“…More recently, the ultraperipheral pA and AA collisions (UPCs) at the LHC have provided clean experimental means for probing the real photoproduction mechanisms of heavy quarkonia in photon-Pomeron fusion with intact colliding nucleons or nuclei, thanks to low QCD backgrounds. Over the past few years, a wealth of phenomenological information on elastic (exclusive) and quasielastic J=ψ ≡ ψð1SÞ and ψ 0 ≡ ψð2SÞ photoproduction in UPCs has become available from the LHC measurements, in particular, from LHCb [12][13][14], ALICE [15][16][17][18][19], and CMS [20,21] experiments. Meanwhile, the existing theoretical approaches remain rather uncertain due to poorly known nonperturbative and a D-wave admixture in the corresponding S-wave quarkonia wave functions [22][23][24], as well as the coherence phenomena particularly relevant for photoproduction in AA UPCs [1,[25][26][27].…”