Exclusive $J/\ddot{I}ˆ$ and $\hat{I}\yen$ photoproduction and the low $x$ gluon

Abstract

We study exclusive vector meson photoproduction, ${\hat{I}}^{3}p\to V+p$ with $V=J/\ddot{I}ˆ$ or $\hat{I}\yen$, 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 $\ln (1/\hat{I}¾)$ can be reabsorbed in the LO part by a choice of the factorisation scale. (In these exclusive processes $\hat{I}¾$ takes the role of Bjorken-$x$.) Then, the scale dependence coming from the remaining NLO contributions has no $\ln (1/\hat{I}¾)$ enhancements. As a result, we find that predictions for the amplitude of $\hat{I}\yen$ production are stable to within about $\pm 15\%$. This will allow data for the exclusive process $pp\to p\hat{I}\yen p$ 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 $J/\ddot{I}ˆ$ photoproduction indicates that the gluon density found in the recent global PDF analyses is too small at low $x$ and low scales.

21 pages, 6 figures. Text significantly improved, references added, version to be published in J.Phys.G