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