Study clarifies key question in particle physics – 01/15/2024 – Science

Magnetic moment is the quantity that quantifies the interaction of a particle with spin with a magnetic field, such as that of a magnet. Just like mass and electric charge, the magnetic moment is one of the fundamental quantities in physics. There is a difference between the theoretical value of the magnetic moment of the 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 it has intrigued scientists since 1948, when it was discovered.

And this is not a detail, as this difference could indicate that the muon interacts with dark matter particles, other Higgs bosons or even that there are forces different from those known involved in the process.

The theoretical value of the muon’s magnetic moment, represented by the letter “g”, obtained from the Dirac equation (formulated by the English physicist Paulo Dirac, 1902-1984, 1933 Nobel Prize in Physics, one of the founders of mechanics and electrodynamics quantum), is equal to 2. But today we know that g is not exactly equal to 2 and, therefore, there is great interest in understanding “g-2”, that is, the difference between the experimental value and the predicted by the Dirac equation. The best experimental value currently available, obtained with impressive precision at Fermilab, the Fermi National Accelerator Laboratory, in the United States, and released in August 2023, is 2.00116592059, plus or minus 0.00000000022. Information about the experiment carried out at Fermilab, called “Muon g-2”, can be accessed at:

“The precise determination of the muon’s magnetic moment has become a central question in particle physics, because investigating this gap between experimental data and theoretical predictions can provide us with information that leads to the discovery of some new and spectacular effect,” Physicist Diogo Boito, professor at the São Carlos Institute of Physics at the University of São Paulo (IFSC-USP), tells Agência Fapesp.

He and collaborators have just published a study on the subject in Physical Review Letters.

“Our results were presented at two important international events. First by me, at a workshop in Madrid, Spain. Then by my colleague Maarten Golterman, from San Francisco State University, at a meeting held in Bern, Switzerland”, says Boito .

These results quantify and point to the origin of a discrepancy between the two methods used in current g-2 forecasts. The researcher details: “There are currently two methods to determine a fundamental component of g-2. The first is based on experimental data. The second on computational simulations of quantum chromodynamics (quantum chromodynamics, or QCD, in English), the theory that studies the strong interactions between quarks. The two methods lead to very different results and this constitutes a major problem. Without solving it, it becomes impossible to investigate the contributions of possible exotic particles, for example, new Higgs bosons or dark matter, in the result of g-2”.

The study managed to explain this discrepancy. But to understand this, 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 class of leptons — the same as the electron. However, it has a much greater mass. And, because of this, it is not stable, surviving only for very short periods of time, in high energy contexts. When they interact with each other, in the presence of magnetic fields, muons disfigure and reconfigure themselves, bringing into the presence of a large number of other particles: electrons, positrons, W and Z bosons, Higgs bosons, photons, etc. Thus, in experimental contexts, the muon is always accompanied by myriads of virtual particles. It is the contributions of these particles that cause the effective magnetic moment, measured in experiments, to be greater than the theoretical magnetic moment, equal to 2, calculated by the Dirac equation.

“To obtain such a difference [g-2], it is necessary to consider all these contributions. Both those that quantum chromodynamics [que compõe o modelo-padrão da física de partículas] predicts, as well as other smaller effects, but which appear in very precise experimental measurements. We are already very familiar with several of these contributions. But not all”, says Boito.

The effects arising from the strong interaction cannot be calculated theoretically alone, as these quantum chromodynamics calculations are impractical in some energy regimes. Thus, there are two possibilities. One of them, which already has a historical basis, is to resort to experimental data obtained in the collisions of electrons with positrons, which generate other particles formed by quarks. The other, which only became competitive in the 2020s, is to simulate, based on theory, the process on supercomputers. This is called “QCD on the network”.

“The central problem with predicting g-2 today is that the results obtained using electron-positron collision data are at odds with the full experimental result, while results based on lattice QCD are in good agreement with the experiment. And no one knew for sure why this happened. Our study clarifies part of this puzzle”, comments Boito.

It was exactly to solve this problem that he and collaborators carried out the study in question. “The current article is the result of a series of our works in which we developed a new method to compare network simulation results with those obtained from experimental data. We showed that it is possible to extract, from the data, contributions that are calculated in the network with great precision: the contribution of the so-called connected Feynman diagrams”, informs the researcher.

Here it is necessary to open a small parenthesis to say that Feynman diagrams, created in the late 1940s by the North American physicist Richard Feynman (1918-1988), Nobel Prize winner in Physics in 1965, are graphical representations used to describe interactions between particles and simplify the respective calculations.

“In the present study, we obtained, for the first time, with great precision, the contributions of the Feynman diagrams connected in the so-called ‘intermediate energy window’. Today, we have eight results for these contributions, obtained with in-lattice QCD simulations, and all they are in good agreement with each other. And we showed that the results coming from the electron-positron interaction data do not agree with these eight simulation results”, says Boito.

According to the researcher, this makes it possible to understand where the problem is and what the possible solutions to it would be. “It became clear that if the experimental data for the two-pion channel [mésons, isto é, partículas formadas por um quark e um antiquark, produzidas em colisões de alta energia] are underestimated for some reason, this could be the cause of the discrepancy”, he summarizes. In fact, new data, still in the process of peer review, from the CMD-3 Experiment, carried out at the University of Novosibirsk, in Russia, seem to indicate that the older two-pion channel data could be, for some reason, underestimated.

All the work done by Boito in this study was carried out in the context of his project “Tests of the standard model: precision QCD and g-2 of the muon”, awarded with Research Grant for Young Researchers Phase 2 by Fapesp.

The article Data-driven determination of the light-quark connected component of the intermediate-window contribution to the muon g-2 can be accessed at: