Magnetic moment is an intrinsic property of a particle with spin, resulting from the interaction between the particle and a magnet or other object with a magnetic field. Like mass and electric charge, the magnetic moment is one of the fundamental quantities of Physics.
There is a difference between the theoretical value of the magnetic moment of a muon, a particle belonging to the same class as the electron, and the values obtained during highenergy experiments carried out in particle accelerators. The difference only appears at the eighth decimal place, but it has intrigued scientists since its discovery in 1948.
This is not a detail: it can indicate whether the muon interacts with dark matter particles or other Higgs bosons or even whether unknown forces are involved in the process.
The theoretical value of the muon’s magnetic moment, represented by the letter g, is given by the Dirac equation — formulated by the English physicist and 1933 Nobel Prize winner Paulo Dirac (19021984), one of the founders of quantum mechanics and quantum electrodynamics — like 2. However, experiments have shown that g is not exactly 2, and there is great interest in understanding “g2”, that is, the difference between the experimental value and the value predicted by the Dirac equation.
The best currently available experimental value, obtained with an impressive degree of precision at the Fermi National Accelerator Laboratory in the United States and announced in August 2023, is 2.00116592059, with an uncertainty range of plus or minus 0.00000000022. Information about the Muon G2 experiment at Fermilab is available at: muong2.fnal.gov/.
“Precisely determining the muon’s magnetic moment has become a key question in particle physics, because studying this discrepancy between experimental data and theoretical predictions can provide insights that could lead to the discovery of a spectacular new effect ”, said physicist Diogo Boito, a physics researcher. professor at the São Carlos Physics Institute of the University of São Paulo (IFSCUSP), told Agência FAPESP.

An article on the subject by Boito and his collaborators is published in the journal Physical Examination Letters.
“Our results were presented at two important international events. First by me at a workshop in Madrid, Spain, and later by my colleague Maarten Golterman from San Francisco State University at a meeting in Bern, Switzerland,” Boito said.
These results quantify and indicate the origin of a discrepancy between the two methods used to make the current predictions of the g2 muon.
“There are currently two methods for determining a fundamental component of g2. The first is based on experimental data and the second on computer simulations of quantum chromodynamics, or QCD, the theory that studies strong interactions between quarks. These two methods produce quite different results, which is a major problem. Until this problem is resolved, we cannot study the contributions of possible exotic particles such as new Higgs bosons or dark matter, for example, to g2,” he explained.
The study was successful in explaining the discrepancy, but to understand it we need to take a few steps back and start again with a slightly more detailed description of the muon.
The muon is a particle that belongs to the lepton class, just like the electron, but whose mass is much greater. For this reason, it is unstable and only survives a very short time in a high energy context. When muons interact with each other in the presence of a magnetic field, they decay and regroup as a cloud of other particles, such as electrons, positrons, W and Z bosons, of Higgs and photons.
In experiments, muons are therefore always accompanied by many other virtual particles. Their contributions make the real magnetic moment measured experimentally greater than the theoretical magnetic moment calculated by the Dirac equation, which is equal to 2.
“To get the difference [g2]it is necessary to consider all these contributions, both those predicted by QCD [in the Standard Model of particle physics] and others that are smaller but appear in highprecision experimental measurements. We are very familiar with many of these contributions, but not all,” Boito said.
The QCD strong interaction effects cannot be calculated theoretically alone, because in some energy regimes they are impractical, so there are two possibilities. One has been used for some time and involves using experimental data obtained from electronpositron collisions, which create other particles made of quarks. The other is networkbased QCD, which has only become competitive in the current decade and involves simulation of the theoretical process in a supercomputer.
“The main problem with the muon g2 prediction at present is that the result obtained using electronpositron collision data does not agree with the total experimental result, while the results based on network QCD are. No one really knew why, and our study clarifies part of that puzzle,” Boito said.
He and his colleagues conducted their research precisely to solve this problem. “The paper reports the results of a number of studies in which we developed a new method to compare results from lattice QCD simulations with results based on experimental data. We show that it is possible to extract from the data the calculated contributions in the network with high precision – the contributions of the socalled connected Feynman diagrams,” he said.
American theoretical physicist Richard Feynman (19181988) won the Nobel Prize in Physics in 1965 (along with Julian Schwinger and Shin’ichiro Tomonaga) for his seminal work in quantum electrodynamics and elementary particle physics. Feynman diagrams, created in 1948, are graphical representations of mathematical expressions that describe the interaction of such particles and are used to simplify the respective calculations.
“In the study, we obtained for the first time the contributions of connected Feynman diagrams in the socalled “intermediate energy window” with high precision. Today we have eight results for these contributions, obtained using lattice QCD simulations, and “They all agree to a large extent. Furthermore, we show that results based on electronpositron interaction data do not agree with these eight results from simulations,” Boito said.
This allowed researchers to locate the source of the problem and brainstorm possible solutions. “It became clear that if the experimental data from the twopion channel is underestimated for some reason, this could be the cause of the discrepancy,” he said. Pions are mesons, particles consisting of a quark and an antiquark produced in highenergy collisions.
In fact, new data (still under peer review) from the CMD3 experiment conducted at Novosibirsk State University in Russia appear to show that the oldest twopion channel data could have been underestimated for whatever reason.
by José Tadeu Arantes, FAPESP