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We present the first measurement at the LHC of exclusive J/$\psi$photoproduction off protons, in ultra-peripheral proton-lead collisions at$\sqrt{s_{\rm NN}}=5.02$ TeV. Events are selected with a dimuon pair producedeither in the rapidity interval, in the laboratory frame, $2.5<y<4$ (p-Pb) or$-3.6<y<-2.6$ (Pb--p), and no other particles observed in the ALICE acceptance.The measured cross sections $\sigma (\gamma + {\rm p} \rightarrow J/\psi + {\rmp})$ are 33.2 $\pm$ 2.2 (stat) $\pm$ 3.1 (syst) $\pm$ 0.7 (theo) nb in p-Pb and284 $\pm$ 36 (stat) $^{+27}_{-32}$ (syst) $\pm$ 26 (theo) nb in Pb-pcollisions. We measure this process up to about 700 GeV in the $\gamma {\rm p}$centre-of-mass, which is a factor of two larger than the highest energy studiedat HERA. The data are consistent with a power law dependence of the $J/\psi$photoproduction cross section in $\gamma {\rm p}$ energies from about 20 to 700GeV, or equivalently, from Bjorken-$x$ between $\sim 2\times 10^{-2}$ to $\sim2\times 10^{-5}$, thus indicating no significant change in the gluon densitybehaviour of the proton between HERA and LHC energies.

Exclusive J/$\psi$ photoproduction off protons in ultra-peripheral p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV