Experimental limits below predictions
Simple estimates of electron EDMs from Supersymmetry and Minimal Super Symmetric Standard Models are orders of magnitude larger than present experimental limits when superpartner masses are set to 100 GeV and CP violating phases to unity .
Other beyond-Standard-Model calculations that can yield larger than experiment electron EDMs include: left-right symmetric models, lepton flavor changing models, neutral Higgs couplings, dilepton, leptoquark, mirror fermion, horizontal gauge, and composite electron models .
Supersymmetry adapts to experimental limits
Larger superpartner mass and smaller CP-violating phases result in smaller EDMs but also make the theory less attractive. One clever work around is to impose large mass on the superpartners that produce the largest contribution to EDMs while leaving the other particles at low mass .
Another is to adjust the CP-violating phases to cancel out EDMs, but limits from electron, neutron and atom EDMs constrain the adjustments. (See: Can an electron EDM be discovered? )
To explore the vast number of possible couplings in SUSY models, fitting packages have been released ,  where the EDMs of fermions can be generated  or used as input .
Axion-like particles with mass above 0.01 eV, that mediate interactions between electrons and nucleons, which violate parity and time reversal, can give rise to EDMs in atoms and molecules . The effects in alkali atoms are predicted to be large enough that an improved atom EDM experiment would be competitive.
Theorests have considered neutron EDMs generated from PeV scale sources of CP violation in PeV scale MSSM extensions . Can electron EDMs be far behind ?
And finally there is always the possibility of a new particle, such as XKCD‘s “The Fixion” that will explain everything .
How can you be sure that the result from your experiment, in combination with other experiments will be reliable?
First, we are using self-verification by looking at it in two different atoms with essentially the same magnetic moments but very different enhancement factors. And the atoms are both simple: one electron outside a closed shell. So we think we can produce pretty convincing result just on our lonesome.
How does your experiment relate to other electron EDM experiments?
Simply by improving the single-atom limit on the electron EDM by a factor of 10, (over thallium) we are in fact providing additional validation to those existing limits using diatomic atoms. We think that's a terrific idea because this is a very high stakes game.
Somebody has to decide when and whether to build the Next Linear Collider to hunt for the exotic particles whose existence would be suggested by detecting an electron EDM.
You do not want to decide not to build the Next Linear Collider based on one experiment on a diatomic atom.The atomic theory of the diatomic atoms and of the single atoms is completely different. The nature of the dominant experimental systematic is completely different. So if you want a reliable upper bound, you will need experiments on both species.
What are the differences between the atomic and the diatomic experiments to measure the electron EDM?
There is a certain difference in philosophy between the diatomic dipole moment experiments currently being run and the alkali experiment we’re working on. We're running on an alkali---one electron outside a closed shell. In fact, we're studying the ground state of cesium, and since the hyperfine splitting is used to define the second this ground state has been studied to exhaustion.
The relativistic effects in the diatomic molecules have not been studied to exhaustion; until somebody thought you could see a permanent electron electric dipole moments using them, such effects were a very obscure little backwater indeed, and the sophistication and reliability of the theory is intrinsically less.
We're offering to come to High Energy Physics and say, we really understand the atomic theory, because we are dealing with an alkali atom: that theory is very reliable but the experiment is very much more challenging because the alkali enhancement factor isn't so big. Experimenters using diatomic polar molecules will say their enhancement factor is big and so the experiment not as challenging technically; but the atomic theory on which they rely and the relativistic corrections in particular are very much newer. So you can legitimately ask, if someone claims to see a CP-violating effect, will I believe the atomic theory?
That's a question which is a much harder for diatomic molecule experiments currently to answer than experiments on alkalis. No doubt the reliability will improve over time, but High Energy Physics needs an answer within five years, and we aren’t just going to wait.
Simply put, why do it?
It takes multiple experiments to determine what is the actual source of CP violation you do see. For example, the neutron EDM is providing information about what is going on in the quark sector, telling us that the CP-violating theta term of QCD is zero; that EDM doesn’t help you with the lepton sector.
Also you can induce an electric dipole moment of an atomic system by a CP-violating interaction that does not cause just an electron EDM. Such interactions can occur in the nucleus between the nucleons, or because of a novel electron-nucleon interaction, and you would need experiments on different atomic and molecular systems in which the possible interactions are of different sizes to figure out the physical origin of any electric dipole moment you see. So experiments on alkali atoms are, at the least, necessary to provide a reliable guide.
Null experiments need confirmation
It is a widely followed practice that important experimental results, positive or negative, be confirmed by another group, preferably at a different laboratory or facility, and preferably using a different experimental method. High Energy and Nuclear Physics have both learned this after embarrassing false positive and some false negative experiments. For major experiments, complementary detectors are built and operated by competing groups.