Polyakov-loop suppression of colored states in a quark-meson-diquark plasma

A quark-meson-diquark plasma is considered within the Polyakov-loop extended Nambu–Jona-Lasinio model for dynamical chiral symmetry breaking and restoration in quark matter. Based on a generalized Beth-Uhlenbeck approach to mesons and diquarks we present the thermodynamics of this system including the Mott dissociation of mesons and diquarks at finite temperature. A striking result is the suppression of the diquark abundance below the chiral restoration temperature by the coupling to the Polyakov loop, because of their color degree of freedom. This is understood in close analogy to the suppression of quark distributions by the same mechanism. Mesons as color singlets are unaffected by the Polyakov-loop suppression. At temperatures above the chiral restoration mesons and diquarks are both suppressed due to the Mott effect, whereby the positive resonance contribution to the pressure is largely compensated by the negative scattering contribution in accordance with the Levinson theorem.

Figure 1

Mass spectrum of pions, sigma mesons and diquarks as functions of the temperature $T$. The diquark mass $m_D^{(B)}$ [$m_D^{(C)}$] corresponds to the case of strong (superstrong) diquark coupling. Also shown is the relevant threshold $2m$ for mesons and diquarks. Upper panel: Without Polyakov loop; lower panel: with Polyakov loop.

Figure 2

Diquark phase shift ${\delta }_D$ as a function of squared center of mass energy $s$ at different temperatures from $T=150$ to 400 MeV for the three cases of diquark coupling: (A) Fierz value $G_D/G_S=3/4$, (B) strong coupling $G_D/G_S=1.0$ and (C) superstrong coupling $G_D/G_S=1.5$. The jump of the phase shift from 0 to $\pi$ indicates the position of a bound state in the spectrum below the threshold of the continuum states which is situated where the phase shift starts decreasing towards zero. With increasing temperature the threshold moves to lower $s$-values and the phase shift jumps from $\pi$ to 0 when the Mott temperature is reached where the bound state gets dissociated. This behavior is in accordance with the Levinson theorem.

Figure 3

Contributions from the resonant (positive) and scattering continuum (negative) parts to the total pressure (thick lines) for diquarks and pions in the NJL model (upper panel) and in the PNJL model (middle panel) as a function of temperature. In the lower panel a direct comparison is made of the diquark pressure with its resonant and continuum contributions for the NJL and the PNJL model, respectively, which demonstrates the strong suppression of the diquark pressure due to the Polyakov-loop coupling in the confining phase at low temperatures. In this figure we have chosen the superstrong coupling case (C) for which the masses of pions and diquarks are degenerate.

Figure 4

Contributions to the diquark pressure in the NJL model (thin lines) compared to that of the PNJL model (thick lines) as a function of temperature: resonance (dotted lines), continuum (dashed lines) and total (solid lines) contributions for two cases of diquark coupling: strong [case (B), upper panels] and Fierz value [case (A), lower panels]. The right panels demonstrate the suppression of the diquark pressure due to the Polyakov-loop coupling by comparing the NJL with the PNJL model results. The diquark pressure contains contributions from both diquarks and antidiquarks.

Figure 5

Pressure of quark-gluon matter with meson and diquark correlations in the PNJL model as function of temperature (solid lines). Also shown are the partial pressures of quarks and gluons (dotted lines), diquarks (long-dash-dotted lines), sigma mesons (dash-dotted lines) and pions (dashed lines). The left panel shows the pressure contributions divided by $T^4$ (dimensionless) while in the right panel they are in units of $\mathrm{MeV}/{\mathrm{fm}}^3$.