Generalized Sum Rules for Spin-Dependent Structure Functions of the Nucleon

The Drell-Hearn-Gerasimov and Bjorken sum rules are special examples of dispersive sum rules for the spin-dependent structure function G 1 (ν, Q 2 ) at Q 2 = 0 and ∞ . We generalize these sum rules through studying the virtual-photon Compton amplitudes S 1 (ν, Q 2 ) and S 2 (ν, Q 2 ). At small Q 2 , we calculate the Compton amplitudes at leading order in chiral perturbation theory; the resulting sum rules will be able to be tested against data soon available from the Jefferson Laboratory. For Q 2 >>Λ QCD 2 , the standard twist-expansion for the Compton amplitudes leads to the well known deep-inelastic sum rules. Although the situation is still relatively unclear in a small intermediate- Q 2 window, we argue that chiral perturbation theory and the twist-expansion alone already provide strong constraints on the Q 2 -evolution of the G 1 (ν, Q 2 ) sum rule from Q 2 = 0 to ∞ .