Three-Loop Contributions to Hyperfine Splitting: Muon Loop Light-by-Light Insertion and Other Closed Lepton Loops

TL;DR

This paper calculates the three-loop quantum electrodynamics contributions, including muon and tauon loops, to hyperfine splitting in muonium, completing the analysis of all such high-order effects involving closed fermion loops.

Contribution

It provides the full calculation of all three-loop radiative-recoil corrections with closed lepton loops to hyperfine splitting, a novel comprehensive result in QED.

Findings

Complete three-loop contributions with closed fermion loops calculated.

Highlights the importance of lepton anomalous magnetic moments in these corrections.

Provides a full set of results for high-precision hyperfine splitting calculations.

Abstract

The muon and tauon light-by-light scattering contributions to hyperfine splitting in muonium are calculated. These results conclude calculation of all hard three-loop contributions to hyperfine splitting containing graphs with closed fermion loops. We discuss the special role that the lepton anomalous magnetic moments play in these calculations. The full result for all three-loop radiative-recoil corrections to hyperfine splitting generated by the graphs with closed lepton loops is presented.