  Generalized Parton Distributions (GPDs) carry information on the internal
structure of hadrons such as the angular momentum of quarks and gluons, or
their spacelike distribution. They can be experimentally studied in exclusive
experiments with hadrons, i.e. processes in which all initial and final states
are measured. The tool that creates the necessary bridge between the
theoretical predictions and the experiments is the collinear factorization. It
allows disentangling perturbatively computable parts of the amplitude, which
describes interactions of quarks and gluons with the external particles, from
the non-perturbative quantities, which are identified as GPDs.
  In this work, I extend the theoretical analysis of the process
photoproduction of photon pairs on a proton to the next-to-leading order in
perturbative Quantum Chromodynamics within the framework of collinear
factorization. I give the proof that all collinear divergences which arise in
one-loop computations cancel at the level of the amplitude. This result
enlarges the family of reactions, which can be studied using the collinear
factorization by processes of the type $2 \rightarrow 3$, which have not been
previously studied within this theoretical framework beyond the leading QCD
order. Furthermore, I compute the full form of the amplitude of the discussed
process at the one-loop order. That improves the accuracy of theoretical
predictions for this experiment, which may be used for planning future
experiments in JLAB or EIC.
