Everyone knew that in order to cross the threshold of discovery, they would need to measure the muon’s gyromagnetic ratio again, and more precisely. So plans for a follow-up experiment got underway. In 2013, the giant magnet used at Brookhaven was loaded onto a barge off Long Island and shipped down the Atlantic Coast and up the Mississippi and Illinois rivers to Fermilab, where the lab’s powerful muon beam would let data accrue much faster than before. That and other improvements would allow the Fermilab team to measure the muon’s g-factor four times more accurately than Brookhaven had.
In 2016, El-Khadra and others started organizing the Theory Initiative, seeking to iron out any disagreements and arrive at a consensus Standard Model prediction of the g-factor before the Fermilab data rolled in. “For the impact of such an exquisite experimental measurement to be maximized, theory needs to get its act together, basically,” she said, explaining the reasoning at the time. The theorists compared and combined calculations of different quantum bits and pieces that contribute to the muon’s g-factor and arrived at an overall prediction last summer of 2.0023318362. That fell a hearty 3.7 sigma below Brookhaven’s final measurement of 2.0023318416.
But the Theory Initiative’s report was not the final word.
Uncertainty about what the Standard Model predicts for the muon’s magnetic moment stems entirely from the presence in its entourage of “hadrons”: particles made of quarks. Quarks feel the strong force (one of the three forces of the Standard Model), which is so strong it’s as if quarks are swimming in glue, and that glue is endlessly dense with other particles. The equation describing the strong force (and thus, ultimately, the behavior of hadrons) can’t be exactly solved.
That makes it hard to gauge how often hadrons pop up in the muon’s midst. The dominant scenario is the following: The muon, as it travels along, momentarily emits a photon, which morphs into a hadron and an antihadron; the hadron-antihadron pair quickly annihilate back into a photon, which the muon then reabsorbs. This process, called hadronic vacuum polarization, contributes a small correction to the muon’s gyromagnetic ratio starting in the seventh decimal place. Calculating this correction involves solving a complicated mathematical sum for each hadron-antihadron pair that can arise.
Uncertainty about this hadronic vacuum polarization term is the primary source of overall uncertainty about the g-factor. A small increase in this term can completely erase the difference between theory and experiment. Physicists have two ways to calculate it.
With the first method, researchers don’t even try to calculate the hadrons’ behavior. Instead, they simply translate data from other particle collision experiments into an expectation for the hadronic vacuum polarization term. “The data-driven approach has been refined and optimized over decades, and several competing groups using different details in their approaches have confirmed each other,” said Stöckinger. The Theory Initiative used this data-driven approach.
But in recent years, a purely computational method has been steadily improving. In this approach, researchers use supercomputers to solve the equations of the strong force at discrete points on a lattice instead of everywhere in space, turning the infinitely detailed problem into a finite one. This way of coarse-graining the quark quagmire to predict the behavior of hadrons “is similar to a weather forecast or meteorology,” Fodor explained. The calculation can be made ultra-precise by putting lattice points very close together, but this also pushes computers to their limits.
The 14-person BMW team — named after Budapest, Marseille and Wuppertal, the three European cities where most team members were originally based — used this approach. They made four chief innovations. First they reduced random noise. They also devised a way of very precisely determining scale in their lattice. At the same time, they more than doubled their lattice’s size compared to earlier efforts, so that they could study hadrons’ behavior near the center of the lattice without worrying about edge effects. Finally, they included in the calculation a family of complicating details that are often neglected, like mass differences between types of quarks. “All four [changes] needed a lot of computing power,” said Fodor.
The researchers then commandeered supercomputers in Jülich, Munich, Stuttgart, Orsay, Rome, Wuppertal and Budapest and put them to work on a new and better calculation. After several hundred million core hours of crunching, the supercomputers spat out a value for the hadronic vacuum polarization term. Their total, when combined with all other quantum contributions to the muon’s g-factor, yielded 2.00233183908. This is “in fairly good agreement” with the Brookhaven experiment, Fodor said. “We cross-checked it a million times because we were very much surprised.” In February 2020, they posted their work on the arxiv.org preprint server.
The Theory Initiative decided not to include BMW’s value in their official estimate for a few reasons. The data-driven approach has a slightly smaller error bar, and three different research groups independently calculated the same thing. In contrast, BMW’s lattice calculation was unpublished as of last summer. And although the result agrees well with earlier, less precise lattice calculations that also came out high, it hasn’t been independently replicated by another group to the same precision.
The Theory Initiative’s decision meant that the official theoretical value of the muon’s magnetic moment had a 3.7-sigma difference with Brookhaven’s experimental measurement. It set the stage for what has become the most anticipated reveal in particle physics since the Higgs boson in 2012.
