Chiral and U(1) axial symmetry restoration in linear sigma models with   two quark flavors
  We study the restoration of chiral symmetry in linear sigma models with two quark flavors. The models taken into consideration have a U(2)_L x U(2)_R and an O(4) internal symmetry. The physical mesons of these models are sigma, pion, eta and a_0 where the latter two are not present in the O(4) model. Including two-loop contributions through sunset graphs we calculate the temperature behavior of the order parameter and the masses for explicit chiral symmetry breaking and in the chiral limit. Decay threshold effects introduced by the sunset graphs alter the temperature dependence of the condensate and consequently that of the masses as well. This correctly reproduces a second-order phase transition for the O(4) model and for the U(2)_L x U(2)_R model with an axial U(1) anomaly as expected from universality class arguments. Chiral symmetry tends to be restored at higher temperatures in the two-loop approximation than in the Hartree-Fock approximation. To model a restoration of the axial U(1) symmetry we imply a temperature-dependent anomaly parameter that sharply drops at about 175 MeV. This triggers the restoration of chiral symmetry before the full symmetry is restored and lowers the transition temperatures significantly below 200 MeV. 
Stefan Michalski