Today is the publication of the latest result from the experiment that I work on at Harvard, the Advanced Cold Molecule Electron Electric Dipole Moment, or ACME EDM (here is a link to read the paper in entirety). In this experiment, we seek to look for an asymmetry in the electron’s shape. What does that exactly mean and why is that important?
What is the electron’s shape?
The electron is a negatively charged particle that is commonly depicted as part of the structure of the atom, orbiting a nucleus of protons and neutrons. The electron is a fundamental particle in the so-called Standard Model of particle physics, the theoretical framework that is our current best guess of explaining the properties and interactions of different fundamental particles in nature. When we talk about the electron’s shape, what we really mean is not its physical, solid shape, but the shape of the electric field that it produces. We are looking for small asymmetries in the behavior of the electron when it is subjected to an electric field. That is roughly what an electric dipole moment (EDM) means.
Why does it matter?
Why do we care about the electron’s shape? There are many reasons. But the most compelling is that the Standard Model is incomplete: we know that it cannot explain certain basic features of the universe. Among them is the question of why there is more matter compared to antimatter, or baryogenesis. As far as we know, matter and antimatter are two perfectly opposite types of matter. Thus, according to the Standard Model, the Big Bang should have resulted in equal amounts of both being produced. The matter and antimatter would have mixed and annihilated each other, releasing pure energy in the form of photons. Clearly this is not what actually happened, because we see more than just light in our universe: we see stars, galaxies, planets, and living things. So there must be something wrong with the Standard Model, some sort of asymmetric process that hasn’t been discovered yet.
Many theories posit such hypothetical asymmetric processes to solve this conundrum. These processes, hypothetical and speculative as they are, are still bound by the laws of physics that we know. Thus, it turns out that many of them will also express this asymmetry in the electron in the form of an EDM. Thus by looking to see if the electron has an EDM, we are also looking to see what really happened at a cosmological scale, many billions of years ago. (For more information, see this past blog post: Why CP Violation Might Explain Everything About the Universe.)
What did we find?
The experiment performed by my collaborators and I looks for the electron EDM by seeing its effect on the energy structure of thorium monoxide (ThO). This experiment is only the latest in a long tradition of similar ones stretching back to the 1950s. (I have also written a blog series describing this history, starting here.) In 2014, the ACME experiment found that the EDM of an electron is zero. More specifically, it found an upper limit for the electron EDM 
. At the time, this was a major advance: an order of magnitude improvement over previous experiments and a test of physics at the ~1-10 TeV scale (depending on how you count). This is comparable to the experiments being run at the Large Hadron Collider.
Today, five years from that date, the ACME collaboration is releasing the results of the second generation of that experiment, something that I’m proud to have taken a part in. Experimental improvements let us measure this quantity with an order of magnitude improvement in precision over ACME I. We are probing physics at the 10-100 TeV scale – uncharted territory in particle physics. This, by itself, was a momentous achievement: it is rare for an EDM experiment to result in two successive order-of-magnitude improvements.
We found that the electron EDM is zero. The electron is still perfectly round, and the Standard Model is still correct, as far as we know. To be more precise, we improved on the upper limit to the electron EDM by 8 times:
.
What does this result mean?
This null result means that the electron’s shape still follows the predictions of the good old Standard Model (SM), which is unable to explain baryogenesis. It also has potentially drastic implications on some theories beyond the SM which predict a non-zero electron EDM at the 
level. It means that some theorists might have to revise their theories. It is a little bit frustrating, as the Standard Model has to fail at some point, but it is still followed perfectly in this case.
Experimentally speaking, it is a major triumph, a powerful demonstration of the power of atomic and molecular techniques to unlock the secrets of fundamental particle physics. Multiple traditional techniques from different areas of atomic physics were used in the experiment. It shows the viability of smaller scale, tabletop experiments to do particle physics.
At the end of the day, a null result in measuring such an important quantity as the electron EDM is a momentous one: a single experiment sheds more light on nature than pages and pages of theoretical speculation.
Where do we go from here?
The search for the electron EDM has continued for almost seven decades, and it will probably still continue for several more. New methods and techniques are being developed. As for the ACME experiment itself, we are far from being over. There are still several major improvements in the pipeline which give good cause to believe that we can further improve on the limit achieved by this ACME II result. These will be the subject of the research of my collaborators and I in the next few years. The future of fundamental physics with atomic molecules remains bright.
How can I learn more?
