The Central Exclusive Production (CEP) process occurs when an object $X$ and nothing else is produced in a hadronic collision, while the hadrons themselves remain intact after the collision.
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The photoproduction of heavy vector mesons, see Fig.~\ref{fig:cep}, is one example of such a process which has possible implications for PDF determination.
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Thus for $pp$ collisions CEP can proceed in a situation where one proton elastically emits a photon, the other interacts via $t$--channel two gluon exchange.
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This may therefore access the gluon PDF at a comparatively low scale $Q^2\sim M_V^2$ and $x\sim M_V/\sqrt{s}$, where it is so far quite poorly determined.
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In this respect, the production kinematics are rather similar as those of
$D$ meson production described in the previous section.

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\begin{figure}[t]
  \begin{center}
 \includegraphics[width=0.36\textwidth]{3-datatheory/plots/cep}
  \end{center}
\caption{\small Photoproduction of heavy vector meson $J/\psi$~\cite{Jones:2013pga}.}\label{fig:cep}
\end{figure}
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LHCb has measured the exclusive production of $J/\psi$ and $\psi(2S)$ mesons at 7 TeV~\cite{Aaij:2014iea} and $\Upsilon$ production at $7$ and $8$ TeV~\cite{Aaij:2014iea}. Preliminary LHCb data on  $J/\psi$ and $\psi(2S)$ production at 13 TeV has also been reported in~\cite{LHCb:2016oce}. This uses the newly installed \texttt{HeRSCheL} shower counters, which greatly extend the rapidity coverage for vetoing additional particle production, reducing significantly the non--exclusive background.
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In addition, the ALICE experiment has measured exclusive $J/\psi$ production in p--Pb collisions at $\sqrt{s}_{NN}=5.02$ TeV~\cite{TheALICE:2014dwa}.
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Due to the large $Z^2$ enhancement for photon emission from the Pb ion, this is dominated by the process where the lead ion emits a photon.

While clearly the photoproduction process shown in Fig.~\ref{fig:cep} proceeds through an initial--state gluon interaction, this does not correspond to a standard inclusive process where collinear PDFs are generally introduced.
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However, as discussed in~\cite{Jones:2013pga} under certain assumptions this process can be related to the standard gluon PDF and may therefore serve as a probe of it at low $x$ and $Q^2$. This analysis has subsequently been performed at NLO~\cite{Jones:2015nna} (see also~\cite{Ivanov:2004vd}) for the cases of $J/\psi$ and $\Upsilon$ production.
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However, here it is found that the NLO correction is significantly larger than, and of the opposite sign to, the LO contribution, indicating a lack of perturbative stability and casting some doubt on the viability of this process as a PDF probe.

Nonetheless, work in the direction of at least partially solving this issue has been reported most recently in~\cite{Jones:2016ldq}, where the stability is shown to be improved through judicious choice of factorization and renormalization scale, and by imposing a cut on the NLO contribution to avoid double counting.
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It is also worth noting that the perturbative stability is naturally improved somewhat by considering the production of the higher mass $\Upsilon$ meson.
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Future studies will determine whether or not central exclusive production can
then be reliable added to the toolbox of global PDF analyses.
