Orbital angular momentum small-x evolution: exact results in the large-Nc limit

A bstract We construct an exact solution to the revised small- x orbital angular momentum (OAM) evolution equations derived in [1], based on an earlier work [2]. These equations are derived in the double logarithmic approximation (summing powers of α s ln 2 (1/ x ) with α s the strong coupling constant and x the Bjorken x variable) and the large- N c limit, with N c the number 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 to be Lq+q̄(x,Q²)~ LG(x,Q²)~ Δ Σ (x,Q²)~ Δ G(x,Q²)~ (1/x)αₕ, L q + q ¯ x Q 2 ∼ L G x Q 2 ∼ ΔΣ x Q 2 ∼ Δ G x Q 2 ∼ 1 x α h , with the intercept α h the same as obtained in the small- x helicity evolution [3], which can be approximated as α h ≈ 3.66074√αₛNc2π 3.66074 α s N c 2 π . This result is in complete agreement with [4]. Additionally, we calculate the ratio of the quark and gluon OAM distributions to the flavor-singlet quark and gluon helicity parton distribution functions respectively in the small- x region.