Finite density fat QCD

Lattice formulation of finite baryon density QCD is problematic from the computer simulation point of view; it is well known that for light quark masses the reconstructed partition function fails to be positive in a wide region of parameter space. For a large bare quark mass, problems related to the phase of the determinant are still present but restricted to a small region in the chemical potential $\mu .$ We present evidence for a transition line that, starting from the temperature critical point at $\mu =0,$ moves towards a smaller $\beta$ with increasing $\mu .$