Written By: Isaiah Hazelwood, Science Staff Writer

The Standard Model of particle physics, developed by dozens of physicists in the 1970s, has been a crowning achievement of modern physics. With extremely high accuracy, it describes the many subatomic particles which make up matter, their properties, and their interactions among each other. However, a recent experiment at the Fermilab particle accelerator has produced results differing from the Standard Model’s predictions. Further experiments are already underway and if the experiment’s conclusions can be replicated at other accelerators around the world, physicists may begin re-examining the Standard Model or looking for a better theory which fits the experimental results.

What is Muon g-2?

The Standard Model predicts several particles, including the muon. The muon has almost completely identical properties to the electron, but it has a mass 207 times as large and will rapidly decay into an electron and two neutrinos (another particle predicted by the Standard Model) in roughly 2 microseconds. This decay rate means the muon is almost completely absent from nature, however, it still can be examined in the laboratory.

The laws of classical physics, which concerns objects larger than atomic particles, predicts that spinning objects with an electrical charge will behave like magnets, with their magnetic strength being measured by their magnetic moment. Both the muon and electron have an electric charge and a spin (the particle equivalent of spinning), indicating that they have a magnetic moment; however, their magnetic moment is roughly twice as large as predicted by classical physics. The laws of quantum physics, which describe subatomic particles, incorporate a particle-specific g-factor into the calculation of magnetic moment to scale the classical prediction to meet the actual particle’s magnetic moment.

For a lone muon and electron, this g-factor should be exactly 2, but the laws of quantum mechanics also state that no particle is ever truly alone: empty space always has virtual particles which spontaneously appear, have slight interactions with nearby particles, then disappear. These interactions with virtual particles mean the actual g-factor is very minimally higher than 2, and the value g-2, which represents virtual interactions’ impact on the magnetic moment, is called the anomalous magnetic moment.

The Fermilab g-2 Experiment

With the Standard Model claiming to describe all particles, it can predict interactions with virtual particles and thus predict the value of g-2. Unfortunately, measuring the value of g-2 for any particle is a difficult task: because g-2 is such a small value and can only be measured from isolated particles, extremely precise equipment is required. To measure the muon g-2, muons must be produced in the lab and sent around a precisely measured circular accelerator under a constant magnetic field. As the muons travel in the magnetic field, their magnetic moment will rotate based on the value of g, and their rotating magnetic moment over time can be measured to calculate g.

For a low-mass electron with few interactions, the theoretical value of the electron g-2 matches the experimental value of the electron g-2, providing a major piece of evidence supporting the Standard Model and Quantum theory. However, the Brookhaven National Laboratory’s measurements of the muon g-2 in the early 2000’s had a very slight difference compared to the theoretical muon g-2 value. The experiment was discontinued in 2001 due to a lack of funding, and no other facility had the instruments to measure muon g-2 at high precision. This changed in 2018, when the massive magnet used in the Brookhaven particle accelerator was moved to the Fermi National Accelerator Laboratory, or Fermilab. They collected data from 2018 to 2020, and published their preliminary results on April 7, 2021. Fermilab’s paper confirmed Brookhaven laboratory’s conclusion: the experimental value of the muon g-2 is higher than the theoretical value.

Alongside the experimental value of the muon g-2, Fermilab also published an analysis of the possible errors or uncertainties in their results. To avoid the researchers unconsciously influencing the results to reach their preferred conclusions, the collected data was offset by a hidden value: all calculations and data analysis was performed with the offset data to prevent bias. Following this, the offset was only reversed after the researchers had recorded and committed to their unbiased answers. Combined with the Brookhaven results, the experimental value for g-2 is 4.2 standard deviations higher than the theoretical value, meaning there is a 1 in 400,000 chance of obtaining the experimental results by chance if the theoretical value is correct. While strong, this is short of the 5.0 standard deviation difference used as a standard in physics (leaving a 1 in 3,000,000 chance of obtaining experimental results by chance). As Fermilab’s current published results only consider their earliest collected data, further publications (either from them or from other labs) will soon provide more certainty into the accuracy of the experimental value for g-2.

The value of g-2 as calculated by the Standard Model, Brookhaven Laboratory (BNL), and Fermilab Experiment (FNAL).
Image credit: Abi et al.

What Does It Mean?

While the Fermilab’s g-2 conclusions have received significant media attention, their current scientific significance is currently uncertain. The 4.2 standard deviation difference is certainly promising, and their agreement with the previous Brookhaven results only increases their strength; however, until further publications provide more evidence, the results cannot be taken as completely certain.

If the experimental value of g-2 is shown to be different than the theoretical value, the Standard Model will need revision – but not replacement. The Standard Model is correct in many areas, from predicting the electron g-2 to predicting the Higgs Boson, so an inaccuracy surrounding its prediction for the muon g-2 would not eliminate all its components. Science is a process of developing theories, performing experiments, correcting theories to account for contradicting experiments, and repeating – and even the Standard Model can become part of that process.






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