Phase structure of three and four flavor QCD

We investigate the phase structure of QCD at finite temperature and light-quark chemical potential. We improve upon earlier results for $N_f=2+1$ dynamical quark flavors and investigate the effects of charm quarks in an extension to $N_f=2+1+1$. We determine the quark condensate and the Polyakov loop potential using solutions of a coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagators of Landau gauge QCD. At zero chemical potential we find excellent agreement with results from lattice-QCD. With input fixed from physical observables we find only a very small influence of the charm quark on the resulting phase diagram at finite chemical potential. We discuss the location of the emerging critical end point and compare with expectations from lattice gauge theory.

Figure 1

The DSE for a background field ${\overline{A}}_0$.

Figure 2

The DSE for the quark propagator. Large blobs denote dressed propagators and vertices.

Figure 3

The truncated gluon DSE for $N_f=2+1+1$ QCD. The yellow dot denotes the quenched (lattice) propagator.

Figure 4

The vacuum quark mass function $M(p^2)=B(p^2)/A(p^2)$ for light, strange and charm quarks in parameter set $B_{2+1+1}$.

Figure 5

Comparison of gluon dressing functions for $N_f=2$ in our DSE approach [12] with lattice data [30]. All results have been evaluated at a pion mass of $m_{\pi }=316\mathrm{MeV}$.

Figure 6

Gluon dressing functions for $N_f=2+1$ and physical quark masses (set $A_{2+1}$) at three different temperatures.

Figure 7

Left: Longitudinal gluon dressing function for $N_f=2+1$ and $N_f=2+1+1$ physical quark masses (sets $B_{2+1}$, $B_{2+1+1}$) at $T\approx 135\mathrm{MeV}$. Right: Corresponding gluon screening mass as a function of temperature.

Figure 8

Left diagram: regularized chiral condensate and the Polyakov loop for $N_f=2+1$ quark flavors (set $A_{2+1}$) as a function of temperature at zero quark chemical potential ${\mu }_q=0$. Right diagram: phase diagram for $N_f=2+1$ quark flavors. Shown are our results for set $A_{2+1}$ together with an extrapolation of a range of curvatures for the chiral transition extracted at imaginary and small chemical potential from different lattice groups [9, 32, 33].

Figure 9

Phase diagram for QCD with $N_f=2+1$ and $N_f=2+1+1$ flavors (sets $B_{2+1}$ and $B_{2+1+1}$). In both cases, the interaction strength and quark masses are fixed to reproduce vacuum physics.