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

TL;DR

This paper constrains the proton's small-$x$ helicity structure using a valence quark model and polarized deep inelastic scattering data, predicting a negative $g_1^p$ at small $x$ and quantifying quark and gluon spin contributions.

Contribution

It introduces a novel approach combining the valence quark model with global data analysis to constrain initial conditions for small-$x$ helicity evolution.

Findings

Good fit to polarized small-$x$ data with 8 parameters

Predicted negative $g_1^p$ at small $x$

Estimated quark and gluon spin contribution to proton spin

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.