Effects of the temperature and magnetic-field dependent coupling on the properties of QCD matter

To reflect the asymptotic freedom in the thermal direction, a temperature-dependent coupling was proposed in the literature. We investigate its effect on QCD matter with and without strong magnetic fields. Compared with the fixed coupling constant, the running coupling leads to a drastic change in the dynamical quark mass, entropy density, sound velocity, and specific heat. The crossover transition of QCD matter at finite temperature is characterized by the pseudocritical temperature $T_{\mathrm{pc}}$, which is generally determined by the peak of the derivative of the quark condensate with respect to the temperature $d\varphi /dT$, or equivalently, by the derivative of the quark dynamical mass $dM/dT$. In a strong magnetic field, the temperature- and magnetic-field-dependent coupling $G(eB,T)$ was recently introduced to account for inverse magnetic catalysis. We propose an analytical relation between the two criteria $d\varphi /dT$ and $dM/dT$ and show a discrepancy between them in finding the pseudocritical temperature. The magnitude of the discrepancy depends on the behavior of $dG/dT$.

Figure 1

The dynamical mass of the quark versus temperature for the coupling constant $G_0$ and the running coupling $G^{\prime }(T)$. The critical temperature $T_0$ is 195 MeV.

Figure 2

The entropy density divided by $T^3$ as a function of the temperature for the couplings $G_0$ and $G^{\prime }(T)$.

Figure 3

Sound velocity and specific heat versus temperature. The two lines are coincident at $T_0$.

Figure 4

The reduced running coupling constant $G(eB,T)/G_0$ as a monotonous decreasing function of the temperature for several fixed magnetic fields.

Figure 5

The derivative of the coupling constant with respect to the temperature, which is multiplied by the vacuum quark condensate $|⟨\overline{\psi }\psi {⟩}_0|$ to give a dimensional quantity.

Figure 6

The pseudocritical temperature determined by the peaks of the derivatives $-dM/dT$ and $d\varphi /dT$ is shown.

Figure 7

The pseudocritical temperature determined by the peaks of the derivatives $-dM/dT$ and $d\varphi /dT$.