Abstract
The perturbative QCD expansion for $J/\psi$ photoproduction appears to be unstable: the NLO correction is large (and of opposite sign) to the LO contribution. Moreover, the predictions are very sensitive to the choice of factorization and renormalization scales. Here we show that perturbative stability is greatly improved by imposing a $`Q_0$ cut' on the NLO coefficient functions; a cut which is required to avoid double counting. $Q_0$ is the input scale used in the parton DGLAP evolution. This result opens the possibility of high precision exclusive $J/\psi$ data in the forward direction at the LHC being able to determine the low $x$ gluon distribution at low scales.
Highlights
It would be valuable to be able to constrain the gluon– parton distribution function (PDF) at low x using J/ψ photoproduction data measured at HERA and at the LHC, via exclusive pp → p + J/ψ + p events, especially events in the forward region measured by the LHCb collaboration
What do we mean by the ‘optimum’ scale? It was shown in Ref. [3] that it is possible to find a scale which resums all the double-logarithmic corrections enhanced by large values of ln(1/ξ ) into the gluon and quark PDFs, where ξ is the skewedness parameter of the generalised parton distributions (GPDs) describing the proton– gluon vertices
The stability achieved by imposing the Q0 cut means that J/ψ photoproduction (γ p → J/ψ p) data and LHC exclusive J/ψ data can be included in the global parton analyses
Summary
It would be valuable to be able to constrain the gluon– parton distribution function (PDF) at low x using J/ψ photoproduction data measured at HERA and at the LHC, via exclusive pp → p + J/ψ + p events, especially events in the forward region measured by the LHCb collaboration. [3] that it is possible to find a scale (namely μF = mc) which resums all the double-logarithmic corrections enhanced by large values of ln(1/ξ ) into the gluon and quark PDFs, where ξ is the skewedness parameter of the generalised parton distributions (GPDs) describing the proton– gluon (and proton–quark) vertices. The details are given in Ref. [3]; see Ref. [4]
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