Existence of the critical endpoint in the vector meson extended linear   sigma model
  The chiral phase transition of the strongly interacting matter is investigated at nonzero temperature and baryon chemical potential mu_B within an extended (2+1) flavor Polyakov constituent quark-meson model which incorporates the effect of the vector and axial vector mesons. The effect of the fermionic vacuum and thermal fluctuations computed from the grand potential of the model is taken into account in the curvature masses of the scalar and pseudoscalar mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values in a chi^2-minimization procedure which selects between various possible assignments of scalar nonet states to physical particles. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates and the chiral partners' masses and of the mixing angles for the pseudoscalar eta-eta' and the corresponding scalar complex. We calculate the pressure and various thermodynamical observables derived from it and compare them to the continuum extrapolated lattice results of the Wuppertal-Budapest collaboration. We study the T-mu_B phase diagram of the model and find that a critical end point exists for parameters of the model, which give acceptable values of chi^2. 
Peter Kov\'acs, Zsolt Sz\'ep and Gy\"orgy Wolf
hep-ph nucl-th