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