Gluon-induced quarkonium production in transverse-momentum-dependent factorisation: applications to the LHC and EIC

With the Large Hadron Collider (LHC) and the upcoming Electron-Ion Collider (EIC) high-energy experiments, we have the opportunity to investigate the fundamental structure of matter. In particular, probing the internal structure of the proton relies on parton distribution functions (PDFs), which describe the probability of finding a parton—either a quark or a gluon—within the proton as a function of its longitudinal momentum. These functions have been studied extensively over the past decades, so the next frontier involves exploring higher-dimensional distributions, such as transverse-momentum–dependent PDFs (TMDs). Although significant progress has been made in understanding quark TMDs, our knowledge of gluon TMDs remains limited. This thesis focuses on the extraction of gluon TMDs through quarkonium production at the LHC and EIC, as quarkonium predominantly originates from gluonic interactions.

We present theoretical predictions for transverse momentum spectra and azimuthal asymmetries of various processes using the TMD-evolution formalism, with a detailed analysis of its nonperturbative model parametrisation. Additionally, we investigate TMD shape functions, which account for smearing effects in quarkonium formation, that are crucial for the transition from a coloured intermediate state to a colourless bound state. From the phenomenological side, we predict measurable effects at the EIC that can probe not only TMDs but also TMD shape functions. Moreover, we take the first step towards constructing a complete transverse momentum spectrum for quarkonium production at the EIC. Furthermore, our predictions for quarkonium-pair production at the LHC show good agreement with recent normalised transverse momentum data.