Phase diagram and isentropic curves from the vector meson extended Polyakov quark meson model

In the framework of the $N_f = 2+1$ flavor (axial)vector meson extended Polyakov quark meson model we investigate the QCD phase diagram at finite temperature and density. We use a $\chi^2$ minimization procedure to parameterize the model based on tree\,-\,level decay widths and vacuum scalar and pseudoscalar curvature masses which incorporate the contribution of the constituent quarks. Using a hybrid approximation (mesons at tree level, fermions at one\,-\,loop level) for the grand potential we determine the phase boundary both on the $\mu_B-T$ and $\rho-T$ planes. We also determine the location of the critical end point of the phase diagram. Moreover by calculating the pressure and other thermodynamical quantities derived from it, we determine a set of isentropic curves in the crossover region. We show that the curves behave very similarly as their counterparts obtained from the lattice in the crossover regime.