Zero mode in a strongly coupled quark gluon plasma

Abstract

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 ${T}_{c}=147\ifmmode\pm\else\textpm\fi{}8\text{ }\text{ }\mathrm{MeV}$, 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 $T\ensuremath{\in}[{T}_{c},{T}_{s}]$, with ${T}_{s}\ensuremath{\simeq}1.5{T}_{c}$, 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.