After leaving the European Organization for Nuclear Research (CERN) physics laboratory years ago, I crossed the Swiss-German border by high-speed train. Looking out the window of the carriage, I was enthralled by the scenes flashing by: a young couple embracing on an otherwise deserted platform, an old man standing by a rusty wagon with a missing wheel, two girls wading into a reedy pond. Each was just a few flickering frames, gone in the blink of an eye, but enough for my imagination to fill in a story.

I had just finished writing up some theoretical work on muon particles—heavier cousins to electrons—and it was out for the scrutiny of my particle physics colleagues during peer review. There was a symmetry between my thoughts as I looked out the train window that day and the research I had been working on. I had been analyzing the flickering effects of unseen “virtual” particles on muons, aiming to use the clues from these interactions to piece together a fuller picture of our quantum universe. As a young theorist just launching my career, I had heard about proposed experiments to measure the tiny wobbles of muons to gather such clues. I had just spent my last few months at CERN working on an idea that could relate these wobbling muons to the identity of the missing dark matter that dominates our universe and other mysteries. My mind fast-forwarding, I thought, “Great—now I just have to wait for the experiments to sort things out.” Little did I suspect that I would end up waiting for a quarter of a century.

Finally, this past April, I tuned in to a Webcast from my home institution, Fermi National Accelerator Laboratory (Fermilab) near Chicago, where scientists were reporting findings from the Muon g-2 (“g minus two”) experiment. Thousands of people around the world watched to see if the laws of physics would soon need to be rewritten. The Fermilab project was following up on a 2001 experiment that found tantalizing hints of the muon wobble effect I had been hoping for. That trial didn’t produce enough data to be definitive. But now Muon g-2 co-spokesperson Chris Polly was unveiling the long-awaited results from the experiment’s first run. I watched with excitement as he showed a collection of new evidence that agreed with the earlier trial, both suggesting that muons are not acting as current theory prescribes. With the evidence from these two experiments, we are now very near the rigorous statistical threshold physicists require to claim a “discovery.”

What is this wobble effect that has me and other scientists so intrigued? It has to do with the way a muon spins when it travels through a magnetic field. This variation in spin direction can be affected by virtual particles that appear and disappear in empty space according to the weird rules of quantum mechanics. If there are additional particles in the universe beyond the ones we know about, they, too, will show up as virtual particles and exert an influence on a muon’s spin in our experiments. And this seems to be what we are seeing. The Fermilab experiment and its precursor measured a stronger wobble in muons’ spins than what we expect based on just the known particles. If the current discrepancy holds up, this will be the biggest breakthrough in particle physics since the discovery of the Higgs boson—the most recent novel particle discovered. We might be observing the effects of particles that could help unveil the identity of dark matter or even reveal a new force of nature.

The Standard Model

My romance with physics began when I was a child, gazing in amazement at the Via Lactea (the Milky Way) in the deep dark sky of Argentina’s Pampas where I grew up. The same wonder fills me now. It is my job as a particle physicist to investigate what the universe is made of, how it works and how it began.

Scientists believe there is a simple yet elegant mathematical structure, based on symmetries of nature, that describes the way microscopic elementary particles interact with one another through the electromagnetic, weak and strong forces; this is the miracle of particle physics that scientists prosaically call the Standard Model. The distant stars are made of the same three elementary matter particles as our bodies: the electron and the “up” and “down” quarks, the two latter of which form protons and neutrons. Starlight is the result of the electromagnetic force acting between the charged protons and electrons, liberating light energy at the hot surface of the star. The heat source of these stars, including our sun, is the strong force, which acts on the protons and neutrons to produce nuclear fusion. And the weak force, which operates on both the quarks and the electrons, turns protons into neutrons and positively charged electrons and controls the rate of the first step in the fusion process. (The fourth force of nature, gravity, is not part of the Standard Model, although integrating it with the other forces is a major goal.)

