The chiral critical line of N-f=2+1 QCD at zero and non-zero baryon density

We present numerical results for the location of the chiral critical line at finite temperature and zero and non-zero baryon density for QCD with N-f = 2 + 1 flavours of staggered fermions on lattices with temporal extent N-t = 4. For degenerate quark masses, we compare our results obtained with the exact RHMC algorithm with earlier, inexact R-algorithm results and find a reduction of 25% in the critical quark mass, for which the first order phase transition changes to a smooth crossover. Extending our analysis to nondegenerate quark masses, we map out the chiral critical line up to the neighbourhood of the physical point, which we confirm to be in the crossover region. Our data are consistent with a tricritical point at (m(u,d) = 0, m(s) similar to 500) MeV. We also investigate the shift of the critical line with finite baryon density, by simulating with an imaginary chemical potential for which there is no sign problem. We observe this shift to be very small or, conversely, the critical endpoint mu(c)(m(u,d), m(s)) to be extremely quark mass sensitive. Moreover, the sign of this shift is opposite to standard expectations. If confirmed on a finer lattice, it implies the absence of a critical endpoint for physical QCD at small chemical potential, or another revision of the QCD phase diagram. We critically examine earlier lattice determinations of the QCD critical point, and find them to be in no contradiction with our conclusion. Hence we argue that finer lattices are required to settle even the qualitative features of the QCD phase diagram.