Exclusive $J/\psi$ and $\Upsilon$ photoproduction and the low $x$ gluon

We study exclusive vector meson photoproduction, $\gamma p \to V + p$ with $V=J/\psi$ or $\Upsilon$, at NLO in collinear factorisation, in order to examine what may be learnt about the gluon distribution at very low $x$. We examine the factorisation scale dependence of the predictions. We argue that, using knowledge of the NLO corrections, terms enhanced by a large $\ln(1/\xi)$ can be reabsorbed in the LO part by a choice of the factorisation scale. (In these exclusive processes $\xi$ takes the role of Bjorken-$x$.) Then, the scale dependence coming from the remaining NLO contributions has no $\ln(1/\xi)$ enhancements. As a result, we find that predictions for the amplitude of $\Upsilon$ production are stable to within about $\pm 15\%$. This will allow data for the exclusive process $p p \to p\Upsilon p$ at the LHC, particularly from LHCb, to be included in global parton analyses to constrain the gluon PDF down to $x\sim 10^{-5}$. Moreover, the study of exclusive $J/\psi$ photoproduction indicates that the gluon density found in the recent global PDF analyses is too small at low $x$ and low scales.