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The possibility to study in-medium modification of $J/ψ$ mesons from their photoproduction on nuclei near threshold in the case of presence of the LHCb pentaquark states $P^+_c$ in this photoproduction

We study the $J/ψ$ photoproduction from nuclei in the near-threshold beam energy region of $E_γ$=5--11 GeV within the nuclear spectral function approach by considering incoherent direct ($γN \to {J/ψ}N$) and two-step ($γp \to P^+_c(4312)$, $P^+_c(4312) \to {J/ψ}p$; $γp \to P^+_c(4440)$, $P^+_c(4440) \to {J/ψ}p$; $γp \to P^+_c(4457)$, $P^+_c(4457) \to {J/ψ}p$) $J/ψ$ production processes. We calculate the absolute excitation functions for the non-resonant and resonant production of $J/ψ$ mesons off $^{12}$C and $^{208}$Pb target nuclei within the different scenarios for in-medium modification of the directly photoproduced $J/ψ$ mesons and for branching ratios of the decays $P^+_c(4312) \to {J/ψ}p$, $P^+_c(4440) \to {J/ψ}p$ and $P^+_c(4457) \to {J/ψ}p$. We show that the non-resonant subthreshold $J/ψ$ production in $γA$ reactions reveals some sensitivity to employed in-medium modification scenarios for $J/ψ$ mesons, which is not masked by the resonantly produced $J/ψ$ mesons, only if above branching ratios are less than 5\%. We also demonstrate that if these branching ratios more than 5\% then the presence of the $P^+_c(4312)$, $P^+_c(4440)$ and $P^+_c(4457)$ resonances in $J/ψ$ photoproduction on nuclei produces above threshold additional enhancements in the behavior of the total $J/ψ$ creation cross section on nuclei, which could be also studied in the future JLab experiments at the CEBAF facility to provide both further evidence for their existence and valuable information on their nature.