Baryon effects on the location of QCD’s critical end point

The location of the critical end point of QCD has been determined in previous studies of $N_f=2+1$ and $N_f=2+1+1$ dynamical quark flavors using a (truncated) set of Dyson-Schwinger equations for the quark and gluon propagators of Landau-gauge QCD. A source for systematic errors in these calculations has been the omission of terms in the quark-gluon interaction that can be parametrized in terms of baryonic degrees of freedom. These have a potentially large dependence on chemical potential and therefore may affect the location of the critical end point. In this exploratory study we estimate the effects of these contributions, both in the vacuum and at finite temperature and chemical potential. We find only a small influence of baryonic contributions on the location of the critical end point. We estimate the robustness of this result by parameterizing further dependencies on chemical potential.

Figure 1

The DSE for the quark propagator (top panel) and the truncated gluon DSE for $N_f=2$ QCD (bottom panel). Large blobs denote dressed propagators and vertices, and the hatched circle represents the quenched (lattice) propagator.

Figure 2

The full, untruncated Schwinger-Dyson equation for the quark-gluon vertex [34] is shown diagrammatically in the first equation. The second equation describes the first terms of an expansion in terms of hadronic and nonhadronic contributions to the quark-antiquark scattering kernel. In both equations, all internal propagators are fully dressed. Internal dashed lines with arrows correspond to ghost propagators, curly lines to gluons and full lines to quark propagators. In the second equation, the dotted line describes mesons and the triple line baryons.

Figure 3

DSE for the quark propagator, where the quark-gluon vertex is separated into nonbaryon and baryon contributions.

Figure 4

Baryonic diagram in the quark DSE with the quark-diquark approximation of the baryon’s Faddeev amplitude.

Figure 5

Quark DSE with diquark and baryon loop. In these loops the right vertices (circles) are Bethe-Salpeter amplitudes whereas the left vertices (hatched circles) are effective ones summing all effects from the diagrams in Fig. 4. In the main text we give arguments why these vertices are well approximated by bare ones.

Figure 6

The Bethe-Salpeter equation for the baryon in the quark-diquark approximation.

Figure 7

Left: quark mass function with and without diquark and baryon loops included. Right: regularized and normalized condensate as a function of temperature with and without diquark and baryon loops. In addition, we display the result with rescaled strength in the quark-gluon interaction; see main text for details.

Figure 8

Comparison of the phase diagram for $N_f=2$ including different types of self-energy contributions.