The Standard Model of particle physics—the best, most thoroughly vetted description of reality scientists have ever devised—appears to have fended off yet another threat to its reign.
At least, that’s one interpretation of a long-awaited experimental result announced on June 3 by physicists at the Fermi National Accelerator Laboratory, or Fermilab, in Batavia, Ill. An alternative take would be that the result—the most precise measurement ever made of the magnetic wobble of a strange subatomic particle called the muon—still remains the most significant challenge to the Standard Model’s supremacy. The results have been posted on the preprint server arXiv.org and submitted to the journal Physical Review Letters.
The muon is the electron’s less stable, 200-times-heavier cousin. And like the electron and all other charged particles, it possesses an internal magnetism. When the muon’s inherent magnetism clashes with an external magnetic field, the particle precesses, torquing to and fro like a wobbling, spinning top. Physicists describe the speed of this precession using a number, g, which almost a century ago was theoretically calculated to be exactly 2. Reality, however, prefers a slightly different value, arising from the wobbling muon being jostled by a surrounding sea of “virtual” particles flitting in and out existence in the quantum vacuum. The Standard Model can be used to calculate the size of this deviation, known as g−2, by accounting for all the influences of the various known particles. But because g−2 should be sensitive to undiscovered particles and forces as well, a mismatch between a calculated deviation and an actual measurement could be a sign of new physics beyond the vaunted Standard Model’s limits.
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That’s the hope, anyway. The trouble is that physicists have found two different ways to calculate g−2, and one of those methods, per a separate preprint paper released on May 27, now gives an answer that closely matches the measurement of the muon anomalous magnetic moment, the final result from the Muon g−2 Experiment hosted at Fermilab. So a cloud of uncertainty still hangs overhead: Has the most significant experimental deviation in particle physics been killed off by theoretical tweaks just when its best-yet measurement has arrived, or is the muon g−2 anomaly still alive and well? Vexingly, the case can’t yet be conclusively closed.
The Latest Word—But Not the Last
The Muon g−2 Collaboration announced the results on Tuesday in a packed auditorium at Fermilab, offering the audience (which included more than 1,000 people watching via livestream) a brief history of the project and an overview of its final outcome. The heart of the experiment is a giant 50-foot-diameter magnet, which acts as a racetrack for wobbling muons. In 2001, while operating at Brookhaven National Laboratory on Long Island, this ring revealed the initial sign of a tantalizing deviation. In 2013 physicists painstakingly moved the ring by truck and barge from Brookhaven to Fermilab, where it could take advantage of a more powerful muon source. The Muon g−2 Collaboration began in 2017. And in 2021 it released the first result that strengthened earlier hints of an apparent anomaly, which was bolstered further by additional results announced in 2023. This latest result is a capstone to those earlier measurements: the collaboration’s final measurement gives a value of 0.001165920705 for g−2, consistent with previous results but with a remarkable precision of 127 parts per billion. That’s roughly equivalent, it was noted during the June 3 announcement, to measuring the weight of a bison to the precision of a single sunflower seed.
Despite that impressive feat of measurement, interpretation of this result remains an entirely different matter. The task of calculating Standard Model predictions for g−2 is so gargantuan that it brought together more than 100 theorists for a supplemental project called the Muon g−2 Theory Initiative.
“It is a community effort with the task to come up with a consensus value based on the entire available information at the time,” says Hartmut Wittig, a professor at the University of Mainz in Germany and a member of the theory initiative’s steering committee. “The answer to whether there is new physics may depend on which theory prediction you compare against. The consensus value should put an end to this ambiguity.”
In 2020 the group published a theoretical calculation of g−2 that appeared to confirm the discrepancy with the measurements. The May preprint, however, brought significant change. The difference between theory and experiment is now less than one part per billion, a number both minuscule and much smaller than the accompanying uncertainties, which has led to the collaboration’s consensus declaration that there is “no tension” between the Standard Model’s predictions and the measured result.
Virtual (Particle) Insanity
To understand what brought this shift in the predictions, one has to look at one category of the virtual particles that cross the muons’ path.
“[Excepting gravity] three out of the four known fundamental forces contribute to g−2: electromagnetism, the weak interaction and the strong interaction,” Wittig explains. The influence of virtual photons (particles of light that are also carriers of the electromagnetic force) on muons is relatively straightforward (albeit still laborious) to calculate, for instance. In contrast, precisely determining the effects of the strong force (which usually holds the nuclei of atoms together) is much harder and is the least theoretically constrained among all g−2 calculations.
Instead of dealing with virtual photons, those calculations grapple with virtual hadrons, which are clumps of fundamental particles called quarks glued together by other particles called (you might have guessed) gluons. Hadrons can interact with themselves to create tangled, precision-scuttling messes that physicists refer to as “hadronic blobs,” enormously complicating calculations of their contributions to the wobbling of muons. Up to the 2020 result, researchers indirectly estimated this so-called hadronic vacuum polarization (HVP) contribution to the muon g−2 anomaly by experimentally measuring it for electrons.
One year later, though, a new way of calculating HVP was introduced based on lattice quantum chromodynamics (lattice QCD), a computationally intensive methodology, and quickly caught on.
Gilberto Colangelo, a professor at the University of Bern in Switzerland and a member of the theory initiative’s steering committee, points out that, currently, “on the lattice QCD side, there is a coherent picture emerging from different approaches. The fact that they agree on the result is a very good indication that they are doing the right thing.”
While the multiple flavors of lattice QCD computations improved and their results converged, though, the experimental electron-based measurements of HVP went the opposite way. Among seven experiments seeking to constrain HVP and tighten predictive precision, only one agreed with the lattice QCD results, while there was also deviation among their own measurements.
“This is a puzzling situation for everyone,” Colangelo notes. “People have made checks against each other. The [experiments] have been scrutinized in detail; we had sessions which lasted five hours…. Nothing wrong was found.”
Eventually, the theory initiative decided to use only the lattice QCD results for the HVP factor in this year’s white paper, while work on understanding the experimental results is going on. The choice moved the total predicted value for g−2 much closer to Fermilab’s measurement.
The Standard Model Still Stands Tall
The Standard Model has seen all of its predictions experimentally tested to high precision, giving it the title of the most successful theory in history. Despite this, it is sometimes described as something unwanted or even failed because it does not address general open questions, such as the nature of dark matter hiding in galaxies.
In the solid terms of experimental deviations from its predictions, this century has seen the rise and fall of many false alarms.
If the muon g−2 anomaly goes away, however, it will also take down some associated contenders for new, paradigm-shifting physics; the absence of novel types of particles in the quantum vacuum will put strong constraints on “beyond the Standard Model” theories. This is particularly true for the theory of supersymmetry, a favorite among theorists, some of whom have tailored a plethora of predictions explaining away the muon g−2 anomaly as a product of as-yet-unseen supersymmetric particles.
Kim Siang Khaw, an associate professor at Shanghai Jiao Tong University in China and a member of Fermilab’s Muon g−2, offers a perspective on what will follow. “The theory initiative is still a work in progress,” he says. “They may have to wait several more years to finalize. [But] every physics study is a work in progress.” Khaw also mentions that currently Fermilab is looking into repurposing the muon “storage ring” and magnet used in the experiment, exploring more ideas that can be studied with it.
Finally, on the theory front, he muses: “I think the beauty of [the g−2 measurement] and the comparison with the theoretical calculation is that no matter if there is an anomaly or no anomaly, we learn something new about nature. Of course, the best scenario would be that we have an anomaly, and then we know where to look for this new physics. [But] if there is nothing here, then we can look somewhere else for a higher chance of discovering new physics.”
