Speaker
Description
We revisit the problem of the small Bjorken-$x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised formalism for small-$x$ helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small $x$ to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the $x$-dependence of the OAM distributions, we derive novel small-$x$ evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of $\alpha_s \ln^2(1/x)$ with $\alpha_s$ the strong coupling constant). We solve these evolution equations numerically and extract the large-$N_c$, small-$x$ asymptotics of the quark and gluon OAM distributions, which we determine to be
\begin{align}
L_{q+\bar{q}}(x, Q^2) \sim L_{G}(x,Q^2) \sim \Delta \Sigma(x, Q^2) \sim \Delta G(x,Q^2) \sim \left(\frac{1}{x}\right)^{3.66 \, \sqrt{\frac{\alpha_s N_c}{2\pi}}},
\end{align}
in agreement with [2] within the precision of our numerical evaluation (here $N_c$ is the number of quark colors). We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-$x$ region.
[1] F. Cougoulic, Y.V. Kovchegov, A. Tarasov and Y. Tawabutr, Quark and gluon helicity evolution at small x: revised and updated, Journal of High Energy Physics 2022 (2022).
[2] R. Boussarie, Y. Hatta and F. Yuan, Proton Spin Structure at Small-x, Phys. Lett. B797 (2019) 134817 [1904.02693].
