Chiral quark models with nonlocal separable interactions at finite temperature and chemical potential

Chiral quark models with nonlocal covariant separable interactions at finite temperature and chemical potential are investigated. We develop a formalism in which the different quark properties are evaluated taking into account the analytic structure of the quark propagator. In this framework we study the chiral restoration phase transition for several definite nonlocal regulators, including that arising within the instanton liquid picture. We find that in all cases the chiral transition is of first order for low values of T, turning into a smooth crossover at a certain end point. Using model parameters which lead to the physical pion mass and decay constant, we find for the position of this end point the values (T-E,mu(E))approximate to(60-70,180-210) MeV. We also discuss the special relevance of the first poles of the quark propagator.