How to include exclusive $J/\psi$ production data in global PDF analyses

We compare the cross section for exclusive J/ψ photoproduction calculated at next-to-leading order (NLO) in the collinear factorization approach with HERA and LHCb data. Using the optimum scale formalism together with the subtraction of the low kt contribution (below the input scale Q0) from the NLO coefficient function to avoid double counting, we show that the existing global parton distribution functions (PDFs) are consistent with the data within their uncertainties. This is the first time that J/ψ production data at HERA were successfully described within the NLO collinear factorization framework using the PDFs of the global parton analyses. However, at lower x the uncertainties of the present global PDFs are large. On the other hand, the accuracy of the LHCb data are rather good. Therefore, these data provide the possibility to directly measure the gluon PDF over the very large interval of x, 10-6<x<10-2, at a fixed low scale.We compare the cross section for exclusive $J/\psi$ photoproduction calculated at NLO in the collinear factorization approach with HERA and LHCb data. Using the optimum scale formalism together with the subtraction of the low $k_t<Q_0$ contribution from the NLO coefficient function to avoid double counting we show that the existing global parton distribution functions (PDFs) are consistent with the data within their uncertainties. However, at low $x$ the uncertainties of the present global PDFs are large. On the other hand, the accuracy of the LHCb data are rather good. Therefore, these data provide the possibility to directly measure the gluon PDF over the very large interval of $x$, $10^{-6}<x