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 sss̄s̄ 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 Λ-Λ̄ or Σ-Σ̄, or by three mesons of π⁺π⁻η', K⁺K⁻η', or KS⁰KS⁰η' 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.