Δ(1232)-Resonance in the Hydrogen Spectrum

The electromagnetic excitation of the Δ(1232)-resonance plays an appreciable role in the Lamb shift and hyperfine structure of muonic and electronic hydrogen. Its effect appears at the subleading order O(α5), together with other proton-polarizability contributions from forward two-photon exchange. We use the large-Nc relations for the nucleon-to-delta transition form factors to compute the effect of the Δ(1232) in the hydrogen spectrum. We pay particular attention to a subtile difference between predictions based on a direct calculation of the two-photon exchange (or Compton scattering amplitudes) (Faustov et al. in Phys At Nucl 62:2099, 1999) and predictions based on the Δ(1232)-production photoabsorption cross sections (Buchmann in Can J Phys 87:773–783, 2009). The mismatch is explained by studying the dispersion relations for tree-level Compton scattering off the proton in more details