Gluon saturation at hadronic colliders: a modern review

The non-abelian character of QCD manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. The latter property allows for the use of perturbation theory and has led to the successful description of a plethora of experiments across different high-energy colliders. The majority of these theoretical predictions rely on the collinear factorization framework, where partonic matrix elements are obtained in perturbation theory and are convoluted with universal parton distribution functions (PDFs) that obey the DGLAP renormalization group equation.

At high energies, perturbation theory must be supplemented with the resummation of large logarithms resulting in the growth and dominance of gluon densities at small-x. If left uncontrolled, this growth can result in the violation of unitarity bounds. The resolution to this issue lies in the non-abelian character of QCD, where gluon emissions are balanced by gluon recombination at high energies resulting in the phenomena of gluon saturation.

High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behaviour of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena in both small and large colliding systems. We will give a review of an ensemble of modern experimental results at medium and high energy colliders pertinent to gluon saturation physics. We will also motivate the need of high energy electron-proton/ion colliders such as the the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge  in the small x kinematic domain.