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 . 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 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 . 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. ).
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 , at the Paul Scherrer Institute (PSI) in Villigen, Switzerland , at the Technical University München, Germany , at the Spallation Neutron Source in Oak Ridge, USA , and a joint project of RCNP KEK and TRIUMF . At the future European Spallation Source in Lund, Sweden, also crystal-diffraction promises to yield competitive limits . 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.
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 e cm  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. ). 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.
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  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  and the COSY storage ring at FZ Jülich .
A dedicated storage ring for an EDM experiment was first considered for muons . 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 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  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 . 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
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.