Temperature fluctuations in a realistic Polyakov-loop extended Nambu--Jona-Lasinio Model along the freeze-out line

Abstract

We extend and reparameterize the Polyakov--Nambu--Jona-Lasinio (PNJL) model to reproduce lattice simulation data at zero baryon chemical potential and to position its critical endpoint (CEP) within the BES-II experimental energy range. Using this realistic PNJL model, we investigate the behavior of the second-order temperature cumulant $C_2$ along the freeze-out line, aiming to understand the non-monotonic energy dependence of the two-particle transverse momentum correlation $C_{p_T}$ observed by the STAR Collaboration. Our results show a distinct dip structure in $C_2$ near the CEP and the first-order phase boundary on the phase diagram. Along the experimentally extracted freeze-out line, the dip minimum occurs around 7.7 GeV, and its trend is consistent with that observed by STAR, suggesting that the non-monotonic dependence of $C_{p_T}$ may be related to the CEP. Our results also indicate that cumulant ratios such as $C_3/C_2^2$ or $C_4/C_2^3$ eliminate the influence of initial volume fluctuations and may better reveal the underlying critical fluctuations. Further verification could be pursued through hydrodynamic or transport simulations that incorporate critical dynamics. These results and predictions might provide an a priori theoretical basis for future experimental measurements of higher-order event-mean transverse momentum fluctuations.