Inclusive photoproduction of vector quarkonium in ultra-peripheral collisions at the LHC.

We explore the possibility of using ultra-periphe- ral proton-lead collisions at the LHC to study inclusive vector-quarkonium photoproduction, that occurs when a quasi-real photon emitted by a fully stripped lead ion breaks a proton to produce a vector quarkonium. Owing to the extremely large energies of the colliding hadrons circulating in the LHC, the range of accessible photon-nucleon centre-of-mass energies, , largely exceeds what has been and will be studied at lepton-hadron colliders, HERA and the EIC. We perform a tune to HERA photoproduction data, use this tune to predict the yields of photoproduced , and estimate the corresponding transverse-momentum reach at LHC experiments. We also model the hadroproduction background and demonstrate that inclusive photoproduction can be isolated at the LHC from such background by imposing constraints on the hadronic activity in the lead-going direction at mid, forward, or far-forward rapidities depending on the capability of the detector under consideration. We find that the resulting cross sections are large enough to be measured by ALICE, ATLAS, CMS, and LHCb. We estimate the background-to-signal ratio after isolation to be of the order of 0.001 and 0.1 in the low and large transverse-momentum regions, respectively. In addition, we propose and assess the Jacquet-Blondel method to reconstruct the photon-nucleon centre-of-mass energy and the fractional energy of the quarkonium with respect to the photon.