Insights into the Temperature Parameters from K*⁰ Spectrum in Nuclear Particle Collisions at the Relativistic High-Energy Collider Beam Energies

The blast-wave model with Boltzmann–Gibbs statistics is used to examine the transverse momentum spectra of ${K\ast }^0$ mesons generated at the Relativistic High-Energy Collider (RHIC) Beam Energies with mid-rapidity ($\left|y\right|<1$) in symmetric $Au-Au$ collisions. There is a clear correlation between the extracted kinetic freeze-out temperature ($T_0$) and transverse flow velocity (${\beta }_T$) in various collision centralities and center-of-mass energies ($\sqrt{s_{NN}}$). Since a larger initial energy density delays freeze-out and a shorter system lifetime limits cooling, $T_0$ is directly proportional to both $\sqrt{s_{NN}}$ and peripheral collisions. On the other hand, ${\beta }_T$ drops in peripheral symmetric collisions due to weaker collective expansion, while it rises with $\sqrt{s_{NN}}$ because of larger pressure gradients. The concurrence between the thermal and collective energy components in the expanding fireball is reflected in the obvious anti-correlation between $T_0$ and ${\beta }_T$. These findings support hydrodynamic predictions and offer important new information about QGP’s freeze-out behavior.