Single-pion contribution to the Gerasimov-Drell-Hearn sum rule and related integrals

Phenomenological amplitudes obtained in partial-wave analyses (PWA) of single-pion photoproduction are used to evaluate the contribution this process Gerasimov-Drell-Hearn (GDH), Baldin and Gell-Mann-Goldberger-Thirring (GGT) sum rules, by integrating up 2 GeV photon energy. Our study confirms that all these rules converges even before highest considered energy, but levels saturation very different three cases. Single-pion production almost saturates GDH rule for proton, while a large fraction is missing neutron case. The integrals proton both saturated about four fifths predicted total strength. For GGT rule, wide variability predictions precludes any definitive statement.