Evaluation of the forward Compton scattering off protons: II. Spin-dependent amplitude and observables

Abstract

The forward Compton scattering off the proton is determined by substituting the empirical total photoabsorption cross sections into dispersive sum rules. In addition to the spin-independent amplitude evaluated previously [Phys. Rev. D 92, 074031 (2015)], we obtain the spin-dependent amplitude over a broad energy range. The two amplitudes contain all the information about this process, and we, hence, can reconstruct the nonvanishing observables of the proton Compton scattering in the forward kinematics. The results are compared with predictions of chiral perturbation theory where available. The low-energy expansion of the spin-dependent Compton scattering amplitude yields the Gerasimov-Drell-Hearn (GDH) sum rule and relations for the forward spin polarizabilities (FSPs) of the proton. Our evaluation provides an empirical verification of the GDH sum rule for the proton, and yields empirical values of the proton FSPs. For the GDH integral, we obtain $204.5(21.4)$ $\mu$b, in agreement with the sum rule prediction: $204.784481(4)$ $\mu$b. For the FSPs, we obtain: ${\gamma }_0=-92.9(10.5)\times 10^{-6}$ fm${}^4$, and $\overline{{\gamma }_0}=48.4(8.2)\times 10^{-6}$ fm${}^6$, improving on the accuracy of previous evaluations.

arXiv comment9 pages, 7 figures, 4 tables; published version

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• Designing Optimal Experiments: An Application to Proton Compton Scattering
• Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method
• Evaluation of the forward Compton scattering off protons: II. Spin-dependent amplitude and observables
• Spin polarizabilities of the proton by measurement of Compton double-polarization observables
• Partial-wave analysis of proton Compton scattering data below the pion-production threshold
• Comprehensive Study of Observables in Compton Scattering on the Nucleon
• Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom
• Single-pion contribution to the Gerasimov--Drell--Hearn sum rule and related integrals
• Measurement of the high-energy contribution to the Gerasimov-Drell-Hearn sum rule
• Energy of a point-like neutron in an external electromagnetic field