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

### Submission summary

 As Contributors: Yossathorn Tawabutr Arxiv Link: https://arxiv.org/abs/2108.04781v1 (pdf) Date submitted: 2021-08-11 03:10 Submitted by: Tawabutr, Yossathorn Submitted to: SciPost Physics Proceedings Proceedings issue: DIS2021 Academic field: Physics Specialties: High-Energy Physics - Experiment High-Energy Physics - Phenomenology Nuclear Physics - Experiment Nuclear Physics - Theory Approach: Theoretical

### Abstract

The small-$x$ quark helicity evolution equations at double-logarithmic order, with the kernel $\sim\alpha_s\ln^2(1/x)$, have been derived previously. In this work, we derive the single-logarithmic corrections to the equations, to order $\alpha_s\ln(1/x)$ 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. (Here, $N_c$ and $N_f$ are the numbers of quark colors and flavors, respectively.) Their solutions will provide more precise estimates of the quark helicity distribution at small $x$, contributing to the resolution of the proton spin puzzle.

###### Current status:
Editor-in-charge assigned