The chiral critical point of Nf=3 QCD at finite density to the order (μ/T)4

QCD with three degenerate quark flavours at zero baryon density exhibits a first order thermal phase transition for small quarkmasses, which changes to a smooth crossover for some critical quark mass m(0)(c), i.e. the chiral critical point. It is generally believed that as an (even) function of quark chemical potential, the critical point m(c)(mu) moves to larger quark masses, constituting the critical endpoint of a first order phase transition in theories with m >= m(0)(c). To test this, we onsider a Taylor expansion of m(c)(mu) around mu=0 and determine the first two coefficients from lattice simulations with staggered fermions on N-t=4 lattices. We employ two different techniques: a) calculating the coefficients directly from a mu=0 ensemble using a novel finite difference method, and b) fitting them to simulation data obtained for imaginary chemical potentials. The mu(2) and mu(4) coefficients are found to be negative by both methods, with consistent absolute values. Combining both methods gives evidence that also the mu(6) coefficient is negative. Hence, on coarse N-t=4 lattices a three-flavour theory with m >= m(0)(c) does not possess a chiral critical endpoint for quark chemical potentials mu less than or similar to T. Simulations on finer lattices are required for reliable continuum physics. Possible implications for the QCD phase diagram are discussed.