Highest Precision Prediction of Muon “Wobble”

Comparing new prediction to measurements of muons’ precession could potentially help scientists discover new subatomic particles.

The Muon g-2 storage ring resides at the Fermi National Accelerator Laboratory

The Science

Muons “wobble.” How much these subatomic particles—heavier cousins of electrons—moved was the question. Theorists released the most precise prediction of how muons wobble as they travel in a powerful magnetic field. This prediction will be compared with upcoming measurements of the muons’ wobble. The measurements will come from an experiment underway at Fermilab. The comparison will test whether previous results indicating a discrepancy between the theoretical prediction and the experimental measurement persists. If this discrepancy still stands, it could point to the existence of new particles.

The Impact

Comparison of the new high-precision prediction and the experimental results at Fermilab will provide a stringent test of the Standard Model, the reigning theory of particle physics. The comparison may offer insight into how new particles might be affecting muons’ behavior. Finding new particles beyond those in the Standard Model has long been a goal for particle physicists. Spotting signs of a new particle affecting the behavior of muons could guide the design of experiments to search for direct evidence of these not-yet-discovered particles.


Scientists at Brookhaven National Laboratory (BNL) ran a version of the “muon wobble” experiment, known as “Muon g-2,” in the late 1990s and early 2000s. That experiment revealed a discrepancy between the measurement and the prediction. However, the discrepancy was at a level not quite significant enough to claim a major discovery. After lingering hints of new discoveries from the Brookhaven experiment, physicists pushed for the opportunity to continue the research using a higher intensity muon beam at Fermilab in Illinois. In 2013, the two labs teamed up to transport Brookhaven’s 50-foot-diameter electromagnet storage ring from New York to Illinois. After making a number of adjustments to the magnet, the team at Fermilab recently started recording data.

The Muon g-2 experiment measures what happens as muons circulate through the large electromagnet storage ring. The muons, which have intrinsic magnetism and spin (somewhat analogous to spinning toy tops), start off with their spins aligned with their direction of motion in the ring. However, as they go ‘round and ‘round the ring, they interact with the ring’s magnetic field and also with a zoo of virtual particles that pop in and out of existence within the vacuum. Sensors surrounding the magnet measure the precession—or the degree to which the muons “wobble” away from their spin-aligned path—with extreme accuracy so that physicists can compare the results with predictions that were calculated based on scientists’ understanding of Standard Model particle interactions.

The latest effort to refine the prediction was led by the Brookhaven team with contributions from the RBC Collaboration (made up of physicists from the RIKEN BNL Research Center, Brookhaven Lab, and Columbia University) and the UKQCD collaboration. The team’s efforts focus specifically on how two of the four fundamental forces—the strong nuclear force and electromagnetism—affect the muons, taking into account all the possible interactions between muons and the known particles of the Standard Model. To tackle the extremely complex mathematical calculations, the physicists used a method known as Lattice QCD, which models all the possible particle interactions on an imaginary 4-D lattice that includes three spatial dimensions plus time. Supercomputers at the Leadership Computing Facility at Argonne National Laboratory and Brookhaven’s Computational Sciences Initiative crunched the numbers taking all those interactions into account. Researchers combined supercomputer simulations with related experimental measurements to produce the highest overall precision prediction to date. The physicists are now eagerly awaiting new experimental data from Fermilab to see if the measurements and theory match up, or, more intriguingly, point to new physics.

A significant discrepancy (stronger than the hints first observed at Brookhaven’s earlier version of the experiment) could mean that a new type of particle—one not included in the Standard Model—pops into existence and interacts with the muon before it interacts with the magnetic field. Such results would give the physicists information about what this unknown particle might be, and, perhaps, how to design an experiment to discover it.


Christoph Lehner
High Energy Theory Group at Brookhaven National Laboratory
clehner@quark.phy.bnl.gov; (631) 344-8194


The theoretical work at Brookhaven National Laboratory was funded by the Department of Energy (DOE) Office of Science, RIKEN, and Lehner’s Early Career Research Award. The Muon g-2 experiment at Fermilab is supported by DOE’s Office of Science and the National Science Foundation. Brookhaven National Laboratory and Fermi National Accelerator Laboratory are both supported by the DOE Office of Science. The researchers used computational resources at the Argonne Leadership Computing Facility, a DOE Office of Science user facility, and at the Computational Sciences Initiative at Brookhaven National Laboratory, which is funded in part by the Lattice Quantum Chromodynamics extension II hardware project under the leadership of the US Lattice Quantum Chromodynamics collaboration.


T. Blum, P.A. Boyle, V. Gülpers, T. Izubuchi, L. Jin, C. Jung, A. Jüttner, C. Lehner, A. Portelli, and J.T. Tsang (RBC and UKQCD Collaborations), “Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.” Physical Review Letters 121, 022003 (2018). [DOI: 10.1103/PhysRevLett.121.022003]

Related Links

Brookhaven National Laboratory press release: Theorists Publish Highest-Precision Prediction of Muon Magnetic Anomaly

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