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We obtain a model-independent prediction for the two-photon exchangecontribution to the hyperfine splitting in muonic hydrogen. We use the relationof the Wilson coefficients of the spin-dependent dimension-six four-fermionoperator of NRQED applied to the electron-proton and to the muon-protonsectors. Their difference can be reliably computed using chiral perturbationtheory, whereas the Wilson coefficient of the electron-proton sector can bedetermined from the hyperfine splitting in hydrogen. This allows us to give aprecise model-independent determination of the Wilson coefficient for themuon-proton sector, and consequently of the two-photon exchange contribution tothe hyperfine splitting in muonic hydrogen, which reads $\delta \barE_{p\mu,\rm HF}^{\rm TPE}(nS)=-\frac{1}{n^3}1.161(20)$ meV. Together with theassociated QED analysis, we obtain a prediction for the hyperfine splitting inmuonic hydrogen that reads $E^{\rm th}_{p\mu,\rm HF}(1S)=182.623(27)$ meV and$E^{\rm th}_{p\mu,\rm HF}(2S)=22.8123(33)$ meV. The error is dominated by thetwo-photon exchange contribution.

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