Production mechanism of the hidden charm pentaquark states $P_{c\bar{c}}$

We investigate hidden-charm pentaquark states using an off-shell coupled-channel formalism involving heavy meson and singly heavy baryon scattering. Our approach utilizes an effective Lagrangian to construct the kernel amplitudes, which respect both heavy quark symmetry and hidden local symmetry. After solving the coupled integral equations, we obtain the transition amplitudes for $J/\psi N$ scattering and various heavy meson and singly heavy baryon scattering processes. We identify seven distinct peaks related to molecular states of heavy mesons $\bar{D}$ ($\bar{D}^*$) and singly heavy baryons $\Sigma_c$ ($\Sigma_c^*$). Four of these peaks can be associated with the known $P_{c\bar{c}}$ states: $P_{c\bar{c}}(4312)$, $P_{c\bar{c}}(4380)$, $P_{c\bar{c}}(4440)$, and $P_{c\bar{c}}(4457)$. We predict two additional resonances with masses around 4.5 GeV, which we interpret as $\overline{D}^* \Sigma_c^*$ molecular states, and identify one cusp structure. Additionally, we predict two $P$-wave pentaquark states with positive parity, which may be candidates for genuine pentaquark configurations. Notably, these pentaquark states undergo significant modifications in the $J/\psi N$ elastic channel, with some even disappearing due to interference from the positive parity channel. The present investigation may provide insight into the absence of pentaquark states in $J/\psi$ photoproduction observed by the GlueX collaboration.