# Is there an electric dipole moment in an electron?

I just read an article in Science News (p7, 11/10/2018, link here) where researchers looked for an electric dipole moment in an electron. They spoke of charge separation between the positive and negative charges. I thought the electron was a basic particle. Does it have sub-particles?

• Nov 18 '18 at 17:12

The electron is a fundamental point particle. It does not have sub-particles “inside”. However, its quantum interactions with other particles should give it a small electric dipole moment, according to the Standard Model of particle physics. (It is a very difficult calculation but there are estimates for it.)

Some people like to picture this in their minds as a halo of virtual particles - photons, electrons and positrons, quarks and antiquarks, etc. — surrounding the electron. Don’t take this picture too seriously, but the mathematics tells us that the dipole moment does come from the interaction of the electron’s quantum field with other quantum fields present in the quantum vacuum.

Once experiments become sensitive enough to measure the electron’s dipole moment, they will be a very good test of the Standard Model. If the expected dipole moment is not found, that will be a big deal. If it has a different value than predicted, it could mean that the electron is interacting with particles we don’t know about! Imagine finding evidence for a new particle this way, without having to build a giant accelerator!

• It will be a long time before experiments can be sensitive enough to probe the SM prediction of the eEDM. They current state of the art is some twelve orders of magnitude short, and that's a long way to go. Nov 17 '18 at 20:54
• I agree. I wasn’t making a prediction of how soon it will happen, or whether it will ever happen. But I would not be surprised if it eventually happens. For example, the sensitivity of gravitational wave detectors increased by quite a few orders of magnitude over the decades. Experimentalists have managed to do amazing things. But nobody should be holding their breath. Nov 17 '18 at 20:58
• The Wikipedia article “Electron electric dipole moment” says that the 2018 limit is $10^{-29}$ e-cm, so this is 9 orders of magnitude, not 12, away from the predicted $10^{-38}$ e-cm. The sensitivity has increased by about two orders of magnitude in the last 20 years. Of course, it will get harder and harder to keep going. I am sorry if my answer got anyone too excited about this. Nov 17 '18 at 21:11
• @Emilio, do you know the status of experiments on the muon’s magnetic moment? Isn’t their sensitivity getting close to probing the Standard Model in an accelerator-less way? Nov 17 '18 at 21:19
• How about muons then? (tauons seeming to be too unstable to do anything with) Nov 18 '18 at 18:48

The reason we believe the electron to be an elementary particle is precisely because people do high precision tests like the one you reference, looking for some kind of sub-structure which would indicate that the electron is made up of more fundamental bits, and come up empty-handed.

Of course, such tests can never definitively rule out an EDM or anything like that. Instead, they place ever-smaller upper bounds on how big it could possibly be (otherwise, they'd have seen it). We're not down to the level predicted by the standard model yet (which predicts an EDM about nine or ten orders of magnitude below the sensitivity of this experiment), but this does place a limit on the influence of non-standard model physics.

Experiments like that are constantly being performed to search for evidence that our current understanding of the universe is flawed. This practice - actively searching for evidence of the inadequacies of our current theories - is a crucial hallmark of science. It's a win-win, because either the results provide further evidence for what we currently think, or they point they way toward new discoveries.

The “positive and negative charges” part in that Science News articles is a bit confusing, so let me back up a bit (and oversimplify the math a lot).

In field theories, space contains lots of virtual particles that pop into and out of existence. In that short time, they experience the local fields and forces. So, each “bare” or “basic” or “fundamental” electron is surrounded by a lot of very transient electron/positron pairs. During their brief lives, those feel the EM force, so the e+ move a (tiny) bit closer and the e- a bit farther away, at least on average. The net of this is a shielding effect on the electron, modifying the bare charge to what we measure. (Incidentally, this is why the EM force gets stronger at higher energy: A higher-energy probe gets closer to the bare electron, so doesn’t see the charge reduced so much)

Electrons have a spin, so they can have a specific direction (the way the spin axis points). But the Standard Model EM force doesn’t care about that spin, so the distribution of e+ and e- doesn’t bunch away toward or away from that axis: the EM force is solely radial and hence the cloud remains round.

The Standard Model weak force does care about spin (via W and Z boson couplings), so can move e+ toward one end of the spin axis and e- toward the other (I can never remember which is which). That makes the electron a bit “pear shaped”, with it’s net charge a tiny bit displaced from the center of mass. We know how (we think) to calculate this and it’s tiny. It’ll be a while before it can be experimentally measured and hence confirmed.

But what it there’s some new particle/force with a stronger coupling than the weak one? It if couples to electron/positrons, and cares about spin, and is significant (that’s a lot of conditions, though; many hypothetical particles don’t have all of them) then it will change the charge distribution of the electron. Perhaps enough to be measurable? Well, the measurements keep getting better, which keeps ruling out proposed theories....

• That makes the electron a bit “pear shaped”, with it’s net charge a tiny bit displaced from the center of mass. Why the asymetry? Does it have anything to do with the different masses of the W and Z? Nov 18 '18 at 18:51
• Not so much the W and Z mass as that their couplings with e+ and e- depend on $cos \theta$. The (small) weak force on e+ varies from one spin pole to the other (a little), with the effect on the e- in the cloud having the opposite dependency. Nov 19 '18 at 0:18