Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $\Delta q^S (x, Q^2) \sim \left(\tfrac{1}{x}
\right)^{\alpha_h}$ with $\alpha_h = \tfrac{4}{\sqrt{3}} \sqrt{\tfrac{\alpha_s
N_c}{2\pi}}$, in excellent agreement with the numerical estimate $\alpha_h
\approx 2.31\sqrt{\tfrac{\alpha_s N_c}{2\pi}}$ 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.

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg