Calculation of the pseudoscalar-isoscalar hadronic current correlation functions of the quark-gluon plasma

We report the results of calculations of pseudoscalar-isoscalar hadronic current correlators using the Nambu Jona-Lasinio model and the real-time finite-temperature formalism. (This work represents a continuation of results reported previously for other current correlators.) Results are presented for the temperatures range 1.2⩽T/T_c⩽6.0, where T_c is the temperature of the confinement-deconfinement transition, which we take to be T_c=170 MeV. Some resonant features are seen in our calculations. In order to understand the origin of these resonances, we have performed relativistic random phase approximation (RPA) calculations of the temperature-dependent spectrum of the η mesons for T<T_c. For the RPA calculations, use is made of a simple model in which we introduce temperature-dependent constituent quark masses calculated in a mean-field approximation and a temperature-dependent confining interaction whose form is motivated by recent studies made using lattice simulations of QCD with dynamical quarks. We also introduce temperature-dependent coupling constants in our generalized NJL model. Our motivation in the latter case is the simulation of the approach to a weakly interacting system at high temperatures and the avoidance of “η condensates” which would indicate instability of the ground state of the model. We present some evidence that supports our use of temperature-dependent coupling constants for the NJL model. We suggest that our results may be of interest to researchers who use lattice simulations of QCD to obtain temperature-dependent spectral functions for various hadronic current correlation functions.