Quark Model Calculations of Spectral Functions of Hadronic Current Correlation Functions at Finite Temperature

Abstract

We calculate spectral functions associated with hadronic current correlation functions for vector and pseudoscalar currents at finite temperature. We make use of the Nambu--Jona--Lasinio (NJL) model with temperature-dependent coupling constants and temperature-dependent momentum cutoff parameters. At low energies, good fits are obtained for the spectral functions that were extracted from lattice data by means of the maximum entropy method (MEM). Our model has two parameters which are used to fix the magnitude and position of the large peak seen in the spectral functions. With those two parameters fixed, we obtain a satisfactory fit to the width of the peak. The model then also reproduces the energy of a second peak seen in the spectral functions. In the case of the pseudoscalar spectral function, the calculated peak is about 20 percent higher than that found for the spectral function obtained from the lattice data. However, it appears that the second peak is a lattice artifact [ P. Petreczky, private communication ] and our fit to the second peak may not be meaningful. We conclude that the NJL model may have a broader range of application than previously considered to be the case, if one allows for significant temperature dependence of the parameters of the model, as well as rather large values of the momentum cutoff parameter. Our treatment of temperature-dependent coupling constants and cutoff parameters is analogous to the procedure introduced by R. Casalbuoni, R. Gatto, G. Nardulli, and M. Ruggieri, [ Phys. Rev. D \textbf{68}, 034024 (2003) ], who make use of the NJL model at finite density and find that they need to use the density-dependent coupling constants and density -dependent cutoff parameters to study matter at high density.