Hadronic Light-by-Light Scattering in the Muonium Hyperfine Splitting

TL;DR

This paper calculates the tiny but significant impact of hadronic light-by-light scattering on muonium's hyperfine splitting, using meson exchange models constrained by QCD to estimate the effect's size and uncertainties.

Contribution

It provides the first detailed estimate of hadronic light-by-light scattering effects on muonium hyperfine structure using meson exchange models constrained by QCD.

Findings

The dominant contribution comes from pseudovector meson exchange.

The estimated shift in hyperfine splitting is approximately -0.0065 Hz.

The effect helps understand hadronic uncertainties in precision measurements.

Abstract

We consider an impact of hadronic light-by-light scattering on the muonium hyperfine structure. A shift of the hyperfine interval $\Delta \nu({\rm Mu}) _{\rm\tiny HLBL}$ is calculated with the light-by-light scattering approximated by exchange of pseudoscalar and pseudovector mesons. Constraints from the operator product expansion in QCD are used to fix parameters of the model similar to the one used earlier for the hadronic light-by-light scattering in calculations of the muon anomalous magnetic moment. The pseudovector exchange is dominant in the resulting shift, $\Delta \nu({\rm Mu})_{\rm\tiny HLBL}= -0.0065(10) {Hz}$. Although the effect is tiny it is useful in understanding the level of hadronic uncertainties.