Transverse momentum dependent parton distributions at small x

@misc{caucal2026transverse,
  title = {{Transverse momentum dependent parton distributions at small $x$}},
  author = {Paul Caucal and Farid Salazar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26004},
  eprint = {2610.26004},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26004},
}

TY  - UNPB
TI  - Transverse momentum dependent parton distributions at small x
AU  - Paul Caucal
AU  - Farid Salazar
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26004
UR  - https://arxiv.org/abs/2610.26004
AB  - Transverse-momentum-dependent (TMD) parton distributions provide a three-dimensional description of the momentum structure of hadrons. They are probed in proton-proton and proton-nucleus collisions at the LHC and RHIC, and are a central part of the physics program of the future Electron-Ion Collider (EIC). While TMD factorization is well established at moderate Bjorken x, the small-x regime requires a different treatment, since large logarithms of 1/x must be resummed and non-linear effects due to high gluon densities become important. The Color Glass Condensate (CGC) effective theory provides a natural framework to describe TMDs in this saturation regime and to connect them with standard TMD factorization. This chapter reviews quark and gluon TMDs at small x, covering operator definitions, gauge-link structures, and Wilson-line correlators in the CGC for unpolarized and polarized distributions. We discuss factorization for inclusive and diffractive observables, highlighting the role of process dependence and the emergence of a limited set of Wilson-line operators. We then summarize the evolution of these distributions, namely the resummation of logarithms of 1/x by the Balitsky-Kovchegov and JIMWLK equations, and of Sudakov logarithms of the hard scale through Collins-Soper-Sterman evolution. We also review TMDs beyond the eikonal approximation, including the sub-eikonal Wilson-line operators that give access to helicity and other spin-dependent distributions, their double-logarithmic small-x evolution and the resulting asymptotics, and the sub-eikonal corrections to the eikonal distributions, which provide a first step toward the moderate-x regime. Finally, we discuss phenomenological implications for present and future experiments, with emphasis on the EIC, and outline the theoretical challenges toward a unified description of TMDs.
ER  -