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Inspired by the observation of the pentaquark states$P_{c}(4312),P_{c}(4440)$ and $P_{c}(4457)$ at LHCb, photoproduction of thesethree $P_{c}$ states via the interaction $\gamma p\rightarrow J/\psi p$ isinvestigated in an effective Lagrangian approach. The $t$-channel Pomeronexchange diffractive process is considered as the main background for the$J/\psi $ photoproduction. The numerical results show that the theoreticalcross section, which is calculated by assuming a branching ratio$Br[P_{c}\rightarrow J/\psi p]\simeq 3\%$, is consistent with the existingexperimental data of the $ \gamma p\rightarrow J/\psi p$ process. With such abranching ratio, if experimental precision reaches 0.1 nb within a bin of 100MeV for photon energy, two peaks are expected to be obviously observed in the$J/\psi $ photoproduction. To observe the two-peak structure from $P_{c}(4440)$and $ P_{c}(4457)$, higher precision, about 0.1nb/10 MeV, is required todistinguish two close pentaquarks. If the physical branching ratio is larger,the requirement of experimental precision will be reduced. The differentialcross sections for reaction $\gamma p\rightarrow J/\psi p$ are also present. Itis found that the $t$-channel Pomeron exchange provides a sharp increase atextreme forward angles and gives a sizable contribution at most energy points,while the contributions from the $s$-channel $P_{c}$ exchanges play importantroles at threshold energies. The experimental measurement of the $\gammap\rightarrow J/\psi p$ process in the near-threshold energy region around$E_{\gamma }\simeq 9.4-10.5$ GeV is suggested, and is accessible at CEBAF@JLaband COMPASS.

Possibility to study pentaquark states $P_{c}(4312), P_{c}(4440)$, and $P_{c}(4457)$ in $\gamma p\rightarrow J/\psi p$ reaction