Bulk viscosity of quark matter across the QCD phase transitions

TL;DR

This work computes the bulk viscosity $\zeta$ and its dimensionless ratios $\zeta/s$ and $\zeta/\\eta$ for quark matter across the QCD phase diagram by combining relativistic kinetic theory in the relaxation-time approximation with in-medium masses from a 2+1 flavor PNJL model. The authors derive $\zeta$ from a kinetic integral that uses quasiparticle energies $E_i=\sqrt{p^2+M_i^2}$, with relaxation times $\tau_i$ set by averaged $2\to2$ quark scatterings and cross sections informed by the PNJL spectrum, including Polyakov-loop effects in the distributions. They find $\zeta/s$ and $\zeta/\\eta$ are suppressed at high $T$, but get enhanced near the chiral crossover and Mott lines, and reveal an additional, sizable peak beyond the chiral phase boundary driven by strange-quark dynamics; along isentropes and near the CEP the behavior becomes particularly sensitive to thermodynamic and phase-structure changes. These results provide qualitative guidance for hydrodynamic simulations of heavy-ion collisions, especially BES-II, while highlighting model dependence and the need for dynamical critical scaling and hadronic degrees of freedom for a more complete description.

Abstract

Based on the kinetic theory with relaxation time approximation, we investigate the bulk viscosity ($ζ$) and its ratio to shear viscosity ($ζ/η$) of quark matter at finite temperature and chemical potential with the in-medium particle masses derived in the 2+1 flavor Polyakov-loop improved Nambu--Jona-Lasinio (PNJL) model. We explore the behaviors of specific bulk viscosity ($ζ/s$) and $ζ/η$ across different QCD phase transitions, including the Mott phase transition, the chiral crossover, and the first-order transition with the associated metastable phase. The calculation shows that both $ζ/s$ and $ζ/η$ are extremely small at high temperatures, approaching the nature of a conformal theory. Larger $ζ/s$ and $ζ/η$ are derived near the chiral phase transition at finite temperature. Along the chiral crossover line, $ζ/s$ and $ζ/η$ generally increase with decreasing temperature, though $ζ/η$ exhibits a slight decline near the critical endpoint (CEP). On the boundary of the first-order transition, $ζ/s$ shows a non-monotonic variation with temperature. Furthermore, an additional peak structure emerges beyond the chiral phase boundary for both $ζ/s$ and $ζ/η$, with magnitudes even exceeding those near the chiral crossover of $u, d$ quarks. Our analysis indicates this peak originates from the chiral crossover transformation of strange quark.

Figures (7)

• Figure 1: $\zeta/s$ as a function of temperature $T$ for baryon chemical potentials $\mu_{B} = 0$, 400, 800, 873, 1200, 1350 $\mathrm{MeV}$. The solid and hollow triangles represent the $\zeta/s$ at the points where these $\mu_B(T)$ lines intersect the chiral crossover line and pion Mott transition line, respectively.
• Figure 2: $\zeta/s$ as a function of $\mu_{B}$ for different temperatures. The solid and hollow triangles represent the $\zeta/s$ at the points where these $T(\mu_B)$ lines intersect the chiral crossover line and pion Mott transition line, respectively. For $T=50, 75, 100\,$MeV, the two dots (cycles) on each isotherm correspond to respectively the high-density chirally restored phase and low-density chirally broken phase on the boundaries (spinodal line) of the first-order phase transition, and the dashed curves mark the metastable phases, including the high-density superheated phase and low-density supercooled phase.
• Figure 3: $\zeta/s$ on the chiral phase boundaries.
• Figure 4: $\zeta/s$ along the isentropic trajectories for different $s/n_B$. The solid triangles, hollow triangles and dots represent the $\eta/s$ at the points where these isentropic lines intersect the chiral crossover line, pion Mott transition line, the high-density boundary of the first-order transition, respectively.
• Figure 5: $\zeta/\eta$ as a function of temperature $T$ for $\mu_{B} = 0$, 400, 800, 873, 1200, 1350 $\mathrm{MeV}$. The star, solid triangles and hollow triangles represent the $\zeta/s$ at the points where these $\mu_B(T)$ lines intersect the CEP, chiral crossover line and pion Mott transition line, respectively.