The constraint on the spin dependent structure function $g_1$ at low $Q^2$ through the sum rule corresponding to the moment at $n=0$

Abstract

The sum rules for the spin dependent structure function $g_1^{ab}$ in the null-plane formalism corresponding to the moment at $n=0$ has been transformed to the sum rule which relates the $g_1^{ab}$ with the cross section of the isovector photon or the real photon. Based on these sum rules, we argue that there is a deep connection among the elastic, the resonance, and the non-resonant contributions, and that it explains why the sign of the generalized Gerasimov-Drell-Hearn sum changes at very small $Q^2$.