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arXiv · 1801.09790

$\Delta(1232)$-Resonance in the Hydrogen Spectrum

Franziska Hagelstein
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Abstract

The electromagnetic excitation of the $\Delta(1232)$-resonance plays an appreciable role in the Lamb shift and hyperfine structure of muonic and electronic hydrogen. Its effect appears at the subleading order $\mathcal{O}(\alpha^5)$, together with other proton-polarizability contributions from forward two-photon exchange. We use the large-$N_c$ relations for the nucleon-to-delta transition form factors to compute the effect of the $\Delta(1232)$ 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) and predictions based on the $\Delta(1232)$-production photoabsorption cross sections. The mismatch is explained by studying the dispersion relations for tree-level Compton scattering off the proton in more details.

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Franziska Hagelstein. 2018-01-29. $\Delta(1232)$-Resonance in the Hydrogen Spectrum. https://doi.org/10.1007/s00601-018-1403-x

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