Title: 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) $\sim {\alpha }_s{ln}^2\left(1/x\right)$ , 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.

Authors:

Tawabutr, Yossathorn ^[1]

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+ Show Author Affiliations

1. The Ohio State University

Publication Date:

Wed Jul 13 00:00:00 EDT 2022

Sponsoring Org.:

USDOE

OSTI Identifier:

1875925

Grant/Contract Number:  

SC0004286

Resource Type:

Published Article

Journal Name:

SciPost Physics Proceedings

Additional Journal Information:

Journal Name: SciPost Physics Proceedings Journal Issue: 8; Journal ID: ISSN 2666-4003

Publisher:

Stichting SciPost

Country of Publication:

Netherlands

Language:

English