This post is part of a series of posts originally written for my blog at Forbes.com that I’m copying to my personal site, so I have a (more) stable (-ish) archive of them. This is just the text of the original post, from October 2018, with only one of the images that originally appeared with it, because that’s essential to the explanation.

Big news in the study of tiny things dropped last week while I was traveling to Washington DC for a meeting: the ACME Collaboration has a new paper in Nature reporting the latest results of their search for a permanent electric dipole moment of the electron. This is huge because it suggest that the new particles predicted by theories of physics beyond the Standard Model should have masses greater than could be directly detected at the Large Hadron Collider.

A lot of people wrote stories about this last week– the collection of links I retweeted from airports includes an NSF press release, a Science News article, and a a post from fellow Forbes blogger Brian Koberlein. Those will give you the basic outline of what’s being reported; in this post, I want to dig a little deeper into the physics at work.

Most of the coverage of this adopts the framing of talking about this as measuring the “shape” of the electron, something that’s been standard for news releases since at least 2011 when I wrote a ScienceBlogs post about an experiment from Ed Hinds’s lab. This provides a nifty visual analogy– most of the press stories quote Dave DeMille of Yale comparing this to shifting a two-nanometer-thick slice from the south pole to the north pole of a perfect sphere the size of the Earth. (Note to the planetary science crowd: Yes, we know that the Earth is not a perfect sphere, but bulges out at the equator by far more than that.) What’s less clear from a lot of these stories, though, is what this has to do with particle physics. For that matter, what does it even mean to talk about the electron having a shape?

As physicists constantly have to emphasize when talking about electron spin, the electron is not literally a tiny ball of charge. In fact, to the best of our knowledge, the “bare” electron is a featureless point. If you could turn off all of its interactions with the rest of the universe, an electron would be infinitesimally tiny and basically uninteresting.

Happily, electrons do interact with the rest of the universe, which is what allows us to measure their properties. Because the universe is quantum, though, those interactions mean that we never get to see a “bare” electron: instead, we see some combination of the “bare” electron and its interaction with the rest of the universe. These interactions change the energy of the electron, and we can use the light absorbed and emitted by an electron to determine its energy to very high precision. We can then look at how that energy changes when we apply other kinds of fields.

The most significant type of interaction is simply between the charge of the electron and an applied electric field (say, from another charged particle nearby). This creates a very large energy shift that makes the electron “want” to get closer to positive charges and farther away from negative charges. This “electric monopole” interaction absolutely dwarfs any other interaction you might be interested in.

The next most significant interaction is a “magnetic dipole” interaction between an applied magnetic field and the intrinsic spin of the electron. This is a tiny shift, but you can see its effects because it’s not symmetric: a magnetic field in one direction will increase the electron’s energy by a tiny amount, and a field in the opposite direction will decrease it by the same amount. If you do something to trap an electron in place, most of its energy comes from the electric monopole interaction with whatever’s trapping it, but if you switch a magnetic field back and forth between two directions, you’ll see a tiny difference between the two states that you can measure using spectroscopy. This shift is something like a millionth of the energy of a typical electronic state in an atom or molecule, but measuring energy differences at that level is pretty routine for atomic physicists.

What ACME is looking for (along with a bunch of other experiments) is an “electric dipole” interaction, which has a mix of the characteristics of the other two. Like the electric monopole interaction, it’s an energy shift caused by an applied electric field, and like the magnetic dipole interaction, it depends on the direction of the applied field, shifting up for one direction and down for the other. Again, this is absolutely minuscule compared to the energy from the monopole interaction, but if you use the monopole interaction to stick an electron to an atom or molecule so it can’t simply move in the direction of the electric field, you can hope to pick this up as a shift in the energy of the electron that changes direction when you change the direction of the field.

The strength of this electric dipole interaction is measured by a thing called an “electric dipole moment,” and in classical electromagnetism, you calculate these all the time for macroscopic distributions of charge. A perfect sphere of charge would have zero dipole moment– no matter what direction you apply the field in, you get the same total energy. Any “lopsided” distribution will have a non-zero dipole moment, which is what leads to the “shape of the electron” characterization of this experiment: a sphere of charge with a tiny “bump” on one pole and a corresponding dent on the other will give you an electric dipole moment, and then you can use the charge and the radius to calculate how big a “bump” you would need to generate a particular value of the electric dipole moment.

But what does any of this have to do with particle physics? Well, again, we never truly see a “bare” electron, only the combination of the electron and its interactions with the rest of the universe. Those interactions include not only the fields applied in the course of an experiment, but also the inescapable vacuum electromagnetic field. Quantum physics tells us that you can never have nothing at all– there’s always zero-point energy around, and the electron interacts with these zero-point fields. In the Feynman picture of these things, that interaction takes the form of a cloud of “virtual particles” surrounding the electrons, and mediating its interactions with those applied fields.

These “virtual particles” are what make precision spectroscopy one of the well-established methods for searching for exotic physics. The interaction between the electron and the virtual particles leads to a shift in the electron’s energy, and in keeping with the “everything not forbidden is mandatory” nature of quantum physics, those virtual particles include absolutely everything, up to (in principle) bunnies made of cheese.

That might seem like a recipe for madness, but happily, the size of the shift caused by the appearance of a particular type of virtual particle decreases as the mass of that particle increases, and the number of virtual particles involved. When theorists try to predict the energy of an electron in some experiment, they don’t have to calculate the effect of every conceivable particle in huge numbers, just those particles whose mass is small enough for small numbers of them to cause a shift in energy large enough to be detected by the experiment. Or, to turn things around, when experimentalists measure some shift in the energy of an electron in some experiment, they can work backwards and determine the mass of the virtual particles that caused it.

In the case of the new ACME results, what they have is actually a lack of a shift: they apply a variety of electric and magnetic fields to a sample of cold thorium monoxide molecules, and look for an energy shift that changes with the direction of the electric field in the way they would expect if the electron has an electric dipole moment. They don’t see a shift that’s bigger than the uncertainty in their experimental measurements, which lets them put a hard upper limit on the size of any possible electric dipole moment of the electron: it has to be smaller than 0.000000000000000000000000000011 e-cm (one e-cm being the dipole moment you would get from an electron and a positron separated by one centimeter).

That hard upper limit for the electron’s electric dipole moment leads to a hard lower limit for the mass of any hypothetical particle with the right characteristics to cause an electric dipole moment. If you assume that the dipole moment would be created by “one-loop” Feynman diagrams, the simplest type shown in the figure above, the minimum mass for these particles would be about 30 TeV, or a bit more than double the maximum energy available at the Large Hadron Collider. If you allow for the possibility that the “one-loop” contribution is zero (something that’s not too difficult to arrange theoretically, but kind of inelegant), and it’s “two-loop” contributions that matter, the lower mass limit drops down to around 3 TeV, which is still pretty huge.

This is, obviously, a pretty stringent constraint on possible theories. Some years back, I wrote an article for Physics World that included a graph of predictions for various exotic theories, and this result takes a big bite out of that chart– they’re at the 10^-29e-cm level now. There’s still some wiggle room for theorists, but this is yet another strong piece of evidence that whatever beyond-the-Standard-Model physics is out there is something very different than the simplest models that particle theorists find aesthetically appealing.