Speaker
Description
The small-$x$ quark helicity evolution equations at double-logarithmic order, with the kernel $\sim \alpha_s\ln^2 (1/x)$, had been derived previously, and the equations were solved analytically at large $N_c$ and numerically at large $N_c$ and $N_f$. (Here, $N_c$ and $N_f$ are the numbers of quark colors and flavors, respectively.) In this work, we derive the single-logarithmic corrections to the double-logarithmic equations derived previously, that is, we find the correction to order $\alpha_s\ln (1/x)$ of the evolution kernel. The new equations include the effects of the running coupling and the unpolarized small-$x$ evolution, both of which are parametrically significant at single-logarithmic order. The large-$N_c$ and large-$N_c \& N_f$ approximations to the equation are computed. Their solution will provide a more precise estimate of the quark helicity distribution at small $x$, contributing to the resolution of the proton spin puzzle.
