# Proton Spin Structure at Small-$x$

## TL;DR

This paper extends existing QCD models to analyze the small-$x$ behavior of orbital angular momentum distributions, providing an analytical solution that sheds light on the proton spin puzzle.

## Contribution

It generalizes the Bartels-Ermolaev-Ryskin approach to include orbital angular momentum at small-$x$, offering a new analytical solution in the double logarithmic approximation.

## Key findings

- Derived the asymptotic behavior of orbital angular momentum distributions at small-$x$
- Provided an exact analytical solution in the double logarithmic approximation
- Discussed implications for the proton spin problem

## Abstract

We generalize the Bartels-Ermolaev-Ryskin approach for the $g_1$ structure function at small-$x$ to determine the small-$x$ asymptotic behavior of the orbital angular momentum distributions in QCD. We present an exact analytical solution of the evolution equation in the double logarithmic approximation and discuss its implications for the proton spin problem.