** The researchers identified the source of the discrepancies in recent predictions of the muon’s magnetic moment. Their discoveries could contribute to the investigation of dark matter and other aspects of new physics.**

The 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. Just like mass and electric charge, the magnetic moment is one of the fundamental magnitudes in physics. There is a difference between the theoretical value of the magnetic moment of a muon, a particle that belongs to the same class as the electron, and the values obtained in high-energy experiments carried out in particle accelerators.

The difference only appears in the eighth decimal place, but scientists have been intrigued by it since it was discovered in 1948. It is not a detail: it can indicate whether the muon interacts with dark matter particles or other Higgs bosons, or even if it does not. It is known whether any forces are involved in the process.

#### Discrepancies in Muon’s magnetic moment

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 (1902-1984), one of the founders of quantum mechanics and quantum electrodynamics – as 2. However, experiments have shown that g is not exactly 2 and there is much interest in understanding “g-2”, 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 (Fermilab) in the United States and announced in August 2023, is 2.00116592059, with an uncertainty range of plus or minus 0.00000000022.

“The precise determination of the muon’s magnetic moment has become a fundamental question in particle physics because investigating this gap between experimental data and theoretical prediction can provide information that could lead to the discovery of some spectacular new effect,” said the physicist. Diogo Boito, a professor at the São Carlos Institute of Physics at the University of São Paulo (IFSC-USP), told Agência FAPESP.

Article on the topic by Boito and collaborators is published in the magazine

The muon is a particle that belongs to the class of leptons, just like the electron, but has a much greater mass. For this reason, it is unstable and only survives for a very short period 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, Higgs bosons, and photons. In experiments, muons are therefore always accompanied by many other virtual particles. Their contributions make the actual magnetic moment measured in experiments greater than the theoretical magnetic moment calculated by the Dirac equation, which is equal to 2.

“To get the difference [*g-2*]it is necessary to consider all these contributions – both those foreseen by QCD [*in the Standard Model of particle physics*] and others that are smaller but appear in high-precision experimental measurements. We know very well several of these contributions – but not all of them”, said Boito.

The strong interaction effects of QCD cannot be calculated theoretically alone, as 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 electron-positron collisions, which create other particles made up of quarks. The other is networked QCD, which has only become competitive in the current decade and involves simulating the theoretical process on a supercomputer.

“The main problem with the g-2 muon prediction at this time is that the result obtained using electron-positron collision data does not agree with the full experimental result, while results based on lattice QCD do. No one knew exactly why, and our study clarifies part of this puzzle”, said Boito.

He and his colleagues conducted their research to solve exactly this problem. “The paper reports the findings of a series of studies in which we developed a new method for comparing results from lattice QCD simulations with results based on experimental data. We have shown that it is possible to extract from data contributions calculated in the network with great precision – the contributions of so-called connected Feynman diagrams,” he said.

American theoretical physicist Richard Feynman (1918-1988) won the Nobel Prize in Physics in 1965 (with Julian Schwinger and Shin’ichiro Tomonaga) for fundamental 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 Feynman diagrams connected in the so-called ‘intermediate energy window’ with great precision. Today we have eight results for these contributions, obtained through lattice QCD simulations, and they all agree significantly. Furthermore, we show that results based on electron-positron interaction data do not agree with these eight simulation results,” said Boito.

This allowed researchers to locate the source of the problem and think of possible solutions. “It became clear that if the experimental two-pion channel data were underestimated for some reason, this could be the cause of the discrepancy,” he said. Pions are mesons – particles composed of a quark and an antiquark produced in high-energy collisions.

In fact, new data (still under peer review) from the CMD-3 Experiment conducted at Novosibirsk State University in Russia appears to show that older two-pion channel data may have been underestimated for some reason.

Reference: “Light-Quark Connected Component Data-Based Determination of Intermediate Window Contribution to the Muon **g−2**” by Genessa Benton, Diogo Boito, Maarten Golterman, Alexander Keshavarzi, Kim Maltman and Santiago Peris, December 21, 2023, *Physical Review Letters*.

DOI: 10.1103/PhysRevLett.131.251803

Boito’s participation in the study was part of the project “Testing the standard model: Precision QCD and g-2 muon”, for which FAPESP awarded him a Phase 2 Young Researcher Grant.