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

Abstract

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-Nc 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 ΔqS(x,Q2)∼(1x)αh with αh=43αsNc2π, in excellent agreement with the numerical estimate αh≈2.31αsNc2π 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.