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arXiv · 1612.05206

Model-independent determination of the two-photon exchange contribution to hyperfine splitting in muonic hydrogen

Clara Peset·Antonio Pineda
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Abstract

We obtain a model-independent prediction for the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen. We use the relation of the Wilson coefficients of the spin-dependent dimension-six four-fermion operator of NRQED applied to the electron-proton and to the muon-proton sectors. Their difference can be reliably computed using chiral perturbation theory, whereas the Wilson coefficient of the electron-proton sector can be determined from the hyperfine splitting in hydrogen. This allows us to give a precise model-independent determination of the Wilson coefficient for the muon-proton sector, and consequently of the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen, which reads $δ\bar E_{pμ,\rm HF}^{\rm TPE}(nS)=-\frac{1}{n^3}1.161(20)$ meV. Together with the associated QED analysis, we obtain a prediction for the hyperfine splitting in muonic hydrogen that reads $E^{\rm th}_{pμ,\rm HF}(1S)=182.623(27)$ meV and $E^{\rm th}_{pμ,\rm HF}(2S)=22.8123(33)$ meV. The error is dominated by the two-photon exchange contribution.

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BibTeXRIS

Clara Peset, Antonio Pineda. 2017-04-04. Model-independent determination of the two-photon exchange contribution to hyperfine splitting in muonic hydrogen. https://doi.org/10.1007/jhep04(2017)060

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