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

Journal Article · 13 July 2022 · SciPost Physics Proceedings

DOI: https://doi.org/10.21468/SciPostPhysProc.8.103 · OSTI ID:1875925

Tawabutr, Yossathorn ^[1]

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1. The Ohio State University

The small- x $x$ quark helicity evolution equations at double-logarithmic order, with the kernel \sim\alpha_s\ln^2(1/x) $\sim {\alpha }_s{ln}^2\left(1/x\right)$ , have been derived previously. In this work, we derive the single-logarithmic corrections to the equations, to order \alpha_s\ln(1/x) ${\alpha }_{s}ln\left(1/x\right)$ 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0004286
• OSTI ID: 1875925
• Journal Information: SciPost Physics Proceedings, Journal Name: SciPost Physics Proceedings Journal Issue: 8; ISSN 2666-4003
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English