM Almaden Research Laboratory in San Jose, USA. Until 2000 he spent extended research periods at the Paul Scherrer Institut, Switzerland, the Rutherford Appleton Laboratory, UK, the Los Alamos National Laboratory, USA, and the Brookhaven National Laboratory, USA. He is now Professor at the Kernfysisch Versneller Instituut of the University of Groningen, Netherlands, with a focus on high precision experiments at low energies and at the interface of atomic, nuclear and particle physics.