A QCD chiral critical point at small chemical potential : is it there or not ?

For a QCD chiral critical point to exist, the parameter region of small quark masses for which the finite temperature transition is first-order must expand when the chemical potential is turned on. This can be tested by a Taylor expansion of the critical surface (mu,d ,ms)c(μ). We present a new method to perform this Taylor expansion numerically, which we first test on an effective model of QCD with static, dense quarks. We then present the results for QCD with 3 degenerate flavors. For a lattice with Nt = 4 time-slices, the first-order region shrinks as the chemical potential is turned on. This implies that, for physical quark masses, the analytic crossover which occurs at μ = 0 between the hadronic and the plasma regimes remains crossover in the μ-region where a Taylor expansion is reliable, i.e. μ . T . We present preliminary results from finer lattices indicating that this situation persists, as does the discrepancy between the curvature of Tc(μ) and the experimentally observed freeze-out curve.