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  • Open Access

Collinear structure of nonlinear small-x evolution

Renaud Boussarie*

Paul Caucal†

Yacine Mehtar-Tani‡

  • SUBATECH UMR 6457 (IMT Atlantique, Université de Nantes, IN2P3/CNRS), 4 rue Alfred Kastler, 44307 Nantes, France

  • *Contact author: renaud.boussarie@polytechnique.edu
  • †Contact author: caucal@subatech.in2p3.fr
  • ‡Contact author: mehtartani@bnl.gov
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Phys. Rev. D 114, 054029 – Published 15 September, 2026

DOI: https://doi.org/10.1103/p5jl-fyqc

Abstract

We introduce a novel approach to high-energy QCD factorization of cross sections for processes involving a dilute projectile and a dense target. Our method preserves the factorization between “fast” and “slow” modes in the longitudinal momentum k+ for a projectile moving along the positive light cone direction, making it compatible with higher-order loop computations done within the standard formulation of the color glass condensate (CGC) effective field theory. Moreover, it eliminates the anomalous double collinear logarithms that typically hinder the convergence of perturbation theory at small-x. Our scheme amounts to a change of basis in the space of CGC operators, introducing an arbitrary transverse scale dependence while leaving physical cross sections invariant. Implementing this scheme requires a modification of the high-energy renormalization group equation for the CGC operators, which we explicitly derive at next-to-leading order and in the nonlinear regime for the case of the dipole operator and the deep inelastic scattering impact factor. This general framework provides a consistent and systematic prescription for computing observables in the small-x regime of QCD, free from double logarithmic collinear instabilities.

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Physics Subject Headings (PhySH)

See Also

Rotating the Color Glass Condensate

Renaud Boussarie, Paul Caucal, Piotr Korcyl, and Yacine Mehtar-Tani
Phys. Rev. Lett. 137, 121903 (2026)

Article Text

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Phys. Rev. D 114, 054029– Published 15 September, 2026
  • Received 24 November 2025
  • Accepted 23 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International 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.

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