  New, more precise data on diffractive J/psi photoproduction and on exclusive
J/psi production in the process pp -> p + J/psi + p at the LHC allow a better
constraint on the low-x gluon distribution in the domain of relatively low
scales Q^2 ~ 2-6 GeV^2. We account for the `skewed' effect and for the real
part of the amplitude, as well as for the absorptive corrections in the case of
the exclusive process pp -> p + J/psi + p. The predictions for exclusive J/psi
production at \sqrt{s}=8 and 14 TeV and for exclusive Upsilon(1S) production at
7, 8 and 14 TeV are also given. We present results at leading and
next-to-leading order.
