Thermodynamics of strong-interaction matter: On the phase structure and thermodynamics of quantum chromodynamics with Dyson–Schwinger equations

Abstract

In this work, which is topically divided into four parts, we study the phase structure and thermodynamics of strong-interaction matter. To this end, we employ a sophisticated, well-studied combination of results for pure Yang-Mills theory from lattice calculations and a truncated set of Dyson-Schwinger equations for the quark and gluon propagators of (2 + 1)-flavor quantum chromodynamics in Landau gauge. First, we solve this coupled set of Dyson-Schwinger equations for the fully nonperturbative quark and gluon propagators, where the backcoupling of quarks onto the gluon is explicitly taken into account. This system agrees at vanishing chemical potential quantitatively with results from lattice-regularized quantum chromodynamics regarding the temperature dependence of the order parameter for chiral symmetry breaking. Furthermore, at nonzero chemical potential, where lattice calculations are not reliable due to the sign problem, we find a critical endpoint at moderate temperatures and large chemical potential. All obtained results are in agreement with previous works. In addition, we compare our results with other recent phase-diagram calculations. Then, we present results for quark and baryon number fluctuations at nonzero temperature and chemical potential that are extracted from the quark propagator. We discuss the changes of these fluctuations and ratios thereof up to fourth order for several temperatures and chemical potentials up to the critical endpoint. In view of recent experimental data for the skewness and kurtosis ratios, our results are compatible with the scenario of a critical endpoint at large chemical potential and with a certain offset from the freeze-out line. Next, we discuss a method to compute thermodynamic quantities within the Dyson-Schwinger approach that is independent of the employed truncation. As a proof of principle, we first apply it to Nambu-Jona-Lasinio model and subsequently to our Dyson-Schwinger framework. As a result, we obtain the pressure, entropy density, energy density, and interaction measure across the phase diagram of quantum chromodynamics. Below and around the chiral transition temperature, we find a satisfactorily agreement with lattice results. The limitation of the method is discussed, too. Finally, the impact of a uniform, finite, three-dimensional volume on the phase structure of quantum chromodynamics is investigated. In particular, we determine the dependence of the location of the critical endpoint on the boundary conditions and the volume of a three-dimensional cube with edge length L. We find that noticeable volume effects appear for L < 5 fm, and volumes as large as L³ > (8 fm)³ are very close to infinite volume. Furthermore, we demonstrate that a proper treatment of finite-size artifacts is crucial for reliable statements about finite-volume effects.