Possibility to study the pentaquark states $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ in the reaction $\gamma p\to J/\psi p$

Inspired by the observation of the pentaquark states $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ at LHCb, photoproduction of these three $P_c$ states via the interaction $\gamma p\to J/\psi p$ is investigated in an effective Lagrangian approach. The $t$-channel Pomeron exchange diffractive process is considered as the main background for the $J/\psi$ photoproduction. The numerical results show that the theoretical cross section, which is calculated by assuming a branching ratio $\mathrm{Br}[P_c\to J/\psi p]\simeq 3\%$, is consistent with the existing experimental data of the $\gamma p\to J/\psi p$ process. With such a branching ratio, if experimental precision reaches 0.1 nb within a bin of 100 MeV 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 $0.1\mathrm{nb}/10\mathrm{MeV}$, is required to distinguish two close pentaquarks. If the physical branching ratio is larger, the requirement of experimental precision will be reduced. The differential cross sections for reaction $\gamma p\to J/\psi p$ are also present. It is found that the $t$-channel Pomeron exchange provides a sharp increase at extreme forward angles and gives a sizable contribution at most energy points, while the contributions from the $s$-channel $P_c$ exchanges play important roles at threshold energies. The experimental measurement of the $\gamma p\to J/\psi p$ process in the near-threshold energy region around $E_{\gamma }\simeq 9.4–10.5\mathrm{GeV}$ is suggested and is accessible at CEBAF@JLab and COMPASS.

Figure 1

Feynman diagrams for the reaction $\gamma p\to J/\psi p$.

Figure 2

Total cross section for the reaction $\gamma p\to J/\psi p$ by assuming branching ratio $\mathrm{Br}[P_c\to J/\psi p]\simeq 3\%$. The black dashed, orange dotted, green dot-dashed, blue dash-double dotted, and violet solid lines are for the Pomeron exchange, $P_c(4312),P_c(4440),P_c(4457)$, and total contributions, respectively. The experimental data are from Refs. [25, 26, 27].

Figure 3

Same as Fig. 2 except that the energy range is reduced.

Figure 4

Same as Fig. 2 except assuming a branching ratio $\mathrm{Br}[P_c\to J/\psi p]\simeq 10\%$.

Figure 5

The differential cross section $d\sigma /d\cos \theta$ of the $\gamma p\to J/\psi p$ process as a function of $\cos \theta$ at beam energies $E_{\gamma }=9.0$, 9.4, 10.0, 10.1, and 10.5 GeV. The coupling constants are extracted by assuming branching ratio $\mathrm{Br}[P_c\to J/\psi p]\simeq 3\%$. The black dashed, orange dotted, green dot-dashed, blue dash-double dotted, and violet solid lines are for the Pomeron exchange, $P_c(4312),P_c(4440),P_c(4457)$, and total contributions, respectively.

Figure 6

Same as Fig. 4 except by assuming branching ratio $\mathrm{Br}[P_c\to J/\psi p]\simeq 10\%$.

Figure 7

The photon beam asymmetries ${\mathrm{\Sigma }}_{\gamma }$ for the reaction $\gamma p\to J/\psi p$ of $E_{\gamma }=9.0–10.5\mathrm{GeV}$. The violet solid curves represent the total results including the $P_c$ states, whereas the black dashed lines only show the result of Pomeron exchange.