@dga471 curious your thoughts on this interesting article.

‘Your electron’s so round it rules out other particles’ sounds like a winning insult.

The Standard Model predicts a vanishingly tiny EDM for the electron — nearly a million times smaller than what current techniques can probe. So if researchers were to detect an oblong shape using today’s experiments, that would reveal definitive traces of new physics and point toward what the Standard Model might be missing.

@dga471 and @PdotdQ I thought standard theory predicted an EDM of precisely zero. Apparently I was wrong.

What gives rise to the tiny-non-zero EDM of standard theory?

Electron EDMs violate CP symmetry. The Standard Model does contain some CP violation (first discovered by Cronin and Fitch in the decay of neutral kaons in 1964), which is parameterized in a complex phase of the Cabibbo–Kobayashi–Maskawa (CKM) matrix. However, this phase is very small, and gives rise to an electron EDM at only three loop or higher order Feynman diagrams. The most recent estimation of the SM prediction for the electron EDM is

d_{e,SM} \approx 10^{-40}~e\cdot\mathrm{cm}

which is many orders of magnitude below the best upper bound on the eEDM (from the JILA II experiment in the linked article),

|d_e| < 4.1 \times 10^{-30}~e\cdot\mathrm{cm}.

So even though the SM eEDM is non-zero, its value is very small, and many new physics theories predict a much larger eEDM. Thus these experiments are exciting to do, since any non-zero result would be an immediate sign of new physics beyond the SM, without the need to carry out a complicated background calculation of the SM contribution first.

(A subtle technical clarification: the SM eEDM is so small that another recent paper found that experiments will see another type of CP-violation in the SM from the electron-nucleon interaction kick in at around 10^{-35}~e\cdot\mathrm{cm} before they see the “pure” eEDM.)

@dga471, so could we say the electron EDM is naively zero and arises only from QFT corrections, sort of like how the g-factor for the magnetic dipole moment is naively 2 and the famous anomalous dipole moment arises from similar QFT corrections?

Can you sketch in a little more detail how the electron EDM relates to CP violation? If I understand things correctly, a C transformation should turn the electron into a positron, and presumably flip the direction of the EDM, and a P transformation should flip the direction of the spin (though I’m not sure how the chirality plays into things here). Does the positron have an EDM that is opposite what we would expect from these transformations, and that is the way that the EDM violates CP symmetry?

Let the Archives of the Internet record that on this day the first ‘Your electron’s so round’ joke was made at this URL.

LOL!

I don’t know, the physicist’s dozens can be brutal.

If an electron EDM exists, then observe what happens when we apply P and T transformations. The following figure is illustrative (taken from my thesis):

We start with an electron with a non-zero EDM, with its spin \vec{S} and EDM \vec{d}_e pointing in the same direction. (This argument applies to any fundamental particle with a permanent EDM, including positrons.) Applying a parity (P) transformation, quantities that relate to electric fields such as \vec{d}_e flip sign but quantities that relate to magnetic fields such as \vec{S} do not. The result is a different electron than what we started with, with the two quantities anti-aligned instead of aligned. Thus, an EDM would violate P. Applying a time transformation, the reverse happens: \vec{d}_e remains but \vec{S} is flipped, and once again we obtain an electron that is different from what we started with. Thus, an EDM would also violate T.

The **CPT theorem** states that the product of three symmetries, C, P, T must be preserved. It has been extensively tested in many experiments that compare the properties of matter and antimatter. In addition, it is a cornerstone of quantum field theory, with far-reaching implications if violated. The preservation of CPT means that the electron EDM, which would violate T, would also violate CP. For this reason, electron EDMs are attractive to theorists who are seeking to explain problems such as matter-antimatter asymmetry, as a resolution requires more CP violation than is currently observed in the Standard Model.

I think the similarity is superficial. While QFT can calculate the corrections to the electron magnetic moment, it cannot by itself predict the existence of CP violation which is necessary for electron EDMs to arise; the CP violating phase in the CKM matrix is one of the Standard Model’s infamous 25 fundamental constants which must be derived experimentally. Thus in general, permanent EDMs of fundamental particles have been considered an experimental rather than a theoretical question as is the case for the anomalous electron magnetic moment. This is true both of the small eEDM predicted by the SM as well as the larger values predicted by new physics models.

Thanks! I mixed up which of the spin and the EDM gets flipped by a parity transformation, oops. Let me see if I understand this.

Applying C should (I think) result in flipping the charge and the EDM but not the spin, so that a CPT-transformed electron with aligned spin and EDM would be a positron with anti-aligned spin and EDM (and vice-versa). By CPT symmetry, whatever mechanism gives rise to the electron EDM should produce a positron EDM with the opposite alignment relative to spin.

Which means that a CP transformation would flip the spin-EDM aligned electron to a spin-EDM aligned positron, while it flips the spin-EDM anti-aligned positron to a spin-EDM anti-aligned electron. Since the relative alignment of the EDM is now assigned to the opposite charges, this isn’t the same theory as before, violating CP symmetry. Is that about right?

(I get it if the answer is “well, that oversimplifies things…”, haha.)

@dga471 @structureoftruth

I have a physics question. I seem to recall that I once read that fraunhofer lines in the spectra from different elements, like those used in astronomy to identify the elemental and molecular meakeup of stars, dust, etc. -and all sorts of different forms of spectroscopy- can be predicted from “first principles” in quantum physics, or something along those lines.

That physicists can show that the element Sodium, say, should have a particular spectral absorption profile, with basically just the fundamental equations of atomic physics and the constituents and configuration of the Sodium atom.

Is that correct?

That sounds basically correct.

You can calculate all the energy levels from first principles basically only for hydrogen - which is why performing precision spectroscopy on hydrogen has been useful to test the Standard Model, as we can calculate the energy levels with very high precision. Starting with helium, you have to start using various approximations. It becomes more complicated with larger atoms and molecules.

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