Document Type

Article

Publication Date

2026

DOI

10.1103/fyld-m5g1

Publication Title

Physical Review D

Volume

113

Issue

1

Pages

014023

Abstract

In this paper, we investigate the small-𝑥 behavior of the flavor-singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) using the light-cone operator treatment. This formalism allows us to express TMD operators at small 𝑥 in terms of polarized dipole amplitudes, enabling a systematic approach to their small-𝑥 evolution. We derive the evolution equations for these TMDs and solve them within the large-𝑁𝑐 approximation under the linearized, double-logarithmic approximation, where 𝑁𝑐 represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-𝑥 asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-𝑥 asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding nonlinear effects and extending beyond the double-logarithmic approximation and large-𝑁𝑐 approximations.

Rights

© 2026 The Authors

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP³.

Data Availability

Article states: "No data were created or analyzed in this study."

Original Publication Citation

Adamiak, D., Santiago, M. G., & Tawabutr, Y. (2026). Small-x asymptotics of the leading-twist flavor-singlet quark TMDs. Physical Review D, 113(1), Article 014023. https://doi.org/10.1103/fyld-m5g1 

ORCID

0000-0003-0770-6279 (Santiago)

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