Linear sigma model at finite temperature and its application to low-lying hadron properties

We study the O(N) symmetric linear sigma model at finite temperature as the low-energy effective models of quantum chromodynamics(QCD) using the Cornwall-Jackiw-Tomboulis effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use another renormalization prescription for the CJT effective potential in the Hartree-Fock approximation. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum corrections up to the 1-loop order. We show the temperature dependence of the effective potential, the sigma condensate, the sigma and pion masses as functions of temperature. (author)