Fluctuations of Temperature in the Polyakov-loop extended Nambu--Jona-Lasinio Model

TL;DR

The paper addresses how temperature fluctuations in hot QCD matter reflect the underlying phase structure by employing a three-flavor Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. It computes temperature fluctuation cumulants c_n from the thermodynamic potential via w = Omega + T s and forms dimensionless ratios R_{n2} = c_n / c_2^{n-1}, connecting these to entropy susceptibilities chi_n = T^{n-4} d^n p / dT^n. The results reveal non-monotonic behavior of R_{n2} across the chiral crossover, first-order transition, and deconfinement region, with strong oscillations near the critical endpoint and distinct peak/dip structures at low mu_B tied to deconfinement. These findings provide a quantitative framework linking temperature fluctuations to QCD phase transitions and offer experimental signatures in heavy-ion collisions through event-by-event mean p_T fluctuations, guiding future BES analyses and model refinements.

Abstract

We investigate temperature fluctuations in hot QCD matter using a 3-flavor Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The high-order cumulant ratios $R_{n2}$ ($n>2$) exhibit non-monotonic variations across the chiral phase transition, characterized by slight fluctuations in the chiral crossover region and significant oscillations around the critical point. In contrast, distinct peak and dip structures are observed in the cumulant ratios at low baryon chemical potential. These structures gradually weaken and eventually vanish at high chemical potential as they compete with the sharpening of the chiral phase transition, particularly near the critical point and the first-order phase transition. Our results indicate that these non-monotonic peak and dip structures in high-order cumulant ratios are associated with the deconfinement phase transition. This study quantitatively analyzes temperature fluctuation behavior across different phase transition regions, and the findings are expected to be observed and validated in heavy-ion collision experiments through measurements of event-by-event mean transverse momentum fluctuations.

Figures (5)

• Figure 1: (color online) QCD phase diagram in the $\mu_B$-$T$ plane based on the three-flavor PNJL model. The black dashed and solid lines represent the chiral crossover and the first-order phase transition line, respectively. The red dot denotes the critical endpoint (CEP) and the shaded region enclosed by the black dash-dotted lines represents the spinodal unstable region. The red short-dashed line indicates the deconfinement transition line and the different isentropic lines with $s/\rho_B = 5, 10, 20, 50, 100$ are also labeled in the plot.
• Figure 2: (color online) Contour maps of the entropy susceptibilities $\chi_n$ in the $\mu_B$-$T$ plane calculated within the three-flavor PNJL model. Here, $\chi_1$ and $\chi_2$ correspond to the dimensionless entropy and heat capacity, respectively. $\chi_3$ and $\chi_4$ represent the skewness and kurtosis of entropy fluctuations, while $\chi_5$ and $\chi_6$ characterize higher-order fluctuation of the entropy distribution.
• Figure 3: (color online) Entropy susceptibilities $\chi_n$ ($n=1$ to $6$) as functions of the temperature at baryon chemical potential $\mu_B$ = 0, 100, 200, 300, 900, and 950 MeV.
• Figure 4: (color online) Contour maps of the dimensionless cumulant ratios of temperature fluctuations $R_{32}=c_3/c_2^2$, $R_{42}=c_4/c_2^3$, $R_{52}=c_5/c_2^4$, $R_{62}=c_6/c_2^5$, in the $\mu_B$-$T$ plane based on the three-flavor PNJL model.
• Figure 5: (color online) Dimensionless cumulant ratios $R_{n2}$ ($n=3$ to $6$) of temperature fluctuations as functions of the temperature for several values of the baryon chemical potential. Insets provide a close-up view of the crossover region in the temperature range of $180-240$ MeV.