Small-x Asymptotics of the Quark Helicity Distribution

We construct a numerical solution of the small-x evolution equations derived in our recent work [J. High Energy Phys. 01 (2016) 072.] for the (anti) quark transverse momentum dependent helicity TMDs and parton distribution functions (PDFs) as well as the g(1) structure function. We focus on the case of large N-c, where one finds a closed set of equations. Employing the extracted intercept, we are able to predict directly from theory the behavior of the quark helicity PDFs at small x, which should have important phenomenological consequences. We also give an estimate of how much of the proton's spin carried by the quarks may be at small x and what impact this has on the spin puzzle.