We determine the small Bjorken $x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton in the double-logarithmic approximation (DLA), which resums powers of $\alpha_s \ln^2 (1/x)$ with $\alpha_s$ the strong coupling constant. Starting with the operator definitions for the quark and gluon OAM, we simplify them at small $x$, relating them, respectively, to the polarized dipole amplitudes for the quark and gluon helicities defined in our earlier works. Using the small-$x$ evolution equations derived for these polarized dipole amplitudes earlier we arrive at the following small-$x$ asymptotics of the quark and gluon OAM distributions in the large-$N_c$ limit: \begin{ align} L_{ q + \bar{ q}} (x, Q^2) = - \Delta \Sigma (x, Q^2) \sim \left(\frac{ 1}{ x}\right)^{ \frac{ 4}{ \sqrt{ 3}} \, \sqrt{ \frac{ \alpha_s \, N_c}{ 2 \pi}} }, \ \ \ \ \ L_G (x, Q^2) \sim \Delta G (x, Q^2) \sim \left(\frac{ 1}{ x}\right)^{ \frac{ 13}{ 4 \sqrt{ 3}} \, \sqrt{ \frac{ \alpha_s \, N_c}{ 2 \pi}}} . \end{ align}
Categories: hep-ph nucl-ex nucl-th