Db. Blaschke et al., Chiral quark model with infrared cut-off for the description of meson properties in hot matter, EUR PHY J A, 11(3), 2001, pp. 319-327
A simple chiral quark model of the Nambu-Jona-Lasinio (NJL) type with a qua
rk confinement mechanism is constructed for the description of the light-me
son sector of QCD at finite temperature. Unphysical quark production thresh
olds in the NJL model are excluded by an infrared cut-off in the momentum i
ntegration within quark loop diagrams. This chiral quark model satisfies th
e low-energy theorems. Using the vacuum masses and decay widths of pi- and
rho -mesons for fixing the model parameters, the properties of the sigma -m
eson are derived. Within the Matsubara formalism, the model is systematical
ly 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 T-c = 186 MeV. Besides the
pion mass and weak decay constant, the masses, coupling constants and deca
y widths of sigma- and rho -mesons in hot matter axe investigated. The quar
k-antiquark decay channel of the light mesons is opened for T > T-c only an
d becomes particularly strong for the rho -meson. The two-pion decay channe
l below T-c, has almost constant width for the rho -meson up to T-c, but fo
r the sigma -meson it closes below T-c such that a scalar meson state with
vanishing width is obtained as a precursor of the chiral/deconfinement tran
sition.