Constraining Proton Spin at Small $x$ with Valence Quark Model

Recently, a global analysis has been performed for longitudinal spin asymmetries in polarized deep inelastic scattering (DIS) processes, combining the polarized valence quark model with the large-$N_c\mathrm{\&}{N}_f$ helicity evolution equations. With a three-fold reduction in the number of free parameters, the valence quark model results in a six-fold reduction of uncertainty for the resulting prediction of total parton spin inside the proton, when compared to previous analysis performed with traditional moderate-$x$ model inspired by Born approximation. The fit based on valence quark model predicts a positive gluon hPDF and negative $g_1$ structure function at small $x$. However, the resulting increase in the ${\chi }^2$-statistic of the fit warrants further examination into the physical uncertainty of the valence quark model, which is a work in progress. We also summarize other possibilities of future research directions towards the end of this article.