Single-Logarithmic Corrections to Small-$x$ Helicity Evolution

Abstract

The small-xx quark helicity evolution equations at double-logarithmic order, with the kernel \sim\alpha_s\ln^2(1/x)∼αsln2(1/x), have been derived previously. In this work, we derive the single-logarithmic corrections to the equations, to order \alpha_s\ln(1/x)αsln(1/x) of the evolution kernel. The new equations include the effects of the running coupling and the unpolarized small-xx evolution, both of which are parametrically significant at single-logarithmic order. The large-N_cNc and large-N_c\ N_fNcNf approximations to the equation are computed. (Here, N_cNc and N_fNf are the numbers of quark colors and flavors, respectively.) Their solutions will provide more precise estimates of the quark helicity distribution at small xx, contributing to the resolution of the proton spin puzzle.