Incompatibility of multipole predictions for the nucleon spin-polarizability and Drell-Hearn-Gerasimov sum rules.

Abstract

Energy-weighted integrals of the difference in helicity-dependent photoreaction cross sections (${\mathrm{\ensuremath{\sigma}}}_{1/2}$-${\mathrm{\ensuremath{\sigma}}}_{3/2}$) provide information on the nucleon's spin-dependent polarizability (\ensuremath{\gamma}), and on the spin-dependent part of the asymptotic forward Compton amplitude through the Drell-Hearn-Gerasimov (DHG) sum rule. Estimates from current \ensuremath{\pi}-photoproduction multipole analyses, particularly for the proton-neutron difference, are in good agreement with relativistic-one-loop chiral calculations for \ensuremath{\gamma} 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.