Small-x asymptotics of the quark helicity distribution: Analytic results

In this Letter, we analytically solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large-N-c limit. These evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an analytic solution. We find that the small-x power-law tail of the quark helicity distribution scales as Delta q(S)(x, Q(2)) similar to (1/x)(alpha h) with alpha(h) = 4/root 3 root alpha N-s(c)/2 pi, in excellent agreement with the numerical estimate alpha(h) approximate to 2.31 root alpha N-s(c)/2 pi obtained previously. We then verify this solution by cross-checking the predicted scaling behavior of the auxiliary "neighbor dipole amplitude" against the numerics, again finding excellent agreement. (C) 2017 Published by Elsevier B.V.