For particle physicists the EDM looks like this:

So, the EDM of the electron is defined as a coefficient

*de*of a particular operator that couples the electron field

*e*to the electromagnetic (photon) field

*Aμ*. By dimensional counting,

*de*is expressed in units of 1/Energy or, equivalently, in units of length. The ACME limit reads |

*de*| ≤ 8.7×10^−29 e*cm or |

*de*| ≤ e/(2×10^14 GeV), where

*e*is the electric charge. This is 12 times stronger than the previous best limit.

The connection to what ordinary people understand as the EDM is that, in the limit of non-relativistic quantum mechanics, the EDM operator above reduces to the interaction Hamiltonian

Thus, at non-relativistic energies the EDM corresponds to a shift of energy levels of the electron in an external electric field

*E*that depends on the direction of electron's spin

*Se*. This is how the EDM is measured in practice, up to a few unexciting details that those with a passion for craftsmanship can find in the ACME paper ;)

The EDM operator is non-renormalizable as it has dimension 5 (actually, dimension 6 when it is rewritten in a form that is invariant under the Standard Model gauge symmetry). For that reason it cannot appear in the Standard Model Lagrangian, and the lowest order prediction is

*de=0.*However, it can be generated by loop effects, much as the closely related operator responsible for the anomalous magnetic dipole moment of the electron. The important difference between these two is that the EDM, unlike the magnetic moment, violates CP symmetry. The Standard Model contains only one source of CP violation - the invariant phase in the CKM matrix. This invariant is proportional to the product of all the CKM mixing angles which are small numbers, therefore CP violating effects in the Standard Model are severely suppressed. Moreover, it turns out that the electron EDM arises only at the 4th order (4 loops) in perturbation theory. All in all, the contribution from the CKM phase is estimated as |

*de*| ≤ 10^-38 e*cm, many orders of magnitude below the current experimental sensitivity. The neutrino sector may bring new sources of CP violation - the Dirac and Majorana phases in the PMNS neutrino mixing matrix - and these contributions to the electron EDM may arise already at 2 loops. Since we don't know the phases in the neutrino sector (or even the absolute values of the neutrino masses for that matter) we cannot compute that contribution exactly. However, we know it should be suppressed by neutrino masses squared and one can estimate it leads to

*Δde*≲ 10^-43 e*cm, even smaller than the CKM phase contribution. At the end of the day, the Standard Model prediction is

*de=0*for all practical purpose. That's great, because it means that the electron EDM offers a clean test of the Standard Model: a measurement of a non-zero value would be an unequivocal proof of new physics beyond the Standard Model.

So what does the new ACME measurement tell us about new physics? Generally, new physics contributions to the EDMs must be of the form

where v=246 GeV is the electroweak scale, M is the mass scale of new physics and c is a numerical coefficient that may be of order 1, or may be smaller depending on a model. For c∼1, the ACME result translates to the mind blowing limit of M ≳ 10^5 TeV. This is the best case scenario that arises when new physics has a completely generic flavor and CP violating structure and couples strongly to the electron. But not every new physics model is constrained so stringently. It is often automatic that new physics contributions to the electron EDM are proportional to the electron mass (if it isn't, an appropriate protection mechanism can be rather easily incorporated into the model). Moreover, the EDM is typically suppressed by a 1-loop factor at least. Then a better estimate is

which leads to the limit M≳10 TeV for the mass scale of CP violating new physics. That's a less impressive but still a non-trivial constraint on models of new physics at the TeV scale.

It is worth commenting on supersymmetry as a particular example of new physics that may come in a package with new sources of CP violation. Even in the minimal supersymmetric model there are dozens of potential new phases that could show up in the electron EDM. To avoid a too complicated and too pessimistic analysis one always introduces additional constraints on the parameter space that hopefully can be explained by an underlying model of supersymmetry breaking. As an example, let's see what happens in the very restricted framework where all superpartner masses are the same, and the only new source of CP violation is the relative phase θ between the μ term and Bμ term in the Higgs sector. Then one obtains

where g is the weak coupling in the Standard Model, and tanβ is a free parameter describing the supersymmetric Higgs sector. This is a very severe constraint for large tanβ, but also a non-trivial one for moderate tanβ. Of course, this kind of arguments does not robustly exclude supersymmetry showing up at the energies achievable at the LHC. The supersymmetric model could have a more elaborate protection mechanism (e.g. leading to a suppression by additional loop factors), or simply the CP violating phases could vanish because of the way how supersymmetry breaking is transferred to the observable sector (see here for one concrete example). But the simplest explanation of the current data is that there are no superpartners up to at least ~10 TeV.

The most exciting aspect about the electron EDM is that there's still a lot of room for improving the experimental sensitivity. Therefore we will be able to indirectly probe new physics at even higher scales. ACME itself boasts that they can improve the limit by another factor of 10 soon. That would translate to a factor of 3 improvement in the new physics reach; that's by the way more than the energy jump from 8 to 13 TeV LHC... Clearly, the EDMs are one of our best chances to pinpoint the scale of new physics in this century.

## 20 comments:

While the EDM measurement favors very high superpartner masses, the anomalous muon magnetic moment pulls the expected mass of superpartners in the opposite direction, favoring an LSP on the order of 100 GeV. The non-detection of neutrinoless double beta decay also disfavors large superpartner masses.

This vise of experimental constraints seems to threaten to close SUSY parameter space in the most popular models of SUSY more quickly than the lower bounds from the collider experiments.

