On The $Q^2$ Dependence of The Spin Structure Function In The Resonance Region

Abstract

In this paper, we show what we can learn from the CEBAF experiments on spin-structure functions, and the transition from the Drell-Hearn-Gerasimov sum rule in the real photon limit to the spin dependent sum rules in the deep inelastic scattering, and how the asymmetry $A_1(x,Q^2)$ approaches the scaling limit in the resonance region. The spin structure function in the resonance region alone can not determine the spin-dependent sum rule due to the kinematic restriction of the resonance region. The integral $\int_0^1 \frac {A_1(x,Q^2)F_2(x,Q^2)}{2x(1+R(x,Q^2))}dx$ is estimated from $Q^2=0$ to $2.5$ GeV$^2$. The result shows that there is a region where both contributions from the baryon resonances and the deep inelastic scattering are important, thus provides important information on the high twist effects on the spin dependent sum rule.