Towards a determination of the chiral critical surface of QCD

The chiral critical surface is a surface of second order phase transitions bounding the region of first order chiral phase transitions for small quark masses in the {m_{u,d}, m_s,\mu} parameter space. The potential critical endpoint of the QCD (T,\mu)-phase diagram is widely expected to be part of this surface. Since for \mu=0 with physical quark masses QCD is known to exhibit an analytic crossover, this expectation requires the region of chiral transitions to expand with \mu for a chiral critical endpoint to exist. Instead, on coarse N_t=4 lattices, we find the area of chiral transitions to shrink with \mu, which excludes a chiral critical point for QCD at moderate chemical potentials \mu_B < 500 MeV. First results on finer N_t=6 lattices indicate a curvature of the critical surface consistent with zero and unchanged conclusions. We also comment on the interplay of phase diagrams between the N_f=2 and N_f=2+1 theories and its consequences for physical QCD.