The study of exotic state $$Z_c^{\pm }(3900)$$ decaying to $$J/\psi \pi ^{\pm }$$ in the pp collisions at $$\sqrt{s}$$ = 1.96, 7, and 13 TeV

A dynamically constrained phase-space coalescence model and PACIAE model are used to predict the exotic resonant state $$Z_c^{\pm }(3900)$$ yield in pp collisions at $$\sqrt{s} = 1.96, 7$$ and 13 TeV, respectively, which are estimated to be around $$10^{-6}$$ to $$10^{-5}$$ based on the $$J/\psi \pi ^{\pm }$$ bound state in the decay chain of b hadrons. The energy dependence of the transverse momentum distributions and rapidity distributions with $$|y|<6$$ and $$p_{T}<10$$ GeV/c are also calculated for $${Z_c^{+}(3900)}$$ and $${Z_c^{-}(3900)}$$ . The production of $${Z_c^{+}(3900)}$$ and its anti-particle $${Z_c^{-}(3900)}$$ are found to be quite similar to each other.