By Alex Masegian, Spring 2021.

For the last 50 years, our understanding of the universe’s fundamental structure has been encapsulated in a set of theories known as the Standard Model. Built from the discoveries of thousands of physicists, the Standard Model states that all matter is made up of a small set of building blocks known as fundamental particles, the interactions of which are governed by four fundamental forces. Though the theory isn’t perfect, it is incredibly comprehensive, having explained nearly all recent experimental results in particle physics. But there’s one glaring exception. On April 7, 2021, scientists at Fermi National Accelerator Laboratory announced the first results of the Muon g-2 experiment, which aimed to measure the magnetic properties of a fundamental particle known as the muon [1]. To the excitement of particle physicists everywhere, Fermilab’s findings differed dramatically from what the Standard Model predicts. Though the difference has not yet reached the level of significance needed to confirm a discovery, it is drastic enough to imply the existence of new physics beyond the Standard Model, a result that would revolutionize the field for the first time in decades.

At the center of the Muon g-2 experiment is, unsurprisingly, the muon: a fundamental particle with the same negative charge as the electron, but nearly 200 times more mass. Because muons are charged particles, they rotate when they come into contact with a magnetic field. This rotation can be described by a quantity called the “gyromagnetic ratio,” or “g-factor,” which relates the way in which a fundamental particle interacts with a magnetic field to its other properties. Particle physicists have known for years that the muon has a g-factor of around 2, hence the “g-2” in the Fermilab experiment’s name. However, measuring the exact value of the muon’s g-factor is no easy task. As a muon travels through space, quantum fluctuations cause it to constantly emit and reabsorb other fundamental particles, such as photons, electrons, and positrons. Chris Polly, one of the lead scientists on the Muon g-2 experiment, described the phenomenon to Quanta Magazine as follows: “‘The particle you thought was a bare muon is actually a muon plus a cloud of other things that appear spontaneously’” [2]. Predicting what particles appear in that cloud is incredibly difficult due to the randomness of the quantum occurrences that produce them. But these spontaneous particles, often called “virtual” particles in reference to their infinitely short lifespans, can affect the muon’s magnetic properties — which are directly linked to the g-factor.

The first highly accurate measurements of the muon’s g-factor were published in 2001 by a team at Brookhaven National Laboratory. Their result of 2.0023318404 was significantly higher than the most comprehensive theoretical predictions at the time, which used the laws of the Standard Model to estimate a value of 2.0023318319 [2]. But the difference was not enough. In particle physics, the golden standard for scientific proof is what’s called a “five-sigma” result, in which there is a 1 in 3.5 million chance of the result occurring due to random errors in the experimental setup rather than the theory that is being tested. With only a “three-sigma” gap between its measurement and the accepted theoretical value of the time, the Brookhaven result could not conclusively prove that there was something missing from the Standard Model’s predictions. In order to confirm the discrepancy, more precise measurements of the muon’s g-factor would be needed — and there was no better place to take those measurements than Fermilab, home to an incredibly powerful muon beam. In 2013, the muon-accelerating magnet used in the Brookhaven experiment was shipped to Illinois, and Fermilab scientists set to work crafting the experiment that would produce the most accurate measurements of the muon’s g-factor to date.

In the meantime, theoretical particle physicists around the world organized the Theory Initiative, a working group dedicated to refining the Standard Model’s predictions of the muon’s g-factor. The work was painstaking. To obtain a highly accurate estimate, every possible combination of virtual particles that the Standard Model allows for must be taken into account and weighted by their likelihood of occurrence. The process took nearly four years, but in the summer of 2020, a result was finally reached: 2.0023318362, 3.7 sigma below the final Brookhaven measurement [2]. With a solid theoretical prediction in hand, the scientific community waited on the results of the Muon g-2 experiment with bated breath. Would the Brookhaven discrepancy be confirmed, or would the Standard Model’s prediction turn out to be correct after all? 

