Generalized Drell-Hearn-Gerasimov Sum Rule at Order {cal O}(p⁴) in Chiral Perturbation Theory

We calculate the forward spin-dependent photon-nucleon Compton amplitudes $S_1$ and $S_2$ as functions of photon energy $\nu$ and mass $Q^2$ at the next-to-leading (${\cal O}(p^4)$) order in chiral perturbation theory, from which we extract the contribution to a generalized Drell-Hearn-Gerasimov sum rule at low $Q^2$. The result indicates a much rapid $Q^2$ variation of the sum rule than a simple dimensional analysis would yield.