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

Inspired by the BESIII newest observation of X (2370) glueball-like particle, we search its productions in both e^+e^- collisions at s= 4. 95 GeV and proton-proton (pp) collisions at s= 13 TeV with a parton and hadron cascade model PACIAE. In this model, the final partonic state (FPS) and the final hadronic state (FHS) are consecutively simulated and recorded. The X (2370) glueball- or tetraquark-state is then, respectively, recombined by two gluons or four quarks ssss in the FPS using the quantum statistical mechanics inspired dynamically constrained phase-space coalescence (DCPC) model. The X (2370) molecular-state is recombined by the baryon-antibaryon of - or -, or by three mesons of ^+^-', K^+K^-', or KS⁰KS⁰' in the FHS using DCPC model. In both e^+e^- and pp collisions, significant discrepancies in the yields, the transverse momentum spectra and the rapidity distributions among the X (2370) glueball-, tetraquark-, and molecular-state are observed. These discrepancies are proposed as valuable criteria identifying the X (2370) different states from each other. Our results not only support the BESIII observation of glueball-like particle X (2370) production in e^+e^- collisions, but also serve as a prediction for the X (2370) production in pp collisions. We strongly suggest the experimental measurement of the X (2370) glueball-like particle production in pp collisions at the LHC energies.