Physicists assembled the Standard Model piece by piece over the course of decades. At particle accelerators around the world, we have been able to create and observe all of the particles that the mathematical structure requires. The last to be found, the Higgs boson, was discovered almost a decade ago at CERN’s Large Hadron Collider (LHC). Yet we know the Standard Model is not complete. It does not explain, for example, the 85 percent of the matter in the universe—dark matter—that holds the cosmos together, making galaxies such as our Milky Way possible. The Standard Model falls short of answering why, at some early time in our universe’s history, matter prevailed over antimatter, enabling our existence. And the Muon g-2 experiment at Fermilab may now be showing that the Standard Model, as splendid as it is, describes just a part of a richer subatomic world.

Particles circle around a 50-foot-diameter ring in the Muon g-2 experiment.
Spinning Muons: Particles circle around this 50-foot-diameter ring in the Muon g-2 experiment. Credit: Reidar Hahn Fermi National Accelerator Laboratory

The subject of the experiment—muons—are produced in abundance by cosmic rays in Earth’s atmosphere; more than 10,000 of them pass through our bodies every minute. These particles have the same physical properties as the familiar electron, but they are 200 times heavier. The extra mass makes them better probes for new phenomena in high-precision laboratories because any deviations from their expected behavior will be more noticeable. At Fermilab, a 50-foot-diameter ring of powerful magnets stores muons created under controlled conditions by smashing a beam of protons from a particle accelerator into a target of mostly nickel. This process produces pions, unstable composite particles that then decay into neutrinos and muons through weak force effects. At this point, the muons enter a ring filled with the vacuum of “empty” space.

Like electrons, muons have electric charge and a property we call spin, which makes them behave as little magnets. Because of the way they were created, when negatively charged muons enter the ring their spins point in the same direction as their motion, whereas for positively charged muons (used in the Fermilab experiment) the spins point in the opposite direction of their motion. An external magnetic field makes the electrically charged muons orbit around the ring at almost the speed of light. At the same time, this magnetic field causes the spin of the muons to precess smoothly like a gyroscope, as the particles travel around the ring, but with a small wobble.

The rate of precession depends on the strength of the muon’s internal magnet and is proportional to a factor that we call g. The way the equations of the Standard Model are written, if the muon didn’t wobble at all, the value of g would be 2. If that were the case, the muon’s direction of motion and direction of spin would always be the same with respect to each other, and g-2 would be zero. In that case, scientists would measure no wobble of the muon. This situation is exactly what we would expect without considering the properties of the vacuum.

But quantum physics tells us that the nothingness of empty space is the most mysterious substance in the universe. This is because empty space contains virtual particles—short-lived objects whose physical effects are very real. All the Standard Model particles we know of can behave as virtual particles as a result of the uncertainty principle, an element of quantum theory that limits the precision with which we can perform measurements. As a result, it is possible that for a very short time the uncertainty in the energy of a particle can be so large that a particle can spring into existence from empty space. This mind-blowing feature of the quantum world plays a crucial role in particle physics experiments; indeed, the discovery of the Higgs boson was enabled by virtual particle effects at the LHC.

Virtual particles also interact with the muons in the Fermilab ring and change the value of g. You can imagine the virtual particles as ephemeral companions that a muon emits and immediately reabsorbs—they follow it around like a little cloud, changing its magnetic properties and thus its spin precession. Therefore, scientists always knew that g would not be exactly 2 and that there would be some wobble as muons spin around the ring. But if the Standard Model is not the whole story, then other particles that we have not yet discovered may also be found in that cloud, changing the value of g in ways that the Standard Model cannot predict.

Muons themselves are unstable particles, but they live long enough inside the Muon g-2 experiment for physicists to measure their spin direction. Physicists do this by monitoring one of the decay particles they create: electrons, from decays of negatively charged muons, or positrons—the antiparticle version of electrons—from decays of positively charged muons. By determining the energy and arrival time of the electrons or positrons, scientists can deduce the spin direction of the parent muon. A team of about 200 physicists from 35 universities and labs in seven countries developed techniques for measuring the muon g-2 property with unprecedented accuracy.

