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

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.

Contribution to the Proceedings of the 11. International Workshop on the Physics of Excited Nucleons, 19 pages, 6 figures, 3 tables, references and comments added

References in corpus (9)

• Electromagnetic excitation of the Delta(1232)-resonance
• A new parameterization of the nucleon elastic form factors
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Chiral Effective-Field Theory in the Delta(1232) Region: Pion Electroproduction on the Nucleon
• The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
• Proton structure corrections to electronic and muonic hydrogen hyperfine splitting
• Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
• Large-$N_c$ relations for the electromagnetic N to Delta(1232) transition
• Model independent determination of the muonic hydrogen Lamb shift and proton radius

Cited by in corpus (7)

• The proton structure in and out of muonic hydrogen
• Nucleon resonances in Compton scattering
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: II. Spin polarizabilities and moments of polarized structure functions
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions
• Precision calculation of the recoil--finite-size correction for the hyperfine splitting in muonic and electronic hydrogen
• Disperon QED
• Laser excitation of the 1s-hyperfine transition in muonic hydrogen