The Revelations
A month ago, the Fermilab Muon g-2 team announced that they would present their first results today. Particle physicists were ecstatic. Laura Baudis, a physicist at the University of Zurich, said she was “counting the days until April 7,” after anticipating the result for 20 years. “If the Brookhaven results are confirmed by the new experiment at Fermilab,” she said, “this would be an enormous achievement.”
And if not — if the anomaly were to disappear — some in the particle physics community feared nothing less than “the end of particle physics,” said Stöckinger. The Fermilab g-2 experiment is “our last hope of an experiment which really proves the existence of physics beyond the Standard Model,” he said. If it failed to do so, many researchers might feel that “we now give up and we have to do something else instead of researching physics beyond the Standard Model.” He added, “Honestly speaking, it might be my own reaction.”
The 200-person Fermilab team revealed the result to themselves only six weeks ago in an unveiling ceremony over Zoom. Tammy Walton, a scientist on the team, rushed home to catch the show after working the night shift on the experiment, which is currently in its fourth run. (The new analysis covers data from the first run, which makes up 6% of what the experiment will eventually accrue.) When the all-important number appeared on the screen, plotted along with the Theory Initiative’s prediction and the Brookhaven measurement, Walton was thrilled to see it land higher than the former and pretty much smack dab on top of the latter. “People are going to be crazy excited,” she said.
Papers proposing various ideas for new physics are expected to flood the arxiv in the coming days. Yet beyond that, the future is unclear. What was once an illuminating breach between theory and experiment has been clouded by a far foggier clash of calculations.
It’s possible that the supercomputer calculation will turn out to be wrong — that BMW overlooked some source of error. “We need to have a close look at the calculation,” El-Khadra said, stressing that it’s too early to draw firm conclusions. “It is pushing on the methods to get that precision, and we need to understand if the way they pushed on the methods broke them.”
That would be good news for fans of new physics.
Interestingly, though, even if the data-driven method is the approach with an unidentified problem under the hood, theorists have a hard time understanding what the problem could be other than unaccounted-for new physics. “The need for new physics would only shift elsewhere,” said Martin Hoferichter of the University of Bern, a leading member of the Theory Initiative.
Researchers who have been exploring possible problems with the data-driven method over the past year say the data itself is unlikely to be wrong. It comes from decades of ultraprecise measurements of 35 hadronic processes. But “it could be that the data, or the way it is interpreted, is misleading,” said Andreas Crivellin of CERN and other institutions, a coauthor (along with Hoferichter) of one paper studying this possibility.
It’s possible, he explained, that destructive interference happens to reduce the likelihood of the hadronic processes arising in certain electron-positron collisions, without affecting hadronic vacuum polarization near muons; then the data-driven extrapolation from one to the other doesn’t quite work. In that case, though, another Standard Model calculation that’s sensitive to the same hadronic processes gets thrown off, creating a different tension between the theory and data. And this tension would itself suggest new physics.
It’s tricky to resolve this other tension while keeping the new physics “elusive enough to not have been observed elsewhere,” as El-Khadra put it, yet it’s possible — for instance, by introducing the effects of hypothetical particles called vector-like leptons.
Thus the mystery swirling around muons might lead the way past the Standard Model to a more complete account of the universe after all. However things turn out, it’s safe to say that today’s news — both the result from Fermilab, as well as the publication of the BMW calculation in Nature — is not the end for particle physics.
- Account
- analysis
- announced
- April
- around
- Beam
- BMW
- breach
- Catch
- CERN
- chief
- Cities
- coming
- community
- computers
- computing
- computing power
- Consensus
- Creating
- dab
- data
- discovery
- Early
- Edge
- European
- experiment
- family
- Finally
- finds
- Firm
- First
- future
- good
- Group
- High
- Home
- How
- HTTPS
- illinois
- Impact
- Increase
- Initiative
- institutions
- IT
- keeping
- lead
- leading
- Long
- measure
- Members
- million
- Mississippi
- model
- Munich
- Near
- news
- Noise
- official
- order
- organizing
- Other
- Others
- particle
- Physics
- power
- Precision
- prediction
- present
- proves
- Quantum
- reaction
- reasons
- reduce
- report
- research
- Results
- Run
- safe
- Scale
- Screen
- set
- shift
- SIX
- Size
- small
- So
- SOLVE
- Space
- Stage
- started
- Study
- summer
- supercomputer
- supercomputers
- swimming
- The Future
- time
- top
- university
- Vacuum
- value
- WHO
- Work
- year
- years
- zoom
- Zurich