Small-$x$ asymptotics of the quark helicity distribution

TL;DR

This paper numerically solves small-$x$ evolution equations for quark helicity distributions, predicting their behavior at small $x$ and estimating their contribution to the proton's spin, with implications for the spin crisis.

Contribution

It provides the first numerical solution of the small-$x$ helicity evolution equations in the large $N_c$ limit, enabling direct predictions of helicity PDFs at small $x$.

Findings

Predicted the small-$x$ behavior of helicity PDFs.

Estimated the contribution of small-$x$ region to proton spin.

Highlighted potential impact on the spin crisis.

Abstract

We construct a numerical solution of the small-$x$ evolution equations recently derived in \cite{Kovchegov:2015pbl} for the (anti)quark helicity TMDs and PDFs as well as the $g_1$ structure function. We focus on the case of large $N_c$ where one finds a closed set of equations. Employing the extracted intercept, we are able to predict directly from theory the behavior of the helicity PDFs at small $x$, which should have important phenomenological consequences. We also give an estimate of how much of the proton's spin may be at small $x$ and what impact this has on the so-called "spin crisis."