Gluon shadowing at small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>x</mml:mi></mml:math> from coherent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mi>J</mml:mi><mml:mo>/</mml:mo></mml:mrow><mml:mi>ψ</mml:mi></mml:mrow></mml:math> photoproduction data at energies available at the CERN Large Hadron Collider

The cross section for coherent $J/\ensuremath{\psi}$ photoproduction in Pb-Pb collisions is the sum of two contributions: one from low-energy and the other from high-energy photon-nucleus interactions. A novel method to disentangle the two contributions, allowing one to extract the coherent photo-nuclear cross section for coherent $J/\ensuremath{\psi}$ production, ${\ensuremath{\sigma}}_{\ensuremath{\gamma}\mathrm{Pb}}$, is presented. The utility of the method is demonstrated using measurements from peripheral and ultraperipheral Pb-Pb collisions at the CERN Large Hadron Collider. Applying the proposed method to the available data, it is possible to obtain ${\ensuremath{\sigma}}_{\ensuremath{\gamma}\mathrm{Pb}}$ up to a photon-lead center-of-mass energy of 470 GeV, which corresponds to $x$ of $4.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. To illustrate a possible use of the extracted photonuclear cross sections, the corresponding nuclear suppression factors are computed and they are compared to predictions of gluon shadowing calculated in the leading-twist approximation approach.