| Summary: | Abstract 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 ln2(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 L q + q ¯ x Q 2 ∼ L G x Q 2 ∼ ΔΣ x Q 2 ∼ Δ G x Q 2 ∼ 1 x α h , $$ {L}_{q+\overline{q}}\left(x,{Q}^2\right)\sim {L}_G\left(x,{Q}^2\right)\sim \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{x}\right)}^{\alpha_h}, $$ 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 α s N c 2 π $$ 3.66074\sqrt{\frac{\alpha_s{N}_c}{2\pi }} $$ . 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.
|
|---|