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 plus PACIAE model was used to predict the exotic resonant state $Z_c^{\pm}(3900)$ yield, transverse momentum distribution, and the rapidity distribution with $|y| < 6$ and $p_T < 10$ GeV/c in $pp$ collisions at $\sqrt{s} = 1.96, 7$ and 13 TeV, respectively. The yield of the $Z_c^{\pm}(3900)$ is estimated to be around $10^{-6}$ to $10^{-5}$. We also present the energy dependence of the transverse momentum distributions and rapidity distributions for ${Z_c^{+}(3900)}$ and ${Z_c^{-}(3900)}$. The production of ${Z_c^{+}(3900)}$ and its anti-particle ${Z_c^{-}(3900)}$ is found to be quite similar to each other.