$$P_{c}(4312)$$, $$P_{c}(4440)$$, and $$P_{c}(4457)$$ productions in $$e^{+} e^{-}$$ collisions

Abstract In the present work, we propose to investigate the productions of $$P_{c}(4312)$$ P c ( 4312 ) , $$P_{c}(4440)$$ P c ( 4440 ) , and $$P_{c}(4457)$$ P c ( 4457 ) in the $$e^{+} e^{-} \rightarrow p \bar{p} J/\psi $$ e + e - → p p ¯ J / ψ process by utilizing an effective Lagrangian approach, where $$P_{c}(4312)$$ P c ( 4312 ) is considered as $$\Sigma _{c} \bar{D}$$ Σ c D ¯ molecular state with $$J^{P}=1/2^{-}$$ J P = 1 / 2 - , while $$P_{c}(4440)$$ P c ( 4440 ) and $$P_{c}(4457)$$ P c ( 4457 ) are considered as $$\Sigma _{c} \bar{D}^{*}$$ Σ c D ¯ ∗