Role of Vector Interaction and Axial Anomaly in the PNJL Modeling of the   QCD Phase Diagram
  Effects of a flavor singlet vector interaction in the Polyakov - Nambu - Jona-Lasinio (PNJL) model are studied in combination with the axial U(1) breaking Kobayashi - Maskawa - 't Hooft interaction. Using a consistent cutoff scheme we investigate the QCD phase diagram and its dependence on the vector coupling strength $g_v$. We find that the first order chiral phase transition at moderate baryon chemical potentials and its critical point, a generic feature of most NJL-type models without vector coupling, disappear for sufficiently large values of $g_v$ that are consistent with lattice QCD results at imaginary chemical potential. The influence of non-zero $g_v$ on the curvature of the crossover boundary in the $T-\mu$ plane close to $\mu = 0$ is also examined. 
Nino M. Bratovic, Tetsuo Hatsuda and Wolfram Weise
hep-ph nucl-th