Identifying an X(3872) tetraquark state versus a molecular state by formation time, velocity, and temperature in relativistic nuclear collisions

The production of exotic hadron $\mathrm{X}\left(3872\right)$ in $pp$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ is investigated by the parton and hadron cascade model PACIAE in this work. In the simulation the final partonic state (quark matter, QM) and the final hadronic state (hadron matter, HM) are continuously processed and recorded. The $\mathrm{X}\left(3872\right)$ compact tetraquark state and loose molecular state are, respectively, coalesced and recombined in the QM and HM with the quantum statistical mechanics inspired dynamically constrained phase-space coalescence model. The formation time, velocity, and temperature of QM (tetraquark state) and HM (molecular state) are proposed as identifying criteria between the two states. Our results in transverse momentum spectrum and rapidity distribution, etc. show a significant discrepancy between the two states and confirm that they are also valuable criteria identifying the $\mathrm{X}\left(3872\right)$ compact tetraquark state or molecular state.