Path integral treatment of coherence effects in charmonium production in nuclear ultra-peripheral collisions

We present for the first time a revised study of charmonium production in nuclear ultra-peripheral collisions (UPC) based on a rigorous Green function formalism. This formalism allows for the proper incorporation of the effects of color transparency, as well as the quantum coherence inherent in the higher twist quark shadowing related to the $Q\bar{Q}$ Fock component of the photon. The significance of this effect gradually decreases towards forward and/or backward rapidities. In the LHC kinematic region we additionally incorporate within the same formalism the leading twist gluon shadowing corrections related to higher multi-gluon photon fluctuations. They represent a dominant source of nuclear phenomena in the mid-rapidity region. Model predictions for the rapidity distributions $d\sigma \mathrm{/}dy$ are in good agreement with available UPC data on coherent charmonium production at RHIC and the LHC. They can also be verified by future measurements at the LHC, as well as at EIC.