Orateur
Description
We perform the first complete one-loop study of exclusive photoproduction of vector quarkonia off a proton, including full generalised parton distribution (GPD) evolution. We confirm the perturbative instability of the cross section at high photon-proton-collision energies at Next-to-Leading Order (NLO) using a Collinear-Factorisation (CF) framework. This issue can be tackled by a scale-fixing criterion and a `$Q_0$-subtraction' procedure to avoid the over-subtraction of the collinear singularities. In this work, we instead resolve this problem by matching the CF calculation with the one performed using High-Energy Factorisation (HEF) in the Doubly-Logarithmic Approximation (DLA). Such a DLA is a subset of the Leading-Logarithmic Approximation (LLA) of HEF which resums higher-order QCD corrections proportional to $\alpha_s^n \ln^{n-1} (\hat{s}/M^2)$ in the Regge limit $\hat{s}\gg M^2$, with $M$ being the quarkonium mass. This is strictly consistent with the NLO DGLAP evolution of GPDs. We use two models for the GPDs entering the calculation: the first one is taken from the PARTONS framework, which includes a full GPD evolution. The second one corresponds to an approximation valid at high energies in terms of Parton Distributions Functions (PDFs) via the Shuvaev transform, in which only PDFs are evolved. We find that our approach alleviates the instability observed for the NLO calculation in the CF framework at high energies. We further compare our results for the two GPD models and assess the reliability of the Shuvaev transform as a means to probe the small $x$ gluon PDFs via the exclusive photoproduction of vector quarkonia.
