Confirming the glueball-like particle $X(2370)$ productions in $e^+e^-$ collisions at BESIII energy with PACIAE model

The parton and hadron cascade model {\footnotesize PACIAE} is employed to confirm the BESIII newest observation of glueball-like particle $\rm X(2370)$ production in $e^+e^-$ collisions at $\sqrt{s}=4.95\,\mathrm{GeV}$. We coalesce the $\rm X(2370)$ glueball state with two gluons in the simulated partonic final state by the Dynamically Constrained Phase-space Coalescence ({\footnotesize DCPC}) model. Alternative configuration of $\rm X(2370)$ molecular state is recombined in the simulated hadronic final state with $\pi^{+},\pi^{-},K^{+}, K^{-},K_{S}^{0},K_{S}^{0}$ and $\eta'$ by {\footnotesize DCPC} model. The resulted particle transverse momentum spectrum and rapidity distribution, etc. show a significant discrepancy between the two states. They are not only serving as criteria to distinguish the $\rm X(2370)$ glueball state or molecular state, but also confirming the BESIII observation of glueball-like particle $\rm X(2370)$ productions in $e^+e^-$ collisions.