Calculation of Temperature-Dependent Hadronic Correlation Functions of Pseudoscalar and Vector Currents

Abstract

We make use of the Nambu-Jona-Lasinio (NJL) formalism and real-time finite-temperature field theory to calculate hadronic current correlation functions in the deconfined phase of quantum chromodynamics (QCD). We consider both pseudoscalar and vector currents and compare our results with those obtained in lattice simulations of QCD. Our results are similar to those obtained in the lattice simulations for $T=1.5 T_c$, where $T_c$ is the temperature of the confinement-deconfinement transition. For $T=3.0 T_c$ our results do not exhibit the resonances obtained from the lattice simulations. However, the errors presented for the lattice results are large and it is possible that our results at $T=3.0 T_c$ are consistent with the lattice results when these errors are taken into account. Since the method used in the lattice analysis to obtain the spectral functions requires assumptions about the likelihood of a particular form for the spectral function, we believe our calculations will be useful to researchers who wish to calculate hadronic current correlation functions at finite temperature using lattice-based methods. Our model makes use of temperature-dependent coupling constants for the NJL model. We present an argument that such temperature dependence is necessary, if the results of the model are to be consistent with what is known concerning QCD thermodynamics.