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. Results are presented for the temperatures range 1.2 $\leq T/T_c\leq$ 6.0, where $T_c$ is the temperature of the confinement-deconfinement transition, which we take to be $T_c=170$ MeV. Two important 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 $\eta$ 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. 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.Comment: 20 pages, 10 figures, Revtex

Description of Gluon Propagation in the Presence of an A^2 Condensate

There is a good deal of current interest in the condensate A^2 which has been seen to play an important role in calculations which make use of the operator product expansion. That development has led to the publication of a large number of papers which discuss how that condensate could play a role in a gauge-invariant formulation. In the present work we consider gluon propagation in the presence of such a condensate which we assume to be present in the vacuum. We show that the gluon propagator has no on-mass-shell pole and, therefore, a gluon cannot propagate over extended distances. That is, the gluon is a nonpropagating mode in the gluon condensate. In the present work we discuss the properties of both the Euclidean-space and Minkowski-space gluon propagator. In the case of the Euclidean-space propagator we can make contact with the results of QCD lattice calculations of the propagator in the Landau gauge. With an appropriate choice of normalization constants, we present a unified representation of the gluon propagator that describes both the Minkowski-space and Euclidean-space dynamics in which the A^2 condensate plays an important role.Comment: 28 pages, 11 figure