Zero mode in a strongly coupled quark gluon plasma

In connection with massless two-flavor QCD, we analyze the chiral symmetry restoring phase transition using three distinct gluon-quark vertices and two different assumptions about the long-range part of the quark-quark interaction. In each case, we solve the gap equation, locate the transition temperature $T_c$, and use the maximum entropy method to extract the dressed-quark spectral function at $T>T_c$. Our best estimate for the chiral transition temperature is $T_c=147\pm 8\mathrm{MeV}$, and the deconfinement transition is coincident. For temperatures markedly above $T_c$, we find a spectral density that is consistent with those produced using a hard thermal loop expansion, exhibiting both a normal and plasmino mode. On a domain $T\in [T_c,T_s]$, with $T_s\simeq 1.5T_c$, however, with each of the six kernels we considered, the spectral function contains a significant additional feature. Namely, it displays a third peak, associated with a zero mode, which is essentially nonperturbative in origin and dominates the spectral function at $T=T_c$. We suggest that the existence of this mode is a signal for the formation of a strongly coupled quark-gluon plasma and that this strongly interacting state of matter is likely a distinctive feature of the QCD phase transition.

Figure 1

Left panel: quasiparticle dispersion relations at $T=3T_c$, where ${\omega }_{+(-)}$ denotes normal (plasmino) mode. Diagonal dashed line: free-fermion dispersion relation at this temperature. Right panel: Momentum dependence of the residues associated with these quasiparticle poles. Results obtained with rainbow vertex, Eq. (3), and QC interaction, Eq. (16).

Figure 2

Numerical check of the momentum sum rule in Eq. (44): solid curve: DB vertex, Eq. (6), with QC interaction, Eq. (16); dashed: rainbow vertex, Eq. (3), plus QC; dotted: ideal reference result. The curves would be indistinguishable with a perfect reconstruction of the spectral density.

Figure 3

Left panels: Temperature dependence of the dressed-quark thermal masses. Notably, spectral strength is associated with a massless mode. Right panels: $T$ dependence of the residue associated with that zero mode. From top to bottom: QC interaction and rainbow vertex; $\mathrm{MT}+\mathrm{BC}$; and $\mathrm{QC}+\mathrm{DB}$.

Figure 4

Left panels: Calculated dispersion relations, ${\omega }_{\pm ,0}$, for all quasiparticles at $T=1.1T_c$; and right panels: momentum dependence of the residues of the poles. As in Fig. 3, from top to bottom: QC interaction and rainbow vertex; $\mathrm{MT}+\mathrm{BC}$; and $\mathrm{QC}+\mathrm{DB}$.

Figure 5

Pictorial representation of results listed in Table 1. Upper panel: Interaction and parameter dependence of the critical temperature for chiral symmetry restoration and deconfinement. (The dashed line and band mark $T_c=0.13\pm 0.014$.) Lower panel: Analogue for upper bound on the zero mode’s survival domain, $T_s$, measured with respect to $T_c$. (The dashed line and band mark $T_s/T_c=1.53\pm 0.12$.)