To learn more, simply read our paper! The official website of the ACME experiment can be accessed here: www.electronedm.info, where there is a link to more papers, posters, and other relevant materials.
For a more popular-level introduction, I have written several articles on this website regarding the experiment, which can be accessed here. A good place to start is Introducing the ACME EDM experiment, while a more detailed (but still gentle) guide to the experiment is found here: A Simple Overview.
Some more news coverage of the result:
Study supports Standard Model of particle physics, excludes alternative models
Subatomic Particles: Scientists Make Unprecedented Measurement Of Electrons
Extremely close look at electron advances frontiers in particle physics
What the electron’s near-perfect roundness means for new physics
Acknowledgements
Even though I am proud to have played a role in the experiment in the last few years, I’m only a small player in an all-star cast. Major credit must be given to our three advisers who guided us through the entire process: Dave, John, and Jerry. (Please send any requests for “official” comments to these three PIs.) The development, maintenance and running of the experiment was led by the efforts of senior graduate students, in particular Cris Panda and Zack Lasner, in addition to many others in the past – Brendon O’Leary, Elizabeth and Adam West. All of the authors on the paper contributed meaningfully to the final result in one way or the other.
Congratulations!
The molecules travel a distance something like 10^17 times the diameter of an electron, and this seems to be rather close to the deviations from spherical symmetry that your supervisor says ACME could detect.
Is there some quick way to understand the similarity of these two orders of magnitude? e.g. in terms of cumulative torque experienced by the electron, as it crossed the 20 cm?
The distance traveled by the molecules is indeed related to the uncertainty of the experiment, though it is hard to relate it with the analogy using the classical electron, which has a physical diameter, whereas real, quantum-mechanical electrons do not. So while we like to use illustrations where we blow up the electron to the size of the Solar System and say that our uncertainty is on the order of a few centimeters, the choice of the Solar System is arbitrary and for illustration purposes only. If you blow up the electron to the size of the Earth instead, for example, then the uncertainty becomes a million times smaller than the human hair.
That being said, I will still try to relate these two different length scales. We measure the electron EDM (i.e. the shape of the electron) by applying an electric field (among other things) to molecules traveling a distance of 22 cm. The molecules’ quantum state precesses by a certain amount due to this electric field depending on the size of the electron EDM. So, your intuition is right – the amount of “torque”, and thus the uncertainty, is directly proportional to this distance. You can phrase this in mathematical terms:
, where 
= precession time, and K is some constant. 
is determined by the distance of 22 cm divided by the speed of the molecular beam (200 m/s), which ends up being about 1 millisecond.
So the question is, what determines K? Among other things, one of the greatest contributing factors to K is the electric field experienced by the electron in the molecule, which is HUGE. Thorium monoxide allows us to apply an internal electric field (or “torque on the electron”) of about 80 GV/cm. (The other contributor to the uncertainty is the number of molecules measured in the experiment.) This is about a billion times amplification of the strength of the electric field we actually apply in the lab, reminiscent of the “blowing up the electron to the size of the Earth” analogy that we like to use. So you can say that this 80 GV/cm is what allows us to bridge these two very different length scales.
I hope this helps!
Thanks for your reply. My original vague idea of how this works, was that the thorium monoxide was just a kind of scaffold for the electron of interest, and that the “torque” somehow came directly from the electron’s motion through the external electric field, carried by its molecular “scaffold”.
However, I’m learning that it’s actually an *internal* electric field of the molecule (induced by the external field) that does the work. So my notion that the distance crossed by the molecule is somehow *directly* relevant to the magnitude of the effect, must just be wrong. Instead, it’s the time of flight which directly matters, since it is the length of time for which that internal electric field is active, and acting on the electron.
That seems right. You’re correct, though, in that the external electric field applied in the lab does play a role, in aligning the molecule’s internal E-field along our experimental (or quantization) axis. The degree of alignment depends on the strength of the external E-field, and if it’s not enough, the experimental uncertainty will suffer accordingly. You can think of it as the precession not happening at the right angle where we can see it most visibly.
Thorium monoxide happens to be a molecule (which besides having a powerful internal E-field) is also extremely easy to align fully with an external E-field: you can do it by applying only tens of V/cm. In past experiments, people had to apply E-fields thousands of times stronger than this to fully align the molecule, creating more possibility for instability and imperfection in the experiment. I cover some of this in this blog post: https://www.danielang.net/2018/08/20/a-brief-history-of-the-electrons-shape-part-5-the-age-of-molecules/