In the present work, we investigate the production of $P_{c}$ and $Z_c(3900)/Z_{cs}(3985)$ states in the processes of $pi p rightarrow Z_{c}(3900) P_{c} $/$Kprightarrow Z_{cs}(3985) P_{c}$ with an effective Lagrangian approach. Our estimations indicates that the cross sections depends on the model parameters and beam energies, in particular, the cross sections for $pi p to Z_c(3900) P_c(4312)$ and $pi p to Z_c(3900) P_c(4440)$ are similar and can reach up to 10 nb, while those for $pi p to Z_c(3900) P_c(4457)$ can be 30 nb. As for $Kp to Z_{cs}(3985)P_c$, the cross sections are about 2.5 times smaller than those for $pi p to Z_c(3900) P_c$. The discussed processes in the present work, especially $pi p to Z_c(3900) P_c(4457)$, may be accessible by the the high-energy pion and kaon beams in the facilities of J-PARC and COMPASS.
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