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\(\varvec{\varDelta }\)(1232)-Resonance in the Hydrogen Spectrum

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Abstract

The electromagnetic excitation of the \(\varDelta (1232)\)-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 \(\varDelta (1232)\) 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 \(\varDelta (1232)\)-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.

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Authors and Affiliations

  1. Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Franziska Hagelstein

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  1. Franziska Hagelstein
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Correspondence to Franziska Hagelstein.

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This article belongs to the Topical Collection “NSTAR 2017—The International Workshop on the Physics of Excited Nucleons”.

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Hagelstein, F. \(\varvec{\varDelta }\)(1232)-Resonance in the Hydrogen Spectrum. Few-Body Syst 59, 93 (2018). https://doi.org/10.1007/s00601-018-1403-x

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