This internship proposal is part of the ANR project “TMD-SAT”, which aims to investigate the partonic structure of hadrons at high energies within Quantum Chromodynamics. It is intended as a preparation for a fully funded PhD within the Theory Group of the Subatech laboratory in Nantes. Despite the great success of QCD in describing a wide variety of hadronic phenomena, including results from current experiments at the Large Hadron Collider (LHC), many fundamental questions remain. For instance, it is still not fully understood how quarks and gluons (collectively referred to as “partons”) are distributed inside hadrons in such a way that the resulting bound state has a definite mass and spin, especially in the regime where the partons carry a very small fraction of the bound state longitudinal momentum. In this regime, first-principles QCD calculations predict a rapid growth in the gluon density of the target, which is eventually tamed by non-linear recombination effects. One of the central goals of current and future collider experiments is to characterize this gluon saturation phenomenon by measuring suitable cross-sections and comparing them with precise QCD predictions. The objective of the internship will be to analytically compute one such cross-section: very-forward photon-jet production in proton–nucleus collisions at the LHC, at leading order and possibly next-to-leading order in the strong coupling, within the high-gluon-density regime of the hadronic target.