Critical Endpoint of QCD and Baryon Number Fluctuations in a Finite Volume

We summarize recent results on the volume dependence of the location of the critical endpoint in the QCD phase diagram. To this end, we employ a sophisticated combination of Lattice Yang--Mills theory and a (truncated) version of Dyson--Schwinger equations in Landau gauge for $2 + 1$ quark flavours. We study this system at small and intermediate volumes and 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 also discuss recent results on baryon number fluctuations in this setup.Comment: 5 pages, 2 figures; contribution to the proceedings of the FAIR next generation scientists workshop (FAIRNESS), 7th edition, 23-27 May 2022, Paralia (Pieria, Greece

QCD's equation of state from Dyson-Schwinger equations

In this contribution, we summarize a truncation-independent method to compute the equation of state within nonperturbative functional approaches. After demonstrating its viability, the method is applied to solutions obtained from a set of truncated Dyson-Schwinger equations for the quark and gluon propagators of (2+1)-flavor QCD to obtain thermodynamic quantities across the phase diagram of strong-interaction matter.Comment: 6 pages, 2 figures; contribution to the proceedings of the FAIR next generation scientists workshop (FAIRNESS), 7th edition, 23-27 May 2022, Paralia (Pieria), Greec

Finite-volume effects in baryon number fluctuations around the QCD critical endpoint

We present results for the volume dependence of baryon number fluctuations in the vicinity of the (conjectured) critical endpoint of QCD. They are extracted from the nonperturbative quark propagator that is obtained as a solution to a set of truncated Dyson-Schwinger equations of (2+1)-flavor QCD in Landau gauge, which takes the backcoupling of quarks onto the Yang-Mills sector explicitly into account. This well-studied system predicts a critical endpoint at moderate temperatures and rather large chemical potential. We investigate this system at small and intermediate finite, three-dimensional, cubic volumes and study the resulting impact on baryon number fluctuations and ratios thereof up to fourth order around the critical endpoint. We find that the fluctuations are visibly affected by the finite volume, particularly for antiperiodic boundary conditions, whereas their ratios are practically invariant.Comment: 7 pages, 5 figure

Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations

We present results for fluctuations of the baryon number for QCD at nonzero temperature and chemical potential. These are extracted from solutions to a coupled set of truncated Dyson-Schwinger equations for the quark and gluon propagators of Landau-gauge QCD with Nf=2+1 quark flavors, that has been studied previously. We discuss the changes of fluctuations and ratios thereof up to fourth order for several temperatures and baryon chemical potential up to and beyond the critical endpoint. In the context of preliminary STAR data for the skewness and kurtosis ratios, the results are compatible with the scenario of a critical endpoint at large chemical potential and slightly offset from the freeze-out line. We also discuss the caveats involved in this comparison

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

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 (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

Quarks and light (pseudo-)scalar mesons at finite chemical potential

We investigate the properties of light scalar and pseudoscalar mesons at finite (light) quark chemical potential. To this end we solve a coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagators in Landau-gauge QCD and extend earlier results for $N_{\mathrm{f}} = 2+1$ dynamical quark flavors to finite chemical potential at zero temperature. We then determine the meson bound state masses, wave functions, and decay constants for chemical potentials below the first-order phase transition from their homogeneous Bethe-Salpeter equation. We study the changes in the quark dressing functions and Bethe-Salpeter wave functions with chemical potential. In particular, we trace charge-conjugation parity breaking. Furthermore, we confirm the validity of the Silver-Blaze property: all dependencies of colored quantities on chemical potential cancel out in observables and we observe constant masses and decay constants up to and into the coexistence region of the first-order chiral phase transition