Authors: Hassan Ali Khan, Hadiqa Qadir
Abstract: Understanding the late-stage evolution of the fireball created in relativistic heavy-ion collisions is essential for constraining the transport properties and the equation of state of the strongly interacting matter. In this study, we extract the kinetic freeze-out temperature, Tkin, from the transverse momentum spectra of identified hadrons produced in Au–Au collisions across the RHIC Beam Energy Scan, spanning √sNN = 7.7 to 200 GeV. Our analysis builds upon effective temperatures obtained in our previous work, from which we isolate the kinetic decoupling temperature by applying a linear fit, Teff = m m0 + Tkin, to the particle mass dependence of the effective temperatures. We present two independent sets of fitting results, which show consistent qualitative behaviors and provide robust estimates of the freeze-out parameters. Our extracted values of Tkin reveal two clear and systematic trends. For any fixed collision energy, the freeze-out temperature decreases monotonically as we move from central to peripheral collisions, reflecting the diminishing system size, lower energy density, and reduced rescattering in the later stages of the fireball evolution. For a fixed centrality bin, the temperature rises with increasing beam energy, but the rise is not uniform: a steep increase at low energies is followed by a plateau around 19.6–39 GeV, which then gives way to a renewed rise at the highest RHIC energies. This non-monotonic behaviour is interpreted as evidence for a change in the underlying degrees of freedom, consistent with the system transitioning from a baryon-rich hadronic phase through a possible crossover region and into a parton-dominated phase at the highest energies. The results demonstrate that the kinetic freeze-out temperature is a sensitive probe of the system size, initial energy density, and the stiffness of the equation of state. Our findings provide important constraints for hydrodynamic models and highlight the utility of the Fokker–Planck approach in extracting freeze-out parameters from experimental data.
