Nucleon spin structure II: Spin structure function $g_1^p$ at small $x$

The spin structure function $g_1^p$ of the proton is studied in a two component framework, where the perturbative evolution of parton distributions and nonperturbative vector meson dominance model are used. We predict the $g_1^p$ asymmetric behavior at small $x$ from lower $Q^2$ to higher $Q^2$. We find that the contribution of the large gluon helicity dominates $g_1^p$ at $x>10^{-3}$ but mixed with nonperturbative component which complicates the asymptomatic behavior of $g_1^p$ at $x<10^{-3}$. The results are compatible with the data including the HERA early estimations and COMPASS new results. The predicted strong $Q^2$- and $x$-dependence of $g_1^p$ at $0.01<Q^2<3 GeV^2$ and $x<0.1$ can be checked on the next Electron-Ion Collider.

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