Can we locate the QCD critical endpoint with the Taylor expansion

Full text: While lattice QCD simulations are more and more successful at vanishing chemical potential, at finite chemical potential the fermion-sign problem is still a serious problem. Different methods have been proposed to access at least the region at small chemical potential. One such approach is the Taylor expansion. Effective models allow calculations at arbitrary chemical potential. We have developed a novel technique to evaluate the coefficients with high-precision up to 24th order in the PQM model. This model yields a good description of the equation of state at zero chemical potential. We discuss the prospects of the Taylor expansion in particular signal of a possible critical point. (author)