Nuclear suppression of coherent $J/\psi$ photoproduction in heavy-ion UPCs and leading twist nuclear shadowing

We determine the nuclear suppression factor $S_{Pb}(x)$, where $x=M_{J/\psi}^2/W_{\gamma p}^2$ with $M_{J/\psi}$ the $J/\psi$ mass and $W_{\gamma p}$ the photon-nucleon energy, for the cross section of coherent $J/\psi$ photoproduction in heavy-ion ultraperipheral collisions (UPCs) at the Large Hadron Collider (LHC) and Relativistic Heavy Ion Collider (RHIC) by performing the $\chi^2$ fit to all available data on the cross section $d\sigma^{AA \to J/\psi AA}/dy$ as a function of the $J/\psi$ rapidity $y$ and the photoproduction cross section $\sigma^{\gamma A \to J/\psi A}(W_{\gamma p})$ as a function of $W_{\gamma p}$. We find that while the $d\sigma^{AA \to J/\psi AA}/dy$ data alone constrain $S_{Pb}(x)$ for $x \geq 10^{-3}$, the combined $d\sigma^{AA \to J/\psi AA}/dy$ and $\sigma^{\gamma A \to J/\psi A}(W_{\gamma p})$ data allow us to determine $S_{Pb}(x)$ in the wide interval $10^{-5} < x < 0.05$. In particular, the data favor $S_{Pb}(x)$, which decreases with a decrease of $x$ in the $10^{-4} < x < 0.01$ interval, and can be both decreasing or constant for $x< 10^{-4}$. Identifying $S_{Pb}(x)$ with the ratio of the gluon distributions in Pb and the proton $R_g(x,Q_0^2)=g_A(x,Q_0^2)/[A g_p(x,Q_0^2)]$, we demonstrate that the leading twist approximation (LTA) for nuclear shadowing provides a good description of all the data on $d\sigma^{AA \to J/\psi AA}/dy$ and $\sigma^{\gamma A \to J/\psi A}(W_{\gamma p})$ as well as on the experimental values for $S_{Pb}(x)$ derived from $\sigma^{\gamma A \to J/\psi A}(W_{\gamma p})$. We also show that modern nuclear PDFs reasonably reproduce $S_{Pb}(x)$ as well.