Orbital Angular Momentum at Small 𝒙 Revisited

We revisit the the quark and gluon orbital angular momentum (OAM) distributions in the proton at small x. Utilizing the revised small-x helicity evolution from an earlier study, we calculate the quark and gluon OAM distributions at small x, and relate them to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the small-x asymptotics 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 αₛ ln²(1/x) with αₛ the strong coupling constant). We solve these evolution equations numerically and extract the large-Nc, small-x asymptotics of the quark and gluon OAM distributions, which we determine to be {align} Lq+q̄(x, Q^2) ~ LG(x,Q^2) ~ Δ Σ(x, Q^2) ~ Δ G(x,Q^2) ~ (1/x)3.66 \, √α_s N_c/2π, {align} in agreement with earlier results in the literature, within the precision of our numerical evaluation (here Nc 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.