On April 7th, the Fermilab Muon g-2 team announced that they had measured the muon’s g-factor to be in agreement with the Brookhaven result from two decades earlier. Averaged together, the two experiments produced a result of 2.00233184122, which differed from the Theory Group’s predicted value by a whopping 4.2 sigma [1]. Though this result still falls short of the five-sigma requirement, only six percent of the data gathered in the Muon g-2 experiment has been analyzed: the results of the experiment’s first “run,” a data-collecting period that lasted several months. “‘Although these first results are telling us that there is an intriguing difference with the Standard Model, we will learn much more in the next couple of years,’” Chris Polly said in an official Fermilab press release [1]. With analysis of the experiment’s second and third runs underway and two more runs planned, it is highly likely that the difference between the theoretical and measured values of the muon’s g-factor will continue to grow. Within the next few years, the Fermilab team’s result could easily pass the five-sigma threshold, dethroning the Standard Model and ushering in a new era of particle physics.

Figure 1: The Fermilab and Brookhaven experiments have produced a value for the muon’s g-factor that is 4.2 sigma above the value predicted by the Standard Model. The significant discrepancy, as highlighted by this graph of the results, may be a sign that something is missing from the Standard Model itself. [4]

There’s just one complication.

Right before the Theory Initiative published their final prediction, a group of researchers known as BMW revealed their own Standard Model-based prediction of the muon’s g-factor: 2.00233183908, which is “in fairly good agreement” with the results of the Brookhaven experiment [3]. The shocking result came from a calculation that is nearly identical to the Theory Initiative’s, with one exception — the determination of the so-called “hadronic vacuum polarization term,” which represents the contribution of a fundamental particle known as hadrons to the muon’s g-factor. Hadrons are uniquely affected by the strong force, one of the four fundamental forces at the heart of the Standard Model and the trickiest to solve for. As a result, determining exactly how hadrons affect the muon’s g-factor is a difficult and imprecise process [2]. The Theory Initiative used a data-driven approach, translating the results of countless particle-collision experiments into predictions of the hadronic vacuum polarization term. But the BMW team used a different, possibly even more precise approach: a computational estimation, which didn’t rely on experimental data at all, and thus avoided potential experimental biases. If their method is physically sound, and the estimate for the muon’s g-factor that they have produced is accurate, there may be no discrepancy between the Standard Model and the Muon g-2 results. After 20 years of anticipation, particle physicists may be forced to accept that there is no need to search for physics beyond the Standard Model after all.

Ultimately, the Theory Initiative decided against incorporating the BMW results into their final estimate, citing the need for further tests and verification before the new computational method could be accepted. Those tests are currently underway, but it is impossible to tell when they will be complete; simulations as complex as those that the BMW team requires can take months to run, even on the world’s most powerful supercomputers. In the meantime, the Fermilab Muon g-2 team will continue to refine their result and incorporate new data, potentially widening the gap between the experimental and theoretical measurements of the muon’s g-factor and raising the stakes for the eventual release of the BMW team’s final estimate. Though scientists cannot yet say if the Muon g-2 results challenge or confirm the Standard Model, one thing is clear: the next few years will involve a lot of exciting science. Regardless of the final outcome, the last 20 years of investigations into the muon’s g-factor represent a groundbreaking advancement in particle physics. Only time will tell whether that advancement will inspire the need for new physics or confirm the long-standing Standard Model once more.

[1] Fermilab News. 2021. “First results from Fermilab’s Muon g-2 experiment strengthen evidence of new physics.” Fermilab/Muon g-2 Collaboration. https://news.fnal.gov/2021/04/first-results-from-fermilabs-muon-g-2-experiment-strengthen-evidence-of-new-physics/. 

[2] Wolchover, Natalie. 2021. “‘Last Hope’ Experiment Finds Evidence for Unknown Particles.” Quanta Magazine. https://www.quantamagazine.org/last-hope-experiment-finds-evidence-for-unknown-particles-20210407. 

[3] Borsanyi, Sz. et al. 2020. “Leading hadronic contribution to the muon magnetic moment from lattice QCD.” ArXiv Pre-print Server, https://arxiv.org/abs/2002.12347. 

[4] Postel, Ryan. 2021. Accessed under the Fermilab News free use policy. Fermilab//Muon g-2 Collaboration. https://news.fnal.gov/wp-content/uploads/2021/04/Muon-g-2-results-plot.jpg.