Thermodynamics of the quark-gluon plasma within a $T$-matrix approach

The strongly coupled phase of the quark-gluon plasma (QGP) is studied here by resorting to a $T$-matrix formulation in which the medium is seen as a nonideal gas of quasiparticles (quarks, antiquarks, and gluons) interacting nonpertubatively. In the temperature range under study, (1–5)$T_c$, where $T_c$ is the temperature of deconfinement, the interactions are expected to be strong enough to generate bound states. The dissociation temperature of such binary bound states is thus computed here. The more the quasiparticles involved in the binary system are heavy, the more the bound state is likely to survive significantly above $T_c$. Then the QGP equations of state at zero and small baryonic potential are computed for $N_f=2$ and $N_f=2+1$ by resorting to the Dashen, Ma, and Bernstein formulation of statistical mechanics. Comparisons with current lattice QCD data are presented.

Figure 1

Normalized pure-gauge pressure $p/p_{\text{SB}}$ and trace anomaly $\mathrm{\Delta }/p_{\text{SB}}$ (without bound states) versus temperature in units of $T_c$ (with $T_c=0.15$ and 0.3 GeV).

Figure 2

(Left) Normalized pure-gauge pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$ (with $T_c=0.15$ GeV), compared to the free-part contribution. (Right) Normalized pure-gauge trace anomaly $\mathrm{\Delta }/p_{\text{SB}}$ versus temperature in units of $T_c$ (with $T_c=0.15$ GeV), compared to the free-part contribution.

Figure 3

(Left) Normalized pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$, compared to the free part, bound state, and scattering contribution. (Right) Different scattering contributions to the normalized pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$. $T_c=0.15$ GeV.

Figure 4

Normalized trace anomaly $\mathrm{\Delta }/p_{\text{SB}}$ (without bound states) versus temperature in units of $T_c$, compared to the free-part contribution. $T_c=0.15$ GeV.

Figure 5

(Left) Normalized pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$, compared to lQCD data from Ref. [30]. (Right) Normalized trace anomaly $\mathrm{\Delta }/p_{\text{SB}}$ versus temperature in units of $T_c$, compared to lQCD data from Ref. [30]. $T_c=0.15$ GeV.

Figure 6

(Left) Normalized pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$. (Right) Normalized trace anomaly $\mathrm{\Delta }/p_{\text{SB}}$ (without bound states) versus temperature in units of $T_c$. In the two figures, the gray (black) line is the free-part contribution of ${\mathrm{\Omega }}_{\left(2\right)}^{\text{QCD}}$ computed with the free (internal) energy. $T_c=0.15$ GeV.

Figure 7

(Left) Normalized pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$. (Right) Normalized trace anomaly $\mathrm{\Delta }/p_{\text{SB}}$ (without bound states) versus temperature in units of $T_c$. $T_c=0.15$ GeV for QGP and $T_c=0.3$ GeV for YM.

Figure 8

Real part of the $T$ matrix ($q\overline{q}$ in $L=0$, here given as example) in function of the energy for $T=0.105$ GeV (left), $T=0.150$ GeV (middle), and $T=0.300$ GeV (right) at different $\mu$ (MeV) with $T_c=0.15$ GeV.

Figure 9

(Left) Normalized pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$ at different $\mu$ (MeV) for a QGP with two light quarks. (Right) Normalized trace anomaly $\mathrm{\Delta }/p_{\text{SB}}$ (without bound states) versus temperature in units of $T_c$ at different $\mu$ (MeV) for a QGP with two light quarks. $T_c=0.15$ GeV.

Figure 10

(Left) Free quark gas contribution to the total normalized pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$ at different $\mu$ (MeV) for a QGP with two light quarks. (Right) Free antiquark gas contribution to the total normalized pressure $p/p_{\text{SB}}$ versus temperature in units of $T_c$ at different $\mu$ (MeV) for a QGP with two light quarks. $T_c=0.15$ GeV.

Figure 11

(Left, top) $qq$-scattering contribution to the total normalized pressure $p/p_{\text{SB}}$. (Right, top) Same for $\overline{q}\overline{q}$. (Left, middle) Same for $qg$. (Right, middle) Same for $\overline{q}g$. (Bottom) Same for $q\overline{q}$. All the scattering contributions are presented versus temperature in units of $T_c$, with $T_c=0.15$ GeV, at different $\mu$ (MeV) for a QGP with two light quarks.

Figure 12

(Left) Normalized pressure $p/p_{\text{SB}}$ compared to lQCD [33] versus temperature in units of $T_c$ at different ${\mu }_B$ (MeV) for a QGP with $N_f=2+1$. (Right) Normalized trace anomaly $\mathrm{\Delta }/p_{\text{SB}}$ compared to lQCD [33] versus temperature in units of $T_c$ at different ${\mu }_B$ (MeV) for a QGP with $N_f=2+1$. $T_c=0.15$ GeV.