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The peripatetic Muon g-2 experiment took data at Brookhaven National Laboratory in New York from 1997 to 2001 and has been taking data at Fermi National Accelerator Laboratory in Illinois since 2018.

Michael Linden CC BY-NC 2.0

Fresh calculation of obscure particle’s magnetism could dim hopes for new physics

Talk about raining on your colleagues’ parade. On 7 April, a collaboration of more than 200 experimenters announced to great fanfare that a particle called the muon is slightly more magnetic than predicted by physicists’ standard model, a discrepancy that could signal new particles waiting to be discovered. But on the same day, 14 theorists published a paper that suggests the consensus theoretical prediction is wrong. Their value sits closer to the experimental result and makes the tantalizing discrepancy nearly vanish.

“The standard model is just fine, according to our calculation,” says Zoltan Fodor, a theorist at Pennsylvania State University, University Park, and the leader of the Budapest-Marseille-Wuppertal (BMW) collaboration, which produced the new theoretical result. However, others say it’s too early to throw out the previous calculation, which is the product of decades of painstaking effort. “We can’t immediately ignore everything we know and switch over to a single new result of a new method,” says Christoph Lehner, a theorist at the University of Regensburg.

A heavier, unstable cousin of the electron, the muon acts like a tiny bar magnet, and its magnetism provides a means to dowse for hints of new particles. Quantum mechanics and relativity demand that the muon have a certain basic magnetism. Thanks to quantum uncertainty, particles and antiparticles also constantly flit in and out of existence around the muon. These “virtual” particles cannot be observed directly, but they can affect the muon’s properties, including magnetism. Standard model particles should increase its magnetism by about 0.1%, and as-yet-unknown particles would add their own boost. Such particles might someday be blasted into existence at an atom smasher.

That’s why physicists were so excited when the Muon g-2 experiment at Fermi National Accelerator Laboratory confirmed a 20-year-old hint that the muon is about 2.5 parts per billion more magnetic than the standard model predicts, according to the consensus value, hammered out last year by the 132-member Muon g-2 Theory Initiative.

To make that prediction, the theorists had to account for the thousands of ways standard model particles can flit about the muon and affect its behavior. One family of processes, known as hadronic vacuum polarization, is especially challenging and limits the precision of the entire calculation. In it, the muon emits and reabsorbs particles known as hadrons, which consist of other particles called quarks. The theory of quarks and the strong nuclear force that binds them, quantum chromodynamics (QCD), is so unwieldy that theorists cannot calculate the effects through the usual series of ever smaller approximations. Instead, they have to rely on data from accelerators that create hadrons by colliding electrons and positrons.

Never mind the gap?

If a new “lattice” value for the magnetism of the muon is correct, a mysterious gap between other predictions and a recent measurement would all but disappear.

–3 –4 –2 –1 New lattice 0 1 2 Difference between measured and theoretical values (parts per billion) Uncertainty New experimental value Theoretical consensus Hybrid
GRAPHIC: V. ALTOUNIAN/SCIENCE; DATA: ABI ET AL., PHYS. REV. LETT., 2021; BORSANYI ET AL., NATURE DOI: 10.1038/ S41586-021-03418-1; BLUM ET AL., PHYS. REV. LETT., 121, 2018; AOYAMA ET AL., PHYSICS REPORTS, 2020

There is another way, however. Theorists can attempt brute-force QCD calculations on supercomputers, if they model the continuum of space and time as a lattice of discrete points occupied by quarks and particles called gluons, which convey the strong force. Twelve years ago, theorists showed this “lattice QCD” technique could calculate the masses of the proton and the neutron, which are both hadrons. Several groups have also applied the lattice to the muon’s magnetism, albeit with sizable uncertainties.

Now, using hundreds of millions of processor hours at the Jülich Research Center in Germany, Fodor’s group has produced a lattice calculation of the hadronic vacuum polarization and a value for the muon’s magnetism that rivals the consensus standard model value in precision. And the new result is only one part per billion below the experimental value, the team reported in Nature. Given the uncertainties, that’s too close to claim a discrepancy, Fodor says.

He also raises questions about the consensus value. For key data, it depends on results mainly from two colliders, and the two data sets disagree to a worrisome extent, Fodor says. His team’s result is free of such uncertainties. “This is the only computation on the market, so some people are uncomfortable,” he says.

Yet some theorists say it’s too early to place so much weight on a single lattice calculation. Aida El-Khadra, a lattice theorist at the University of Illinois, Urbana-Champaign, and, with Lehner, a co-leader and a leader of the Muon g-2 Theory Initiative, notes that the uncertainties in the consensus value reflect mainly the limited precision of the input data. In contrast, the uncertainties in the lattice value reflect the reliability of the method itself and are harder to quantify and interpret, El-Khadra says. “The meaning of the errors is very different,” she says.

Also, in 2018 Lehner and colleagues performed an analysis combining accelerator data and a lower-precision lattice calculation. Their hybrid estimate of the muon’s magnetism agrees well with the consensus prediction, Lehner says.

“The BMW result needs to be confirmed by other independent lattice calculations,” says Alexey Petrov, a theorist at Wayne State University. Those high-precision calculations should appear within a year. But if the lattice results agree with one another, but not the data-driven approach, then theorists will still have to figure out why the two methods disagree, Petrov says.

Until then, it would be premature to say the tantalizing mystery raised by the g-2 measurements has been explained away, El-Khadra says. “The standard model calculation is solid,” she insists. So, too, is the experimental value. And to the best of physicists’ knowledge, they’re different.