A sign change of the moment at $n=0$ of the polarized structure function $g_1^{p}$

Abstract

The sum rule for the structure function $g_1^{p}$ which is related to the cross section of the photo-production is used to show that a sign change of the integral corresponding to the appropriately defined moment at $n=0$ where the integral is cut at the point $x=x_c(Q^2)$ occurs at very small $Q^2$ near $Q^2\sim 0.09$(GeV/c)$^2$ and $x_c\sim 0.024$. This fact shows that the origin of the sign difference between the Ellis-Jaffe sum rule and the Drell-Hearn-Gerasimov sum rule lies in the rapid change of the elastic contribution at low $Q^2$ which is compensated by the inelastic contribution to satisfy the sum rule at $n=0$. Hence it occurs at very small $Q^2$.