Three-Loop Vacuum Polarization in Muonic Atoms

The spectrum of muonic atoms offers a few intricacies for a theoretical analysis. One predominant feature is the dominance of electronic vacuum-polarization effects in the spectrum, which necessitates quite involved efforts from theorists, and requires theorists to look at multi-loop (two-loop and three-loop) effects, as well as to analyze combinations of the vacuum-polarization effects with self-energy diagrams. In the muonic systems, the n-loop vacuum polarization enters at the order alpha^n * alpha^2 m_mu c^2, where m_mu is the muon mass, c is the speed of light, and alpha is the fine-structure constant. The n-loop effects are thus suppressed only a single power of alpha in comparison to the previous loop order. The most challenging corrections come from irreducible three-loop diagrams, which have recently been analyzed in the preprint arXiv:2412.17535 [hep-ph]. We shall discuss the methods used for tackling the three-loop effects, discuss remaining challenges for muonic systems, and highlight various other recent advances.