No EDMs in the Standard Model
Permanent EDMs of fundamental particles arise through radiative corrections that involve charge-parity (CP) violation. Although the CP-violating phase in the quark sector of the Standard Model is not small, the Standard Model's special structure allows its EDMs to arise only from diagrams with so many loops, with so many virtual particles of large mass, and so many other special cancelations that the EDMs, though nonzero, are predicted to be orders of magnitude below the reach of any experiment yet conceived.
EDMs in Standard Model extensions
Standard Model extensions generically possess new particles with new sources of CP violation. They do so because the CP violation already in the Standard Model has effects too small to explain the observed excess of matter over antimatter in the universe, and because efforts to embed the Standard Model in larger theoretical structures, such as supersymmetry, have so far produced overwhelmingly, only theories with large numbers of CP-violating phases none of which have any reason to be small.
The Minimal SuperSymmetric Standard Model (specifically MSSM-124), for example, possesses no fewer than 40. The new particles and phases typically cause EDMs at one-loop order. Presently claimed EDM limits are already about a factor of 100 below simple Supersymmetry estimates that use superpartner masses of 100 GeV and CP-violating phases of order unity.
EDMs and accelerator searches for new particles
The great strength of a tighter limit on the electric dipole moment is not just that will constrain Supersymmetry, or any one specific model, but that it will constrain all proposed theories, including ones yet undreamed of.
And even if a direct accelerator search for a new particle succeeds, and provides evidence of a new CP-violating interaction, measurement of an EDM will likely remain useful, since it is likely that the combination of theoretical parameters probed in accelerator experiments will be orthogonal to the combination that is probed in an EDM experiment.
However much information might become available from accelerators, experiments on EDM will be a inexpensive source of more; and indeed, information about EDMs from inexpensive experiments may instead inform the construction of very expensive accelerators.
Electron, neutron, and atomic EDMs
It is becoming more difficult to maintain a Minimal Supersymmetric Standard Model (MSSM) and not have observed EDMs , especially when EDM limits on the electron, the neutron, and diamagnetic atoms are used together to constrain adjustments to CP-violating phases .
The advantages of searching for an EDM in multiple systems are:
Together, electron, neutron and diamagnetic atom EDM experiments presently constrain Supersymmetry better than do just any one or two of these. Using only neutron and electron EDM experiments, it was possible to suppress the EDM, maintain large CP-violating phases, and keep small superpartner mass limits by arranging cancellations [3, 4]. But when the diamagnetic atom EDM experiment was added, the largest CP-violating phases (and smallest superpartner masses) were no longer allowed [5 ‐ 8].
If non-Standard Model EDMs exist, we do not know if they will easiest to observe in the electron or other lepton, the neutron, or a diamagnetic atom.
If an EDM is discovered in one system, results in others will be needed to distinguish between theoretical models. An electron EDM limit will help to distinguish a neutron EDM that arises from θQCD, for example, from one arising from Supersymmetry.