Hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon from Lattice Quantum Chromodynamics

The anomalous magnetic moment of the muon, $a_\mu$, provides a stringent test for the Standard Model of particle physics, as it is so far one of the most precisely measured quantities. On the theory side, the Standard Model prediction has reached the same level of precision as experiment. However, a long-standing discrepancy between the Standard Model theory prediction and the experimental result exists. In order for the tension to potentially reach the critical level of five standard deviations, it is essential to further reduce the errors. The uncertainty on the theory side is dominated by the hadronic contributions.

In this talk, I will present various aspects related to the Mainz program for computing the Hadronic Light-by-Light scattering contribution $a_\mu^{\rm{hlbl}}$ from Lattice Quantum Chromodynamics. Although starting at next-to-leading order in $\alpha_{\rm{QED}}$-counting, the large relative error on $a_\mu^{\rm{hlbl}}$ constitutes a non-negligible contribution to the overall error budget of the Standard Model prediction. In the first part of the talk, I will give an overview of the theoretical background and computational techniques involved in our determination of $a_\mu^{\rm{hlbl}}$, accompanied with examples of application. After that, I will come to the analysis of our published results for $a_\mu^{\rm{hlbl}}$.