Effects Of The Quantity ${\sigma }_{TS}$ On The Spin Structure Functions Of Nucleons In The Resonance Region

Abstract

In this paper, we investigate the effects of the quantity ${\sigma }_{TS}$ on the spin-structure functions of nucleons in the resonance region. The Schwinger sum rule for the spin structure function $g_2(x,Q^2)$ at the real photon limit is derived for the nucleon treated as a composite system, and it provides a crucial constraint on the longitudinal transition operator which has not been treated consistently in the literature. The longitudinal amplitude $S_{\frac{1}{2}}$ is evaluated in the quark model with the transition operator that generates the Schwinger sum rule. The numerical results of the quantity ${\sigma }_{TS}$ are presented for both spin structure functions $g_1(x,Q^2)$ and $g_2(x,Q^2)$ in the resonance region. Our results show that this quantity plays an important role in the low $Q^2$ region, which can be tested in the future experiments at CEBAF.

Comments: 20 pages, latex, 4 postscript figures can be obtained from the author