Quark number fluctuations at finite temperature and finite chemical potential via the Dyson-Schwinger equation approach

We investigate the quark number fluctuations up to the fourth order in the matter composed of two light flavor quarks with isospin symmetry and at finite temperature and finite chemical potential using the Dyson-Schwinger equation approach of QCD. In order to solve the quark gap equation, we approximate the dressed quark-gluon vertex with the bare one and adopt both the Maris-Tandy model and the infrared constant (Qin-Chang) model for the dressed gluon propagator. Our results indicate that the second, third, and fourth order fluctuations of net quark number all diverge at the critical endpoint (CEP). Around the CEP, the second order fluctuation possesses obvious pump while the third and fourth order ones exhibit distinct wiggles between positive and negative. For the Maris-Tandy model and the Qin-Chang model, we give the pseudocritical temperature at zero quark chemical potential as $T_c=146\mathrm{MeV}$ and 150 MeV, and locate the CEP at $({\mu }_E^q,T_E)=(120,124)\mathrm{MeV}$ and (124,129) MeV, respectively. In addition, our results manifest that the fluctuations are insensitive to the details of the model, but the location of the CEP shifts to low chemical potential and high temperature as the confinement length scale increases.

Figure 1

The second and fourth order fluctuations in the MT model with ${\omega }^{\mathrm{MT}}=0.4\mathrm{GeV}$ and the QC model with ${\omega }^{\mathrm{QC}}=0.5\mathrm{GeV}$. The lattice QCD results (taken from Refs. [22, 23, 30] and denoted by data points with error bars) are also displayed for comparison.

Figure 2

The temperature dependence of the ratio of the second to fourth order fluctuations in the MT model with ${\omega }^{\mathrm{MT}}=0.4\mathrm{GeV}$ and the QC model with ${\omega }^{\mathrm{QC}}=0.5\mathrm{GeV}$. For comparison, the lattice QCD results (taken from Ref. [22]) are denoted by data points.

Figure 3

The variation behaviors of the second order fluctuation with respect to temperature at several values of the quark chemical potentials (upper panels) and those with respect to quark chemical potential at several values of the temperature (lower panels). For the two cases, the left panel shows the result in the MT model with ${\omega }^{\mathrm{MT}}=0.4\mathrm{GeV}$, and the right panel in the QC model with ${\omega }^{\mathrm{QC}}=0.5\mathrm{GeV}$.

Figure 4

The variation behaviors of the third (upper panels) and fourth (lower panels) order fluctuations against quark chemical potential at several temperatures. The left panels show the results in the MT model with ${\omega }^{\mathrm{MT}}=0.4\mathrm{GeV}$, and the right panels in the QC model with ${\omega }^{\mathrm{QC}}=0.5\mathrm{GeV}$.

Figure 5

The quark chemical potential dependence of the ratio of the third to second order fluctuations at several temperatures (upper panels) and that of the fourth to second order fluctuations (lower panels). The left panels show the results in the MT model with ${\omega }^{\mathrm{MT}}=0.4\mathrm{GeV}$, and the right panels in the QC model with ${\omega }^{\mathrm{QC}}=0.5\mathrm{GeV}$.

Figure 6

The QCD phase diagram obtained with the fluctuation criterion. The lower curves stand for the result in the MT model with ${\omega }^{\mathrm{MT}}=0.4\mathrm{GeV}$, and the upper curves in the QC model with ${\omega }^{\mathrm{QC}}=0.5\mathrm{GeV}$.