Analyses of the collective properties of hadronic matter in Au-Au collisions at 54.4 GeV

Abstract: We investigated the strange hadrons transverse momentum ($p_T$) spectra in Au-Au collision at $\sqrt {s_{NN}}$ = 54.4 GeV in the framework of modified Hagedorn function with embedded flow. We extracted the kinetic freeze-out temperature $T_0$, transverse flow velocity $\beta_T$, kinetic freeze-out volume $V$, mean transverse momentum $<p_T>$, the entropy parameter $n$ and the multiplicity parameter $N_0$. We reported that all these parameters increase towards the central collisions. The larger kinetic freeze-out temperature , transverse flow velocity, kinetic freeze-out volume and the entropy parameter (n) in central collisions compared to peripheral collisions show the early decoupling of the particles in central collisions. In addition, all the above parameters are mass dependent. The kinetic freeze-out temperature ($T_0$), the entropy parameter $n$ and mean transverse momentum ($<p_T>$) are larger for massive particles, while the transverse flow velocity ($\beta_T$), kinetic freeze-out volume ($V$) and the multiplicity parameter ($N_0$) show the opposite behavior. Larger $T_0$, $n$ and smaller $\beta_T$ as well as $V$ of the heavier particles indicates the early freeze-out of the heavier particles, while larger $<p_T>$ for the heavier particles evince that the effect of radial flow is stronger in heavier particles. The separate set of parameters for each particle shows the multiple kinetic freeze-out scenario, where the mass dependent kinetic freeze-out volume shows the volume differential freeze-out scenario. We also checked the correlation among different parameters, which include the correlation of $T_0$ and $\beta_T$, $T_0$ and $V$, $\beta_T$ and $V$, $<p_T>$ and $T_0$, $<p_T>$ and $\beta_T$, $<p_T>$ and $V$, $n$ and $T_0$, $n$ and $\beta_T$, and $n$ and $V$, and they all are observed to have positive correlations with each other which validates our results.