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

Abstract

We consider an impact of hadronic light-by-light scattering on the muonium hyperfine structure. A shift of the hyperfine interval $\Delta \nu (\mathrm{Mu}{)}_{\mathrm{HLBL}}$ 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, $\Delta \nu (\mathrm{Mu}{)}_{\mathrm{HLBL}}=-0.0065(10)Hz$. Although the effect is tiny it is useful in understanding the level of hadronic uncertainties.

16 pages, 7 figures, a reference added

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Cited by in corpus (12)

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• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
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• Three-Loop Contributions to Hyperfine Splitting: Muon Loop Light-by-Light Insertion and Other Closed Lepton Loops
• Muon Loop Light-by-Light Contribution to Hyperfine Splitting in Muonium