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

$$\varvec{\varDelta }$$ Δ (1232)-Resonance in the Hydrogen Spectrum The electromagnetic excitation of the $$\varDelta (1232)$$ 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 $$\mathcal {O}(\alpha ^5)$$ O ( α 5 ) , together with other proton-polarizability contributions from forward two-photon exchange. We use the large- $$N_c$$ N c relations for the nucleon-to-delta transition form factors to compute the effect of the $$\varDelta (1232)$$ 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 $$\varDelta (1232)$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Few-Body Systems Springer Journals

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

, Volume 59 (5) – Jun 5, 2018
15 pages

/lp/springer_journal/varvec-vardelta-1232-resonance-in-the-hydrogen-spectrum-ST7GeaRySD
Publisher
Springer Vienna
Subject
Physics; Particle and Nuclear Physics; Nuclear Physics, Heavy Ions, Hadrons; Atomic, Molecular, Optical and Plasma Physics
ISSN
0177-7963
eISSN
1432-5411
D.O.I.
10.1007/s00601-018-1403-x
Publisher site
See Article on Publisher Site

### Abstract

The electromagnetic excitation of the $$\varDelta (1232)$$ 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 $$\mathcal {O}(\alpha ^5)$$ O ( α 5 ) , together with other proton-polarizability contributions from forward two-photon exchange. We use the large- $$N_c$$ N c relations for the nucleon-to-delta transition form factors to compute the effect of the $$\varDelta (1232)$$ 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 $$\varDelta (1232)$$ 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.

### Journal

Few-Body SystemsSpringer Journals

Published: Jun 5, 2018

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