### New calculations based on fundamental theories deviate from the currently accepted theoretical value

21 October 2022

The anomalous magnetic moment of the muon is a crucial parameter in particle physics as it allows for precision tests of the established Standard Model. A new measurement of this quantity in 2021 caused a furore as it reaffirmed a significant deviation from the theoretical prediction – in other words, the anomalous magnetic moment is greater than anticipated.

Physicists calculate the theoretical prediction on the basis of the currently valid Standard Model of particle physics. In 2020, the Muon g-2 Theory Initiative – a group of 130 physicists with a strong representation from Mainz – produced a consensual estimate that has since been accepted as the reference value. Since then, several teams, including that of Professor Hartmut Wittig of the PRISMA+ Cluster of Excellence at Johannes Gutenberg University Mainz (JGU), have published new results for the contribution from the strong interaction using numerical simulations of lattice QCD, which suggest that the theoretical prediction is moving towards the experimental value. "Even if it turns out that the deviation between the theoretical and experiment results is actually smaller than we thought, this would still represent a major divergence," said Wittig. "But it is still imperative for us to first understand why the use of differing theoretical methods leads to such dissimilar results."

#### A new mystery that requires a solution

The anomalous magnetic moment receives contributions from all fundamental interactions except gravity. The strong interaction or strong nuclear force which acts between the elementary particles of matter known as quarks and which is mediated by the exchange of gluons is of particular importance when it comes to testing the Standard Model. Recent calculations have focused on the so-called hadronic vacuum polarization (HVP) contribution to the muon magnetic moment, in which quark-antiquark pairs are continually generated from a vacuum for a split second before disappearing again. "This is an extremely complex process to handle, and the level of uncertainty of the theoretical prediction is thus largely determined by the effects of the strong interaction," added Wittig. As the standard computational techniques either cannot be used in this context or have to date not been precise enough, in the current consensus paper the HVP contribution was determined by employing experimental data at various particle accelerators.

It would be ideal if the HVP contribution could be calculated without relying on experimental data, using Quantum Chromodynamics (QCD) alone. QCD is the fundamental theory of the strong interaction between quarks mediated by gluons. However, QCD is an extremely difficult theory to handle in practice. The Mainz team uses a technique known as lattice field theory for this purpose. Here the quarks and gluons are distributed over a discrete grid of points that represent space-time, very much like atoms in a crystal. The HVP contribution to the anomalous magnetic moment of the muon can then be determined with the help of supercomputers.

"Until just a few years ago, the huge technical challenges of such a calculation made it impossible to determine the HVP contribution with the necessary accuracy using lattice QCD. In the meantime we have refined the method so that the precision of our result can match that of the traditional approach that resorts to using experimental data," said Professor Hartmut Wittig. In the newly published paper, Wittig and his team present the results of calculation of a fraction of HVP that is particularly suitable for testing the consistency of the results of various lattice calculations and comparing these with the estimates based on the traditional method. "As our result is just as precise, you could say that lattice QCD calculation has passed its baptism of fire, which in itself is a huge success. Moreover, it is becoming increasingly clear that our QCD-based calculations actually correspond with the newly presented results of other teams."

Wittig now turns his attention back to the magnetic moment of the muon: "Our new lattice calculations are making it more apparent that the theoretical prediction value is likely to move closer to the measured result. This has generated quite a bit of excitement among my colleagues. We are now focusing on the problem of why different methods used to evaluate the HVP contribution should produce discrepant results. And those of our colleagues who may be disappointed that the discrepancy with the Standard Model is shrinking can take comfort in the fact that our new calculation has not made the deviation between theory and experiment go away completely. Whichever way you look at it, there is no doubt that there is a discrepancy that requires explanation. There is still a lot we need to understand."