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

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 δEpμ,HFTPE​(nS)=−n31​1.161(20) meV. Together with the associated QED analysis, we obtain a prediction for the hyperfine splitting in muonic hydrogen that reads E th pμ,HF (1S) = 182.623(27) meV and E th pμ,HF (2S) = 22.8123(33) meV. The error is dominated by the two-photon exchange contribution