Hadronic modes and quark properties in the quark-gluon plasma

Based on interaction potentials between a heavy quark and antiquark as extracted from recent QCD lattice calculations, we set up a Brueckner-type many-body scheme to study the properties of light (anti-) quarks in a quark-gluon plasma at moderate temperatures, $T\simeq$ 1–2 $T_c$. The quark-antiquark T matrix, including both color-singlet and color-octet channels, and corresponding quark self-energies and spectral functions are calculated self-consistently. The repulsive octet potential induces quasiparticle masses of up to 150 MeV, whereas the attractive color-singlet part generates resonance structures in the $q\text{−}\overline{q}$ T matrix, which in turn lead to quasiparticle widths of ~200 MeV. This corresponds to scattering rates of ~1 fm${}^{-1}$ and may reflect liquid-like properties of the system.

Figure 1

(Color online) Left panel: Lattice QCD results for the color-singlet free energy from unquenched simulations [27] for six different values of the temperature (symbols) compared to our fit function, Eq. (1), represented by the various curves. Right panel: Corresponding potential in the color-singlet channel obtained with Eq. (5) for the six different values of the temperature.

Figure 2

(Color online) Comparison of $Q\text{−}\overline{Q}$ color-singlet potentials as determined from various lattice data in our (MR) and other works (SZ [21], MP [18], and Wo [17]); the left (right) panel is for $T=1.5T_c$ $(2\hspace{1em}{T}_c)$.

Figure 3

Schematic representation of the self-consistency problem composed of the Bethe-Salpeter equation (7) in ladder approximation and the quark self-energy, Eq. (8). Thick lines represent full fermionic propagators. The four different blocks correspond to the T matrix (T), potential (V), self-energy (Σ) and, “gluon-induced” self-energy ($\tilde{\Sigma }$).

Figure 4

(Color online) Real part (full red line) and imaginary part (absolute value, dashed blue line) of T matrix in the color-singlet channel for charmonium (with a charm-quark mass of $m=1.8$ GeV) at $T\hspace{1em}=\hspace{1em}1.2\hspace{1em}{T}_c,T\hspace{1em}=\hspace{1em}1.5\hspace{1em}{T}_c$, and $T\hspace{1em}=\hspace{1em}2\hspace{1em}{T}_c$ (left, middle, and right panels, respectively) as a function of c.m. energy E, based on our potential parametrization extracted from unquenched lQCD.

Figure 5

(Color online) Real part (full red line) and imaginary part (absolute value, dashed blue line) of T matrix in the color-singlet channel for charmonium (with a charm-quark mass of $m=1.8$ GeV) at $T\hspace{1em}=\hspace{1em}1.2\hspace{1em}{T}_c,T\hspace{1em}=\hspace{1em}1.5\hspace{1em}{T}_c,\hspace{1em}\mathrm{and}\hspace{1em}T\hspace{1em}=\hspace{1em}2\hspace{1em}{T}_c$ (left, middle, and right panels, respectively) as a function of c.m. energy E, based on a potential [17] extracted from quenched lQCD.

Figure 6

(Color online) Real part (full red line) and imaginary part (absolute value, dashed blue line) of the light-quark (on-shell) T matrix in the color-singlet channel at temperatures $T\hspace{1em}=\hspace{1em}1.2\hspace{1em}{T}_c,T\hspace{1em}=\hspace{1em}1.5\hspace{1em}{T}_c$, and $T\hspace{1em}=\hspace{1em}1.75\hspace{1em}{T}_c$ (left, middle, and right panels, respectively) as a function of the $q\overline{q}$ c.m. energy E, with a “gluon-induced” quark-mass term $m=0.1$ GeV.

Figure 7

(Color online) Light-quark T matrix in the color-octet channel vs. $q\overline{q}$ c.m. energy at $T\hspace{1em}=\hspace{1em}1.2T_c,T\hspace{1em}=\hspace{1em}1.5T_c$, and $T\hspace{1em}=\hspace{1em}1.75T_c$ (left, middle, and right panels, respectively) with $m=0.1$ GeV. Solid (red) line: real part; dashed (blue) line: imaginary part (absolute value).

Figure 8

(Color online) Real part (solid line, red) and imaginary part (dashed line, blue) of the on-shell quark self-energy as a function of three-momentum at temperatures $T\hspace{1em}=\hspace{1em}1.2T_c,T\hspace{1em}=\hspace{1em}1.5T_c$, and $T\hspace{1em}=\hspace{1em}1.75T_c$ (left, middle, and right panels, respectively) with $m=0.1$ GeV.

Figure 9

(Color online) Real part (full line, red) and imaginary part (dashed line, blue) of the T matrix in the color-singlet channel (left panel), color-octet channel (middle panel), and corresponding (singlet + octet) self-energy (right panel) at a temperature $T\hspace{1em}=\hspace{1em}1.5\hspace{1em}{T}_c$ using a “gluon-induced” mass term of $m=0.25$ GeV.

Figure 10

(Color online) Off-shell spectral function $A(\omega ,k)$ as given by Eq. (27) vs. quark energy for different values of the quark momentum at $T\hspace{1em}=\hspace{1em}1.5T_c$ and for $m=0.25$ GeV.