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

### Submission summary

 As Contributors: Yossathorn Tawabutr Arxiv Link: https://arxiv.org/abs/2108.04781v2 (pdf) Date accepted: 2022-05-06 Date submitted: 2022-03-22 03:44 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.

Published as SciPost Phys. Proc. 8, 103 (2022)

The author would like to thank the editor-in-charge for the recommendation and suggestion. In this resubmission, the editor-in-charge's suggestions have been implemented, together with minor additional changes that will further enhance the proceedings. All the changes made in this resubmission are listed in the next item: List of changes.

### List of changes

- In-text references using colors, i.e. "the blue terms", have been clarified in such a way that readers can understand without access to text colors. However, the explicit colors in the text are still kept, that is, some terms in some equations are still written in blue, as the author believes that it will provide a better illustration for those who can access them.
- Additional references have been added to better put results into context and to provide more resources for interested readers to study the subject further.