Evolution of the transverse-momentum dependent gluon distribution at small x

Using the color dipole picture for photon-nucleus interactions at small x together with the color glass condensate (CGC) effective theory, we demonstrate that the next-to-leading (NLO) order corrections to the cross section for the inclusive production of a pair of hard jets encode not only the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (JIMWLK) evolution with decreasing x, but also the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution of the gluon distribution function and the Collins-Soper-Sterman (CSS) evolution of the gluon transverse momentum dependent (TMD) distribution. The emergent CSS equation takes the form of a rate equation describing the evolution of the dijet distribution in the transverse momentum imbalance K⊥ when increasing the dijet relative momentum P⊥. All three types of evolution become important when both P⊥ and K⊥ are much larger than the nuclear saturation momentum Qs(x) and we propose a framework which encompasses all of them. The solution to the JIMWLK equation provides the source term for the DGLAP evolution with increasing K⊥, which in turn generates the initial condition for the CSS evolution with increasing P⊥. Published by the American Physical Society 2025