Chiral quark model with infrared cut-off for the description of meson properties in hot matter

A simple chiral quark model of the Nambu-Jona-Lasinio (NJL) type with a quark confinement mechanism is constructed for the description of the light-meson sector of QCD at finite temperature. Unphysical quark production thresholds in the NJL model are excluded by an infrared cut-off in the momentum integration within quark loop diagrams. This chiral quark model satisfies the low-energy theorems. Using the vacuum masses and decay widths of π- and ρ-mesons for fixing the model parameters, the properties of the σ-meson are derived. Within the Matsubara formalism, the model is systematically extended to finite temperatures where chiral symmetry restoration due to a dropping constituent quark mass entails a vanishing of the infrared cut-off (deconfinement) at the pion Mott temperature Tc=186 MeV. Besides the pion mass and weak decay constant, the masses, coupling constants and decay widths of σ- and ρ-mesons in hot matter are investigated. The quark-antiquark decay channel of the light mesons is opened for T>Tc only and becomes particularly strong for the ρ-meson. The two-pion decay channel below Tc has almost constant width for the ρ-meson up to Tc, but for the σ-meson it closes below Tc such that a scalar meson state with vanishing width is obtained as a precursor of the chiral/deconfinement transition. (orig.)