Proton spin from small-$x$ with constraints from the valence quark model

Abstract

We apply the valence quark model recently calculated for polarized proton to constrain the non-perturbative initial condition for the small-$x$ helicity evolution. The remaining free parameters are constrained by performing a global analysis to the available polarized small-$x$ deep inelastic scattering data. A good description of the world data is obtained with only 8 free parameters. The model parameters are tightly constrained by the data, allowing us to predict the proton polarized structure function $g_1^p$ to be negative at small $x$. Furthermore, we obtain the small-$x$ quark and gluon spins to give a contribution ${\int }_{10^{-5}}^{0.1}dx\left(\frac{1}{2}\Delta \Sigma +\Delta G\right)=0.76\pm 0.13$ or $1.70\pm 0.20$ to the proton spin, depending on the applied running coupling prescription.

13 pages, 6 figures, including main text and supplementary material; 2 additional supplementary files in csv format; minor updates to reflect the final published version

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