The gyromagnetic ratio is the ratio of a particle’s magnetic moment and its angular momentum. This value determines how a particle responds to a magnetic field. According to classical physics, muons should have a gyromagnetic ratio equal to 2. However, owing to quantum mechanics, there is a small difference between the expected gyromagnetic ratio and the observed value. This discrepancy is known as the anomalous magnetic moment.

The anomalous magnetic moment is incredibly sensitive to quantum fluctuations. It can be used to test the Standard Model of physics, and previous consistent experimental discrepancies have hinted at new physics beyond the Standard Model. The search for the anomalous magnetic moment is one of the most precise tests in modern physics.

To calculate the anomalous magnetic moment, experiments such as Fermilab’s Muon g-2 experiment have been set up where researchers measure the muon’s wobble frequency, which is caused by its magnetic moment. But effects such as hadronic vacuum polarization and hadronic light-by-light scattering cause uncertainty in the measurement. Unlike hadronic vacuum polarization, hadronic light-by-light cannot be directly extracted from experimental cross-section data, making it dependent on the model used and a significant computational challenge.

In this work, the researcher took a major step in resolving the anomalous magnetic moment of the muon. Their method calculated how the neutral pion contributes to hadronic light-by-light scattering, used domain wall fermions to preserve symmetry, employed eight different lattice configurations with variational pion masses, and introduced a pion structure function to find the key contributions in a model-independent method. The pion transition form factor was computed directly at arbitrary space-like photon momenta, and a Gegenbauer expansion was used to confirm that about 98% of the π⁰-pole contribution was determined in a model-independent way. The analysis also included finite-volume corrections and chiral and continuum extrapolations and yielded a value for the π⁰ decay width.

The development of a more accurate and model-independent anomalous magnetic moment for the muon has reduced major theoretical uncertainties and can make Standard Model precision tests more robust.

Do you want to learn more about this topic?

The muon Smasher’s guide Hind Al Ali et al (2022)