The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory

Understand

We compute the spin-dependent and spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon effective theory including the Delta particle.

• We compare with previous results when existing.
• Using these results we obtain the leading hadronic contributions, associated to the pion and Delta particles, to the Wilson coefficients of the lepton-proton four fermion operators in NRQED.
• The spin-independent coefficient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, $\Delta E_{\rm TPE}(\pi\&\Delta)=34(13)$ $\mu$eV.