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

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 alpha(s) ln(2)(1/x) with alpha(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+ (q) over bar(x, Q(2)) similar to L-G(x, Q(2)) similar to Delta Sigma(x, Q(2)) similar to Delta G(x, Q(2)) similar to (1/x)(alpha h), with the intercept alpha(h) the same as obtained in the small-xhelicity evolution [3], which canbe approximated as alpha(h) approximate to 3.66074 root alpha N-s(c)/2 pi. 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.