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We calculate large mass diphoton exclusive photoproduction in the framework of collinear QCD factorization at next to leading order in {\alpha}s and at leading twist. Collinear divergences of the coefficient function are absorbed by the evolution of the generalized parton distributions (GPDs). This result enlarges the existing factorization proofs to 2 -> 3 processes, opening new reactions to a trustable extraction of GPDs., Comment: Submission to SciPost Proceedings

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.

The Bessel operator, that is, the Schr\"odinger operator on the half-line with a potential proportional to $1/x^2$, is analyzed in the momentum representation. Many features of this analysis are parallel to the approach \`a la K. Wilson to Quantum Field Theory: one needs to impose a cutoff, add counterterms, study the renormalization group flow with its fixed points and limit cycles.