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Hadrons and Nuclei


Eur. Phys. J. A 11, 319-327 (2001)

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

D.B. Blaschke1, 2, G.R.G. Burau1, M.K. Volkov2 and V.L. Yudichev2

1  Fachbereich Physik, Universität Rostock, D-18051 Rostock, Germany
2  Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russian Federation

david@darss.mpg.uni-rostock.de

(Received: 11 July 2001 Communicated by V.V. Anisovich)

Abstract
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 $\pi$- and $\rho$-mesons for fixing the model parameters, the properties of the $\sigma$-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 $T_{\rm c}=186$ MeV. Besides the pion mass and weak decay constant, the masses, coupling constants and decay widths of $\sigma$- and $\rho$-mesons in hot matter are investigated. The quark-antiquark decay channel of the light mesons is opened for $T> T_{\rm c} $ only and becomes particularly strong for the $\rho$-meson. The two-pion decay channel below $T_{\rm c} $ has almost constant width for the $\rho$-meson up to $T_{\rm c} $, but for the $\sigma$-meson it closes below $T_{\rm c} $ such that a scalar meson state with vanishing width is obtained as a precursor of the chiral/deconfinement transition.

PACS
11.30.Rd - Chiral symmetries.
12.38.Lg - Other nonperturbative calculations.
13.25.-k - Hadronic decays of mesons.
11.10.Wx - Finite-temperature field theory.

© Società Italiana di Fisica, Springer-Verlag 2001