Thermodynamics of two flavor QCD to sixth order in quark chemical potential

We present results of a simulation of two flavor QCD on a ${16}^3\times 4$ lattice using p4-improved staggered fermions with bare quark mass $m/T=0.4$. Derivatives of the thermodynamic grand canonical partition function $Z(V,T,{\mu }_u,{\mu }_d)$ with respect to chemical potentials ${\mu }_{u,d}$ for different quark flavors are calculated up to sixth order, enabling estimates of the pressure and the quark number density as well as the chiral condensate and various susceptibilities as functions of ${\mu }_q=({\mu }_u+{\mu }_d)/2$ via Taylor series expansion. Furthermore, we analyze baryon as well as isospin fluctuations and discuss the relation between the radius of convergence of the Taylor series and the chiral critical point in the QCD phase diagram. We argue that bulk thermodynamic observables do not, at present, provide direct evidence for the existence of a chiral critical point in the QCD phase diagram. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model.