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  • Open Access

Small-x asymptotics of the leading-twist flavor-singlet quark TMDs

Daniel Adamiak*

M. Gabriel Santiago†

Yossathorn Tawabutr‡

  • Jefferson Lab, Newport News, Virginia 23606, USA and Department of Physics, Michigan State University, East Lansing, Michigan 48824, USA

  • Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA; Department of Physics, Old Dominion University, Norfolk, Virginia 23606, USA;Jefferson Lab, Newport News, Virginia 23606, USA; and Center for Nuclear Femtography, SURA, 1201 New York Avenue NW, Washington, DC 20005, USA

  • *Contact author: adamiak1@msu.edu
  • †Contact author: melvin.santiago@temple.edu
  • ‡Contact author: yossathorn.t@chula.ac.th
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Phys. Rev. D 113, 014023 – Published 22 January, 2026

DOI: https://doi.org/10.1103/fyld-m5g1

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.

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Phys. Rev. D 113, 014023– Published 22 January, 2026
  • Received 17 February 2025
  • Accepted 30 October 2025
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