Physicists, who devote their lives to studying the subject, don’t seem to really like physics because they always hope it’s broken. But we will have to forgive them; discovering that a little theory cannot possibly explain the experimental results is a sign that we probably need a new theory, something that would excite any physicist.
In recent years, one of the things that has looked the most broken is a seemingly simple measurement: the proton’s charge radius, which is a measure of its physical size. Measurements made with hydrogen atoms, which have a single electron orbiting a proton, gave us one answer. Measurements where the electron was replaced by a heavier particle called a muon gave us a different answer – and the two results were incompatible. A lot of effort has gone into getting rid of this discrepancy, and it’s gotten smaller, but it hasn’t gone away.
That makes theorists salivate. The Standard Model doesn’t allow for these kinds of differences between electrons and muons, so could this be a sign that the Standard Model is wrong? The team behind some of the earlier measurements are now back with a new one, tracking the behavior of a muon orbiting a helium nucleus. The results are consistent with other measurements of helium’s charge radius, suggesting there’s nothing funny about the muon. The Standard Model can therefore breathe a sigh of relief.
The measurement involved is, to put it simply, pretty insane. Muons are essentially heavy versions of electrons, so it’s relatively easy to replace one with another in an atom. And the mass of a muon offers some advantages for this kind of measurement. The mass causes the orbitals of the muon to become so compact that its wave function overlaps with the wave function of the nucleus. As a result, the behavior of the muon when it orbits a nucleus is very sensitive to the charge radius of the nucleus.
All of this would be great if muons weren’t unstable and typically decay in less than two microseconds. Placing one in orbit around a helium nucleus increases the complications, since helium usually has two electrons in orbit and they can interact with each other. The expected three-way interactions of a nuclear muon electron are currently beyond our ability to calculate, meaning we would have no idea if the actual behavior would differ from the theory.
So the researchers solved this problem by creating a positively charged ion made up of a helium nucleus and a single muon spinning around it. Making one of these – or, more accurately, making hundreds – is where the madness begins.
The researchers had access to a beam of muons created by a particle accelerator, and they decided to direct the beam into some helium gas. In this process, when the muons enter, they have too much energy to stay in orbit around a helium nucleus, so they bounce around and lose energy with each collision. Once the muons slow down enough, they can enter a high-energy orbit in a helium atom, knocking out one of its electrons. But the second electron is still nearby, ruining all potential measurements.
But the muon has a lot of momentum because of its mass, and energy transfers within an atom are faster than losing the energy to the environment. So if the muon transfers some of its energy to the electron, the electron’s smaller mass makes it enough for the electron to jump out of the atom, and we’re left with a muonic helium ion. Fortunately, this all happens quickly enough that the muon has not had a chance to decay.
Let the madness begin
At this point, the muon is usually in a lower energy orbit but has more energy than the ground state. In the experiment, the researchers set up a trigger that is sensitive to the appearance of muons. After a delay to allow the muons to power up the two electrons, the trigger causes a laser to hit the sample with the right amount of energy to stimulate the muon from the 2S orbital to the 2P orbital. From there, it decays to the ground state, releasing an X-ray.
Many of the muons will not be in a 2S orbital and the laser will have no effect on it. The researchers were willing to sacrifice much of the muonic helium they were making in order to get accurate measurements of the ones that were in the right state. Their presence was signaled by the detection of an X-ray of the correct energy. Further, to make sure they were looking at the right thing, the researchers only took data associated with a high-energy electron produced by the decay of the muon.
And remember, this all had to happen fast enough to happen within the microsecond time window for the muon to decay.
The first step was to tune the laser used to the correct frequency to bring the muon into the 2P orbit, as this is the value we need to measure. This was done by tuning a tunable laser over a frequency range until the helium started producing X-rays. Once the frequency was established, the researchers recorded data for 10 days, which was enough for accurate measurements of the frequency. During this time, the researchers observed 582 muonic helium ions.
Based on calculations using the laser frequency, the researchers found that the charge radius of the helium core is 1.6782 femtometers. Measurements made by bouncing electrons off the nucleus indicate it is 1,681. These two values fall within experimental error, so they are very similar.
We’re sorry, it’s not broken
At the simplest level, the fact that the muon measurements correspond to measurements taken independently indicates that there is nothing special about muons. Consequently, the Standard Model, which says the same, is intact to rather small limits allowed by the experimental errors here. (Of course, that’s not to say it hasn’t been broken in some other way.) So theorists everywhere will be disappointed.
As an aside, the researchers compared their value to a value generated decades ago in CERN’s particle accelerators. It turns out that this value is similar, but only by accident, because the previous work had two compensating errors. “Their quoted charge radius is not far from our value,” the researchers note, “but this can be traced to an inconvenient coincidence of an erroneous experiment combined with an incomplete 2P-2S theory prediction, which accidentally yielded a not-so. -wrong value.” So in this case, two mistakes made a near right.
In any case, this work will turn the researchers’ attention back to trying to figure out why different experiments with protons continue to yield results that don’t quite match, since we can’t blame things that the muon is weird. By now we can all realize how amazing it is that we manage to do so much with muons in the tiny fraction of a second in which they exist.
Nature, 2021. DOI: 10.1038/s41586-021-03183-1 (About DOIs).