Vector-quarkonium production in photon-photon and photon-proton collisions up to one loop in QCD

The thesis focuses on one of the most studied particles at high-energy colliders, the quarkonium, which is a bound state of a heavy quark-antiquark pair. Part I starts with a review of the main features of QCD, the theory of the strong interaction and discusses the Non-Relativistic QCD (NRQCD) framework for the calculation of the quarkonium-production cross sections and decay widths, restricted to the leading Fock state of the quark-antiquark pair, as in the Colour-Singlet Model (CSM). We then present our methodology for the computation of the next-to-leading order (NLO) corrections in the strong coupling to vector quarkonium production. In particular, the main steps of the calculation methodology of virtual and real corrections are described. To perform such calculations, we have developed an algorithm based on the Catani-Seymour dipole subtraction and a numerically efficient implementation of the NLO cross section with the scaling-function formalism. Part II presents a selection of our results for quarkonium production at various experimental facilities such as the LHC, HERA, the CEPC, the FCC, the EIC and the CLIC. We have studied the production of the vector quarkonium states J/psi and Upsilon in the photoproduction limit of lepton-hadron collisions, where a quasi on-shell photon breaks a proton to produce the quarkonium with at least one recoiling hard parton. In particular, we show that the CSM can describe the HERA2 H1 data. For this study we have included a QED-induced contribution via an off-shell photon which was thought to be negligible but which becomes the leading contribution at the largest transverse momenta accessible with the EIC. Another novel ontribution we have considered is a J/psi and another charm quark associated production with the variable-flavour-number scheme. This process can be observed at the future EIC and can be used to probe the non-perturbative charm content of the proton at high momentum fractions. Furthermore, we have studied the origin of an unphysical behaviour of the photoproduction cross sections, which has been found to be related to an over-subtraction of collinear divergences in the parton distribution functions (PDFs). The scale-fixing method we have used solves this problem at NLO in the strong coupling, so we could provide a qualitative analysis of the possibility of constraining the PDFs using future J/psi and Upsilon (1S) photoproduction data. The cross sections we obtained show that the corresponding yields are expected to be measured at high energies with very good accuracy at the future EIC and other future facilities such as the LHeC or the FCC-eh. The lower energy measurements at AMBER-COMPASS++ and the EicC can be useful to probe the valence region. The second part also includes a review of our study which revisits the inclusive NLO calculation for the J/psi production via direct photon and single-resolved photon in photon fusion in electron-positron collisions. Our study includes all significant direct-photon contributions: the direct-photon production of J/psi and a photon, the associated production of J/psi and a charm quark-antiquark pair, and the production of J/psi along with three gluons. We have also considered the single-resolved-photon contributions up to NLO in the coupling constant. We have provided phenomenological predictions for the kinematics of the DELPHI, the future CEPC, the FCC-ee and the CLIC experiments, where all these CS contributions have been brought together for the first time.