What does the Standard Model predict for the muon’s magnetic moment?

Predicting the numerical value of the muon’s magnetic moment is one of the most challenging calculations in high-energy physics. Some physicists spend most of their careers improving their calculations with greater precision.

Why do physicists care about the magnetic properties of this particle? Because the information of each particle and force is encoded in the numerical value of the magnetic moment of the muons. If we can both measure and predict this number with extremely high accuracy, we can test whether the Standard Model of elementary particles is complete.

Muons are identical to electrons except that they are about 200 times more massive, are not stable, and disintegrate into electrons and neutrinos after a short time. At the simplest level, the theory predicts that the magnetic moment of muons, typically represented by the letter g, should equal 2. Any deviation from 2 can be attributed to quantum contributions from the interaction of muons with other known and unknown particles and forces. So scientists focus on predicting and measuring g-2.

There are already several measurements of the g-2 muon. Scientists working on the Muon g-2 experiment at the US Department of Energy’s Fermi National Accelerator Laboratory plan to announce the result of the most precise measurement ever of the magnetic moment of muons by the end of the year.

The high-energy physics community is eagerly awaiting the announcement of the world’s best measurement from the Fermilab Muon g-2 experiment later this year, while the Muon g-2 Theory Initiative is working to bolster the predicted value using new data and a new grid calculations. Photo: Reidar Hahn, Fermilab

At the same time, a large number of scientists are working to improve the Standard Model’s prediction of the muon g-2 value. Several parts come together in this calculation, relating to the electromagnetic force, the weak nuclear force and the strong nuclear force.

The contribution of electromagnetic particles such as photons and electrons is considered to be the most accurate calculation in the world. The contribution of weakly interacting particles such as neutrinos, the W and Z bosons and the Higgs boson is also well known. The most challenging part of g-2 muon prediction comes from the contribution of strongly interacting particles such as quarks and gluons; the equations governing their contribution are very complex.

Even though the contributions of quarks and gluons are so complex, they are computable, in principle, and several approaches have been developed. One such approach evaluates the contributions using experimental data related to the strongly interacting nuclear force. When electrons and positrons collide, they annihilate each other and can produce particles made of quarks and gluons such as pions. Measuring the frequency with which pions are produced in these collisions is precisely the data needed to predict the strong nuclear contribution to the g-2 muon.

For several decades, experiments on electron-positron colliders around the world have measured the contributions of quarks and gluons, including experiments in the United States, Italy, Russia, China and Japan. The results of all these experiments were compiled by a collaboration of experimental and theoretical physicists known as the Muon g-2 Theory Initiative. In 2020, this group announced the best Standard Model prediction for the g-2 muon available at that time. Ten months later, the Muon g-2 collaboration at Fermilab unveiled the result of their first measurement. Comparison of the two indicated a large discrepancy between the experimental result and the standard model prediction. In other words, the comparison of the measurement with the Standard Model provided strong evidence that the Standard Model is not complete and that muons could be interacting with as yet unknown particles or forces.

A second approach uses supercomputers to compute the complex equations for quark-gluon interactions with a numerical approach called lattice gauge theory. While this is a well-proven method for calculating strong force effects, the computing power has only recently become available to perform the calculations for the g-2 muon with the required accuracy. As a result, lattice calculations published before 2021 were not accurate enough to test the standard model. However, a calculation published by a group of scientists in 2021, the Budapest-Marseille-Wuppertal collaboration, came up with a big surprise. Their prediction using lattice gauge theory was far from the prediction using electron-positron data.

In recent months, the landscape of predictions for the contribution of the strong force to the g-2 muon has only become more complex. A new set of electron-positron data has emerged from the SND and CMD3 collaborations. These are two experiments taking data at the VEPP-2000 electron-positron collider in Novosibirsk, Russia. A result from the SND collaboration agrees with previous electron-positron data, while a result from the CMD3 collaboration disagrees with previous data.

What is going on? While there is no simple answer, there are concerted efforts by all involved communities to better quantify the prediction of the standard model. The lattice theory community is working around the clock to test and examine the prediction of BMW collaborations in independent lattice calculations with improved accuracy using different methods. The electron-positron collider community is working to identify possible reasons for the differences between the CMD3 result and all previous measurements. More importantly, the community is repeating these experimental measurements using much larger datasets. Scientists are also introducing new independent techniques for understanding the contribution of the strong force, such as a new experiment proposed at CERN called MUonE.

What does this mean for the muon g-2? The Fermilab Muon g-2 collaboration will publish its next result, based on data taken in 2019 and 2020, later this year. Because of the large amount of additional data going into the new analysis, the Muon g-2 collaboration expects its result to be twice as accurate as the first result from their experiment. But the current uncertainty in the predicted value makes it difficult to use the new result to bolster our earlier indication that the standard model is incomplete and there are new particles and forces affecting the g-2 muon.

What’s next? The Fermilab Muon g-2 experiment concluded data acquisition this spring. It will still take a couple of years to analyze the entire data set, and the experiment expects to publish its final result in 2025. At the same time, the Muon g-2 Theory Initiative is working to support the predicted value by using new data and new lattice calculations that should be available even before 2025. It will be a very exciting showdown. Meanwhile, the high-energy physics community is eagerly awaiting the announcement of the world’s best measurement from the Fermilab Muon g-2 experiment later this year.

Fermi National Accelerator Laboratory is supported by the US Department of Energy’s Office of Science. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information please visit science.energy.gov.