Contribution of hadronic vacuum polarization determined with unprecedented accuracy
The magnetic moment of the muon is an important precision parameter for putting the standard model of particle physics to the test. After years of work, the research group led by Professor Hartmut Wittig of the PRISMA⁺ Cluster of Excellence at Johannes Gutenberg University Mainz (JGU) has calculated this quantity using the so-called lattice quantum chromodynamics method (lattice QCD method). Their result, which was recently published, agrees with the latest experimental measurements, in contrast to earlier theoretical calculations. After the experimental measurements had been pushed to ever higher precision in recent years, attention had increasingly turned to the theoretical prediction and the central question of whether it deviates significantly from the experimental results and thus provides evidence for the existence of new physics beyond the Standard Model.

The anomalous magnetic moment is an intrinsic property of elementary particles such as the electron or its heavier brother, the muon. Calculating this quantity with sufficient accuracy within the framework of the Standard Model is an enormous challenge. With the only exception of gravity, all fundamental interactions contribute to the anomalous magnetic moment. In particular, the contributions of the strong interaction, which describes the forces between the basic building blocks of protons and neutrons, the quarks, cause great difficulties for physicists. The main source of uncertainty in the theoretical calculation of the anomalous magnetic moment of the muon is the contribution of the so-called hadronic vacuum polarization (HVP). Traditionally, this contribution has been determined using experimental data – this is called the "data-driven" method. In fact, over many years this technique provided a significant deviation from the experimental measured value and thus also one of the most promising indications of the existence of new physics.

Result of the PRISMA⁺ Cluster of Excellence
Wittig's group has now published a new result for the HVP contribution as a preprint in the open access archive arXiv, which was obtained using the complementary method of lattice QCD. "Our work confirms earlier evidence suggesting a clear divergence between the data-driven method and lattice QCD calculations," says Wittig. "At the same time, we have to conclude from our result that the standard model has once again been confirmed, because our result agrees with the experimental measurement."

In 2020, the "Muon g-2 Theory Initiative" – an international group of 130 physicists with strong participation from Mainz – published a reference value for the theoretical prediction of the anomalous magnetic moment of the muon within the framework of the Standard Model, which is based on the data-driven method. This actually showed a clear deviation from the new direct measurements of this quantity, which have been carried out at Fermilab near Chicago since 2021.
However, since the publication of new results from the CMD-3 experiment in Novosibirsk in February 2023, this reference value has come into question, as the standard model prediction varies greatly depending on which data set is used. In order to overcome the disadvantages of the data-driven method, Wittig's group has focused on calculations using the lattice QCD method, which allows the contributions of the strong interaction to be calculated numerically using supercomputers. The advantage of such an approach is that, unlike the value published in 2020, it provides results that do not require experimental data.

Agreement with the experimental mean value
Wittig's group has focused on calculating the contribution of the HVP, which provides the largest contribution of the strong interaction to the anomalous magnetic moment of the muon. In their recent work, the team has found a new value for the muon's anomalous magnetic moment that is consistent with the current experimental mean and far from the 2020 theoretical estimate. "After years of work on reducing the uncertainties of our calculations and overcoming the computational challenges associated with performing such lattice QCD calculations, we have obtained the HVP contribution with an overall accuracy of just below 1% and a good balance between statistical and systematic uncertainties," says Wittig. "This allows us to reassess the validity of the standard model."

Even if the new result once again confirms the standard model, here are still many puzzles. Where the difference between the lattice QCD and the data-driven method comes from and how the result of the CMD-3 experiment should be evaluated is not yet fully understood. "We still have a long way to go to achieve our long-term goal of reducing the total error to around 0.2 %. No matter how you look at it: We can't get around the fact that there are discrepancies in the anomalous magnetic moment of the muon that need to be explained. There is still a lot for us to understand," concludes Wittig.