Graphic shows setup of Muon g-2 experiment and particle interactions that may cause muons’ spins to wobble so much.
Credit: Jen Christiansen

A Confirmation

The first experiments to measure the muon g-2 took place at CERN, and by the late 1970s they had produced results that, within their impressive but limited precision, agreed with standard theory. In the late 1990s the E821 Muon g-2 experiment at Brookhaven National Laboratory started taking data, with a similar setup to that at CERN. It ran until 2001 and got impressive results showing an intriguing discrepancy from the Standard Model calculations. It collected only enough data to establish a three-sigma deviation from the Standard Model—well short of the five-sigma statistical significance physicists require for a “discovery.”

A decade later Fermilab acquired the original Brookhaven muon ring, shipped the 50-ton apparatus from Long Island to Chicago via highways, rivers and an ocean, and started the next generation of the Muon g-2 experiment. Nearly a decade after that, Fermilab announced a measurement of muon wobble with an uncertainty of less than half a part in a million. This impressive accuracy, achieved with just the first 6 percent of the expected data from the experiment, is comparable to the result from the full run of the Brookhaven trial. Most important, the new Fermilab results are in striking agreement with the E821 values, confirming that the Brookhaven findings were not a fluke.

To confirm this year’s results, we need not just more experimental data but also a better understanding of what exactly our theories predict. Over the past two decades we have been refining the Standard Model predictions. Most recently, more than 100 physicists working on the Muon g-2 Theory Initiative, started by Aida El-Khadra of the University of Illinois, have strived to improve the accuracy of the Standard Model’s value for the muon g-2 factor. Advances in mathematical methods and com putational power have enabled the most accurate theoretical calculation of g yet, taking into account the effects from all virtual Standard Model particles that interact with muons through the electromagnetic, weak and strong forces. Just months before Fermilab revealed its latest experimental measurements, the theory initiative unveiled their new calculation. The number disagrees with the experimental result by 4.2 sigma, which means that the chances that the discrepancy is purely a statistical fluctuation are about one in 40,000.

Still, the latest theoretical calculation is not iron-clad. The contributions to the g-2 factor governed by effects from the strong force are extremely difficult to compute. The Muon g-2 Theory Initiative used input from two decades of judiciously measured data in related experiments with electrons to evaluate these effects. Another technique, though, is to try to calculate the size of the effects directly from theoretical principles. This calculation is way too complex to solve exactly, but physicists can make approximations using a mathematical trick that discretizes our world into a gridlike lattice of space and time. These techniques have yielded highly accurate results for other computations where strong forces play a dominant role.

Teams around the world are tackling the lattice calculations for the muon g-2 factor. So far only one team has claimed to have a result of comparable accuracy to those based on experimental data from electron collisions. This result happens to dilute the discrepancy between the experimental and Standard Model expectations—if it is correct, there may not be evidence of additional particles tugging on the muon after all. Yet this lattice result, if confirmed by other groups, would itself conflict with experimental electron data—the puzzle then would be our understanding of electron collisions. And it would be hard to find theoretical effects that would explain such a result because electron collisions have been so thoroughly studied.

Muon g-2 ring being transported.
By boat and big rig: Getting the Muon g-2 ring to Fermilab from Brookhaven required a barge and a specialized truck. Credit: Reidar Hahn Fermi National Accelerator Laboratory

A Message from the Void

If the mismatch between Fermilab’s measurements and theory persists, we may be glimpsing an uncharted world of unfamiliar forces, novel symmetries of nature and new particles. In the research I published 25 years ago searching for clues about the muon’s wobble, my collaborators and I considered a proposed property of nature called supersymmetry. This idea bridges two categories of particles—bosons, which can be packed together in large numbers, and fermions, which are antisocial and will share space only with particles of opposite spin. Supersymmetry postulates that each fermion matter particle of the Standard Model has a yet to be discovered boson particle superpartner, and each Standard Model boson particle also has an undiscovered fermion superpartner. Supersymmetry promises to unify the three Standard Model forces and offers natural explanations for dark matter and the victory of matter over antimatter. It may also explain the striking Muon g-2 results.

Just after the Fermilab collaboration announced its measurement, my colleagues Sebastian Baum, Nausheen Shah, Carlos Wagner and I posted a paper to a preprint server investigating this intriguing notion. Our calculations showed that virtual superparticles in the vacuum could make the muons wobble faster than the Standard Model predicts, just as the experiment saw. Even more exhilarating, one of those new particles—called a neutralino—is a candidate for dark matter. Supersymmetry can take numerous forms, many of them already ruled out by data from the LHC and other experiments—but plenty of versions are still viable theories of nature.

The paper my team submitted was just one of more than 100 that have appeared proposing possible explanations for the Muon g-2 result since it was announced. Most of these papers suggest new particles that fall into one of two camps: either “light and feeble” or “heavy and strong.” The first category includes new particles that have masses comparable to or smaller than the muon and that interact with muons with a strength millions of times weaker than the electromagnetic force. The simplest theoretical models of this type involve new, lighter cousins of the Higgs boson or particles related to new forces of nature that act on muons. These new light particles and feeble forces could be hard to detect in terrestrial experiments other than Muon g-2, but they may have left clues in the cosmos. These light particles would have been produced in huge numbers after the big bang and might have had a measurable effect on cosmic expansion. The same idea—that light particles and feeble forces wrote a chapter missing from our current history of the universe—has also been proposed to explain discrepancies in observations of the expansion rate of space, the so-called Hubble constant crisis.

The second category of explanations for the muon results—heavy and strong—involves particles with masses about as heavy as the Higgs boson (roughly 125 times the mass of a proton) to up to 100 times heavier. These particles could interact with muons with a strength comparable to the electromagnetic and weak interactions. Such heavy particles might be cousins of the Higgs boson, or exotic matter particles, or they might be carriers of a new force of nature that works over a short range. Supersymmetry offers some models of this type, so my youthful speculations at CERN are still in the running. Another possibility is a new type of particle called a leptoquark—a strange kind of boson that shares properties with quarks as well as leptons such as the muon. Depending on how heavy the new particles are and the strength of their interactions with Standard Model particles, they might be detectable in upcoming runs of the LHC.

Some recent LHC data already point toward unusual behavior involving muons. Recently, for instance, LHCb (one of the experiments at the LHC) measured the decays of certain unstable composite particles similar to pions that produce either muons or electrons. If muons are just heavier cousins of the electron, as the Standard Model claims, then we can precisely predict what fraction of these decays should produce muons versus electrons. But LHCb data show a persistent three-sigma discrepancy from this prediction, perhaps indicating that muons are more different from electrons than the Standard Model allows. It is reasonable to wonder whether the results from LHCb and Muon g-2 are different, flickering frames of the same story.

One Puzzle Piece

The Muon g-2 experiment may be telling us something new, with implications far beyond the muons themselves. Theorists can engineer scenarios where new particles and forces explain both the muons’ funny wobbling and solve other outstanding mysteries, such as the nature of dark matter or, even more daring, why matter dominates over antimatter. The Fermilab experiment has given us a first glimpse of what is going on, but I expect it will take many more experiments, both ongoing and yet to be conceived, before we can confidently finish the story. If supersymmetry is part of the answer, we have a fair chance of observing some of the superparticles at the LHC. We hope to see evidence of dark matter particles there or in deep underground labs seeking them. We can also look at the behavior of muons in different kinds of experiments, such as LHCb.

All of these experiments will keep running. Muon g-2 should eventually produce results with nearly 20 times more data. I suspect, however, that the final measured value of the g-2 factor will not significantly change. There is still a shadow of doubt on the theory side that will be clarified in the next few years, as lattice computations using the world’s most powerful supercomputers achieve higher precision and as independent teams converge on a final verdict for the Standard Model prediction of the g-2 factor. If a big mismatch between the prediction and the measurement persists, it will shake the foundations of physics.

Muons have always been full of surprises. Their very existence prompted physicist I. I. Rabi to complain, “Who ordered that?” when they were first discovered in 1936. Nearly a century later they are still amazing us. Now it seems muons may be the messengers of a new order in the cosmos and, for me personally, a dream come true.