We investigate the processes , $\gamma J/\psi\omega\pi^0 J/\psi\eta$ to search for the charmnium-like states with hidden , such as , , and . These processes will receive contributions from the charmed-strange meson rescatterings. When the center-of-mass energies of the scatterings are taken around the , or threshold, the anomalous triangle singularities can be present in the rescattering amplitudes, which implies a non-resonance explanation about the resonance-like structures. The positions of the anomalous triangle singularities are sensitive to the kinematics, which offers us a criterion to distinguish the kinematic singularities from genuine particles.

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