Effective theories for the chiral symmetry restoring phase transition in quantum chromodynamics

Effective chiral theories of quantum chromodynamics (QCD) are used to investigate different aspects of the chiral symmetry restoring phase transition as well as the in-medium properties of the scalar and pseudoscalar mesons. The temperature dependence of the sigma meson and pion masses as well as the nonstrange quaxk condensate is studied in the framework of the SU (2)_r × SU(2) _l linear sigma model. The Cornwall-Jackiw-Tomboulis (CJT) formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes and the resulting difficulties are examined. Using these masses, the on-shell decay widths for sigma mesons and pions at rest are computed at nonzero temperature. The SU(3)_r × SU(3) _l linear sigma model is then used to investigate the properties of the scalar and pseudoscalar nonet particles (mesons). Various patterns of symmetry breaking are studied and the CJT formalism is used to derive gap equations for the masses of the scalar and pseudoscalar nonet mesons and the strange and nonstrange quark condensates as a function of temperature. Finally, the line of second order phase transitions separating the first order and smooth crossover regions is located in the plane of the current strange and nonstrange quark masses using the SU(3)_r × SU(3)_l linear sigma model for the cases of exact and explicitly broken U(1) _A symmetry.