Towards clarifying the possibility of observation of the LHCb hidden-charm pentaquarks $P_{c}^+(4312)$, $P_{c}^+(4337)$, $P_{c}^+(4440)$ and $P_{c}^+(4457)$ in near-threshold charmonium photoproduction off protons and nuclei

We study the near-threshold $J/\psi$ meson photoproduction from protons and nuclei by considering incoherent direct non-resonant (${\gamma}p \to {J/\psi}p$, ${\gamma}n \to {J/\psi}n$) and two-step resonant (${\gamma}p \to P_{ci}^+ \to {J/\psi}p$, ${\gamma}n \to P_{ci}^0 \to {J/\psi}n$, $i=1$, 2, 3, 4; $P_{c1}^{+,0}=P_c^{+,0}(4312)$, $P_{c2}^{+,0}=P_c^{+,0}(4337)$, $P_{c3}^{+,0}=P_c^{+,0}(4440)$, $P_{c4}^{+,0}=P_c^{+,0}(4457)$) charmonium production processes. We calculate the absolute excitation functions, energy and momentum distributions for the non-resonant, resonant and for the combined (non-resonant plus resonant) production of $J/\psi$ mesons on protons as well as, using the nuclear spectral function approach, on carbon and tungsten target nuclei at near-threshold incident photon energies by assuming the spin-parity assignments of the hidden-charm resonances $P_{c}^{+,0}(4312)$, $P_{c}^{+,0}(4337)$, $P_{c}^{+,0}(4440)$ and $P_{c}^{+,0}(4457)$ as $J^P=(1/2)^-$, $J^P=(1/2)^-$, $J^P=(1/2)^-$ and $J^P=(3/2)^-$ within three different realistic scenarios for the branching ratios of their decays to the ${J/\psi}p$ and ${J/\psi}n$ modes (0.25, 0.5 and 1%). We show that will be very hard to measure the $P_{ci}^+$ pentaquark states through the scan of the $J/\psi$ total photoproduction cross section on a proton target in the near-threshold energy region around the resonant photon energies of 9.44, 9.554, 10.04 and 10.12 GeV if these branching ratios $\sim$ 1% and less. We also demonstrate that at these photon beam energies the $J/\psi$ energy and momentum combined distributions considered reveal distinct sensitivity to the above scenarios, respectively, at "low" $J/\psi$ total energies and momenta, which implies that they may be an important tool to provide further evidence for the existence of the pentaquark $P_{ci}^+$ and $P_{ci}^0$ resonances.