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

Abstract

The small- x x quark helicity evolution equations at double-logarithmic order, with the kernel \sim\alpha_s\ln^2(1/x) ∼ α s ln 2 ( 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) α s ln ( 1 / x ) of the evolution kernel. The new equations include the effects of the running coupling and the unpolarized small- x x evolution, both of which are parametrically significant at single-logarithmic order. The large- N_c N c and large- N_c\ N_f N c N f approximations to the equation are computed. (Here, N_c N c and N_f N f are the numbers of quark colors and flavors, respectively.) Their solutions will provide more precise estimates of the quark helicity distribution at small x x , contributing to the resolution of the proton spin puzzle.