Speakers
Description
We present an exact analytic solution of the revised large-$N_c$ small-$x$ helicity evolution equations derived recently. We find the corresponding small-$x$ asymptotics of the flavor-singlet helicity PDFs to be
\begin{align}
\Delta \Sigma (x, Q^2) \sim \Delta G (x, Q^2) \sim \left( \frac{1}{x} \right)^{\alpha_h}
\end{align}
with the intercept given by an exact analytic expression which numerically evaluates to $\alpha_h \approx 3.661 \sqrt{\tfrac{\alpha_s N_c}{2 \pi}}$. This appears to slightly disagree with the results of Bartels at al from 1996, where the intercept at large $N_c$ is given by a different analytic expression, evaluating to $\alpha_h \approx 3.664 \sqrt{\tfrac{\alpha_s N_c}{2 \pi}}$. We also obtain the all-order small-$x$ and large-$N_c$ polarized anomalous dimension $\Delta \gamma_{GG} (\omega)$ and demonstrate that it agrees with the existing finite-order results up to the three known loops.
We then turn our attention to the orbital angular momentum (OAM) distributions. We derive new small-$x$ evolution equations needed to extract small-$x$ asymptotics of OAM distributions. Solving these equations we obtain
\begin{align}
L_{q + {\bar q}} (x, Q^2) \sim L_G (x, Q^2) \sim \left( \frac{1}{x} \right)^{\alpha_h}
\end{align}
with the same intercept as for the helicity PDFs.
