Exclusive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:mrow></mml:math> photoproduction in ultraperipheral Pb+Pb collisions at the CERN Large Hadron Collider calculated at next-to-leading order perturbative QCD

We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections coherent exclusive photoproduction $J/\ensuremath{\psi}$ mesons in heavy-ion ultraperipheral collisions (UPCs) at CERN Large Hadron Collider (LHC), $d\ensuremath{\sigma}/dy(\text{Pb}+\text{Pb}\ensuremath{\rightarrow}\text{Pb}+J/\ensuremath{\psi}+\text{Pb})$. For this, we account for photon-nucleon NLO forward limit, $t$ dependence using a standard nuclear form factor, and photon fluxes colliding nuclei. Approximating generalized parton distributions with their forward-limit distribution functions (PDFs), quantify contributions sections, show that real part amplitude quark-PDF must not be neglected, uncertainties arising from scale choice PDFs, compare our results ALICE, CMS, LHCb data $\mathrm{Pb}+\mathrm{Pb}$ UPCs, HERA, $p+p$. The $d\ensuremath{\sigma}/dy(\text{Pb}+\text{Pb}\ensuremath{\rightarrow}\text{Pb}+J/\ensuremath{\psi}+\text{Pb})$ is significant, but can find reproduces UPC both 2.76 5.02 TeV collision energies. This process has traditionally been suggested to direct probe gluon distributions. situation changes rather dramatically LO NLO: reflect effects gluons quarks complicated manner, where relative signs terms play significant role.