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 G1(ν,Q 2) at Q2 = 0 and ∞. We generalize these sum rules through studying the virtualphoton Compton amplitudes S1(ν,Q 2) and S2(ν,Q 2). At small Q2, we calculate the Compton amplitudes at leading-order in chiral perturbation theory; the resulting sum rules can be tested by data soon available from Jefferson Lab. For Q2 >> ΛQCD, 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-Q2 window, we argue that chiral perturbation theory and the twist-expansion alone already provide strong constraints on the Q2-evolution of the G1(ν,Q 2) sum rule from Q2 = 0 to Q2 = ∞. Typeset using REVTEX