Kinetic freeze-out conditions for the production of resonances, hadronic molecules, and light nuclei

We investigate the freeze-out conditions of a particle in an expanding system of interacting particles in order to understand the productions of resonances, hadronic molecules, and light nuclei in heavy-ion collisions. Applying the kinetic freeze-out condition with explicit hydrodynamic calculations for the expanding hadronic phase to the daughter particles of $K^{*}$ mesons, we find that the larger suppression of the yield ratio of $K^{*}/K$ at the Large Hadron Collider (LHC) than at the Relativisitic Heavy Ion Collider (RHIC) compared to the expectations from the statistical hadronization model based on chemical freeze-out parameters reflects the lower kinetic freeze-out temperature at LHC than at RHIC. Furthermore, we point out that for the light nuclei or hadronic molecules that are bound, the freeze-out condition should be applied to the respective particle in the hadronic matter. It is then shown through the rate equation that when the nucleon and pion numbers are kept constant at the chemical freeze-out value during the hadronic phase, the deuteron number quickly approaches an asymptotic value that is close to the statistical model prediction at the chemical freeze-out point. We argue that the reduction seen in $K^{*}$ numbers is a typical result for a particle that has a large natural decay width decaying into daughter particles, while that for deuteron is typical for a stable hadronic bound state.

Figure 1

Variations of the ${\tau }_{\mathrm{scatt}}^{\pi }$ and the expansion time of the system, ${\tau }_{\exp }=V/(dV/dt)$ at RHIC and LHC both in time (a) and temperature (b) during the hadronic stage.

Figure 2

Deuteron abundances as functions of an expansion time in the hadronic phase.