Finite T meson correlations and quark deconfinement

Abstract

Finite temperature spatial $\bar{q}q$ correlation modes in the $\pi$ and $\rho$ channels are studied with the rainbow-ladder truncated quark Dyson-Schwinger equation and Bethe-Salpeter equation in the Matsubara formalism. To retain the finite range of the effective interaction while facilitating summation over fermion Matsubara modes necessary to ensure continuity at {T=0}, a separable kernel is used. The model is fixed by {T=0} properties and it implements dynamical chiral symmetry breaking and quark confinement. Above and below the deconfinement and chiral restoration transitions, we study $M_{\pi }(T)$, $f_{\pi }(T)$ and the 3-space transverse and longitudinal masses $M_{\rho }^T(T)$ and $M_{\rho }^L(T)$. For the $\rho$ mode we also study the strong and electromagnetic partial widths to determine the $T$-dependence that is generated by the quark content. The $\rho \to \pi \pi$ width decreases sharply just above the chiral restoration transition leaving the $\rho$ with only its narrow {$e^{+}{e}^{-}$} width. We discuss improvements needed by this model, especially in regard to the high $T$ behavior of the masses where we compare to lattice QCD simulations.

Comments: Revised, shortened version that has been published; 24 pages, REVTEX, 7 figs, epsfig