Not sure what is the connection between the neutrinoless beta decay and heavy superpartners

See, e.g., M. Hirsch et al., "Supersymmetry and Neutrinoless Double Beta Decay." (1995) http://arxiv.org/abs/hep-ph/9502385 and Allanach et al., http://arxiv.org/pdf/0902.4697v1.pdf

Generically, a higher characteristic mass scale of a SUSY theory implies higher rates of SUSY mediated neutrinoless double beta decay (mostly via the R-parity violating parameter lamdaprime111). See, e.g., figures 9 and 10 in Vergados http://arxiv.org/pdf/hep-ph/0409319v1.pdf See also Gozdz http://arxiv.org/abs/hep-ph/0305123

"n0νββ-decay provides a probe of the heavy SUSY mass scale and imposes constraints on RPV SUSY parameters" Prezeau http://arxiv.org/pdf/hep-ph/0303205v2.pdf

Is no EDM a viable possibility?

Or is this like the WIMP hunt where "failure is not an option"?

Looking at the websites of folks in the ACME collaboration, I get the impression that non-detection is very much an option for them. They're basically launching a very cheap (by particle physics standards) search through a 1D parameter space. They will either find something not in the Standard Model or rule out any theory that predicts an EDM above a certain value.

Frankly, these sorts of optical experiments are healthy for particle physics on a lot of levels: they're (relatively) cheap, they keep a dialogue open with other branches of physics, they can rule out certain things and verify fundamental assumptions, and the grad students who work on them can get good jobs in industry because they understand high-precision optics.

But do we keep looking for ever-smaller EDM values forever?

Is there some point at which we say there is probably no EDM and any model that predicts one is probably wrong?

At some point they will presumably reach sensitivity to the SM prediction. Whatever they find or don't find there will be significant. Might take several decades, but in the mean time they will constrain many BSM theories. And it will be way cheaper than building accelerators.

There are points in the parameter space of the MSSM where the EDMs vanish. One can also construct explicit models of supersymmetry breaking and mediation where no new phases (thus no new contributions to the EDMs) arise. Nevertheless, the lack of electron's EDM at the level of 10^-26 ecm is, along with the flavor problem, one of the strongest hints against SUSY at the TeV scale.

But, regardless, searching for EDMs down to the SM level makes perfect sense. As Alex said, it's a cheap and efficient way of probing new physics at a mass scale unreachable for colliders in this century.

But it sounds to me, from what Jester says, that the parameter space and the plasticity of certain theories are unlimited.

Where are the definitive, non-adjustable predictions of healthy science?

Robert Oldershaw says:

But do we keep looking for ever-smaller EDM values forever?Is there some point at which we say there is probably no EDM and any model that predicts one is probably wrong?

I think we did that for the cosmological constant. It turned out to be a bad idea.

"But do we keep looking for ever-smaller EDM values forever?

Is there some point at which we say there is probably no EDM and any model that predicts one is probably wrong?"

The more important question is: do we keep looking for SUSY sparticles in experiments incapable of detecting sub-10 TeV sparticles, or do we focus scarce physics research dollars on projects less likely to produce a null result?

"Clearly, the EDMs are one of our best chances to pinpoint the scale of new physics in this century."

Clearly. And I'm sure I speak for many of your readers when I say we are always interested to hear about any more of those best chances that you may know of.

As long as the measurement is not TOO expensive, physicists should embrace these searches for null results. By all means, continue to look for lab-scale deviations from Newtonian gravity, for violations of the Bell inequalities in weird contexts, for Lorentz violations at one part in ten to the whatever, etc. Part of the intellectual strength of physics is that there are incredibly smart people who are willing to work very, very hard to do very precise experiments that give null results. To pursue a null result with that much ingenuity requires a certain type of commitment to intellectual honesty. And it enables me to stand up in front of freshmen and tell them that what I am teaching them about has been relentlessly tested to one part in ten to the whatever by some of the most talented experimenters around.

Moreover, innovations in precision measurement (and the training of the people who do it!) lead to benefits in other branches of pure and applied science. I am actually in an applied area of physics, and one of the better experimentalists in my field started off doing something much more "pure" than his current work, using some very demanding experimental techniques.

Besides, if one of those experiments finds something other than a null result it will make history.

Dear Jester,

That was a nice write up on EDMs and the recent measurement. Thanks!

Just wanted to point out that unlike the electron EDM, the neutron EDM can be generated in the standrad model by the strong CP phase (theta term) which is renormalizable.

@Robert Oldershaw

"But it sounds to me, from what Jester says, that the parameter space and the plasticity of certain theories are unlimited."

But not of the Standard Model. We haven't reached the sensitivity to see the predicted value yet, so one has to keep looking to confirm whether there are deviations. If there are deviations, we have made a discovery.

"Where are the definitive, non-adjustable predictions of healthy science?"

see above

Einstein said that if general relativity was conceptually and analytically correct, then the stellar displacements during the 1919 eclipse would have a definitive quantitative relationship with distance from the eclipsed solar disk.

He also said that if this definitive prediction turned out to be wrong, then general relativity would not be a viable theory of gravitation.

It seems to me that in certain branches of theoretical physics these definitive predictions are AWOL, and have been very rare for decades.

I also think Jim Baggott's new book, Farewell To Reality is spot-on, and deserves much more consideration that it is getting in the US.

Bitch please...

Dear andrew,

considering the other experimental evidence, the history of the theory predictions to g-2 and the current modelling for the hadronic contribution, I think it is fair to say that the tension of SM prediction and experiment in this particular observable should probably not be taken too seriously at the moment. Different estimates of the hadronic contribution currently put the tension between 2.6 and 3.6 sigma. Until we eliminate e+e- data and the modelling in the light-by-light contributions, standard model predictions of the muon g-2 should be taken with a bit of caution.

Good writeup, Jester.

I have written a blog post about the same issue that is longer, especially when it comes to SUSY scenarios that overcome (some) naturalness, flavor, and CP hurdles.

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