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Understanding gluon density distributions and how they are modified in nucleiare among the most important goals in nuclear physics. In recent years,diffractive vector meson production measured in ultra-peripheral collisions(UPCs) at heavy-ion colliders has provided a new tool for probing the gluondensity. In this Letter, we report the first measurement of $J/\psi$photoproduction off the deuteron in UPCs at the center-of-mass energy$\sqrt{s_{_{\rm NN}}}=200~\rm GeV$ in d$+$Au collisions. The differential crosssection as a function of momentum transfer $-t$ is measured. In addition, datawith a neutron tagged in the deuteron-going Zero-Degree Calorimeter isinvestigated for the first time, which is found to be consistent with theexpectation of incoherent diffractive scattering at low momentum transfer.Theoretical predictions based on the Color Glass Condensate saturation modeland the gluon shadowing model are compared with the data quantitatively. Abetter agreement with the saturation model has been observed. With the currentmeasurement, the results are found to be directly sensitive to the gluondensity distribution of the deuteron and the deuteron breakup, which providesinsights into the nuclear gluonic structure.

Probing the gluonic structure of the deuteron with $J/\psi$ photoproduction in d+Au ultra-peripheral collisions