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We construct an exact solution to the revised small-$x$ orbital angularmomentum (OAM) evolution equations derived recently, based on an earlier work.These equations are derived in the double logarithmic approximation (summingpowers of $\alpha_s \ln^2(1/x)$ with $\alpha_s$ the strong coupling constantand $x$ the Bjorken $x$ variable) and the large-$N_c$ limit, with $N_c$ thenumber of quark colors. From our solution, we extract the small-$x$,large-$N_c$ expressions of the quark and gluon OAM distributions. Additionally,we determine the large-$N_c$ small-$x$ asymptotics of the OAM distributions tobe  \begin{align}  \notag  L_{q+\bar{q}}(x,Q^2) \sim L_G(x,Q^2) \sim \Delta \Sigma (x,Q^2) \sim \DeltaG(x,Q^2) \sim \left(\frac{1}{x} \right)^{\alpha_h},  \end{align}  with the intercept $\alpha_h$ the same as obtained in the small-$x$ helicityevolution, which can be approximated as $\alpha_h \approx 3.66074\sqrt{\frac{\alpha_s N_c}{2\pi}}$. This result is in complete agreement withthe literature. Additionally, we calculate the ratio of the quark and gluon OAMdistributions to the flavor-singlet quark and gluon helicity partondistribution functions respectively in the small-$x$ region.

Orbital Angular Momentum Small-$x$ Evolution: Exact Results in the Large-$N_c$ Limit