Color path-integral Monte-Carlo simulations of quark-gluon plasma: Thermodynamic and transport properties

Based on the quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for the calculation of thermodynamic properties and—closely related to the latter—a Wigner dynamics method for calculation of transport properties of the QGP are formulated. The QGP partition function is presented in the form of a color path integral with a new relativistic measure instead of the Gaussian one traditionally used in the Feynman-Wiener path integral. A procedure of sampling color variables according to the SU(3) group Haar measure is developed for integration over the color variable. It is shown that the PIMC method is able to reproduce the lattice QCD equation of state at zero baryon chemical potential at realistic model parameters (i.e., quasiparticle masses and coupling constant) and also yields valuable insight into the internal structure of the QGP. Our results indicate that the QGP reveals quantum liquidlike(rather than gaslike) properties up to the highest considered temperature of 525 MeV. The pair distribution functions clearly reflect the existence of gluon-gluon bound states, i.e., glueballs, at temperatures just above the phase transition, while mesonlike $q\overline{q}$ bound states are not found. The calculated self-diffusion coefficient agrees well with some estimates of the heavy-quark diffusion constant available from recent lattice data and also with an analysis of heavy-quark quenching in experiments on ultrarelativistic heavy-ion collisions, however, appreciably exceeds other estimates. The lattice and heavy-quark-quenching results on the heavy-quark diffusion are still rather diverse. The obtained results for the shear viscosity are in the range of those deduced from an analysis of the experimental elliptic flow in ultrarelativistic heavy-ions collisions, i.e., in terms the viscosity-to-entropy ratio, $1/4\pi \lesssim \eta /S<2.5/4\pi$, in the temperature range from 170 to 440 MeV.

Figure 1

Input data for the PIMC simulations. (a) Running coupling constant versus temperature fitted to experimental data [58, 59] (solid line). Points present the coupling deduced from lattice QCD simulations in Refs. [60] [lattice (Bielefeld 2012)] and [61] [lattice (Banerjee et al. 2012)]. (b) Mass-to-temperature ratio for quark and gluon quasiparticles versus temperature. Points are values used in simulations. The solid lines are smooth interpolations between points.

Figure 2

Pressure (a), entropy (b), and trace anomaly (c) scaled with corresponding powers of temperature versus temperature from PIMC simulations (open squares). These are compared with lattice data of Refs. [4, 5] (solid circles). The solid line in the panel (a) is a smooth interpolation between the PIMC points. Entropy and trace anomaly are calculated based on this smooth interpolation. The shaded area in the panel (a) indicates uncertainties of the PIMC calculations.

Figure 3

Quark degeneracy parameter ${\chi }_u$ and the plasma coupling parameter $\Gamma$ [see Eq. (71)] versus temperature. Lines are smooth interpolations between points.

Figure 4

Pair correlation functions of identical (a), (c) and different (b), (d) quasiparticles at temperatures $T=525\text{MeV}$ (a), (b) and $T=193\text{MeV}$ (c), (d).

Figure 5

Gluon-gluon and quark-antiquark pair correlation functions multiplied by $R^2$ at $T=193\text{MeV}$.

Figure 6

Velocity autocorrelation function (a) and temperature-scaled self-diffusion function $TD\left(t\right)$ (b) versus time for two temperatures.

Figure 7

Temperature-scaled stress-energy-tensor autocorrelation function (a) and shear-viscosity function $\eta \left(t\right)/T^3$ (b) versus time for two temperatures.

Figure 8

(a) The self-diffusion constant [self-diffusion, Wigner dynamics] as a function of temperature, compared with heavy-quark diffusion constants predicted by QCD lattice computations [76] [$c$-quark, lattice (Ding et al. 2011)] and [61] [$c$-quark, lattice (Banerjee et al. 2012)] and deduced from analysis of experimental data [74] [$c$-quark, “exp.” (Gossiaux et al. 2012)] and [75] [$c$-quark, “exp.” (He at al. 2012)]. (b) The ratio of shear viscosity to entropy density as a function of temperature [shaded area marked “Wigner dynamics”]. Horizontal dashed lines indicate the range of constraint on the viscosity-to-entropy ratio deduced from numerous hydrodynamical simulations of heavy-ion experimental data, as summarized in Ref. [72].