Energy-weighted integrals of the difference in helicity-dependent photoreaction cross sections (${\mathrm{\sigma }}_{1/2}$-${\mathrm{\sigma }}_{3/2}$) provide information on the nucleon’s spin-dependent polarizability (γ), and on the spin-dependent part of the asymptotic forward Compton amplitude through the Drell-Hearn-Gerasimov (DHG) sum rule. Estimates from current π-photoproduction multipole analyses, particularly for the proton-neutron difference, are in good agreement with relativistic-one-loop chiral calculations for γ but predict large deviations from the DHG sum rule. Either (a) both the two-loop corrections to the spin-polarizability are large and the existing multipoles are wrong, or (b) modifications to the Drell-Hearn-Gerasimov sum rule are required to fully describe the isospin structure of the nucleon.

DOI:https://doi.org/10.1103/PhysRevD.50.R6681