Finite Density Fat QCD

Lattice formulation of Finite Baryon Density QCD is problematic from 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 large bare quark masses, instead, it is possible to obtain more sensible results; problems are still present but restricted to a small region. We present evidence for a saturation transition independent from the gauge coupling $\beta$ and for a transition line that, starting from the temperature critical point at $\mu =0$, moves towards smaller $\beta$ with increasing $\mu$ as expected from simplified phenomenological arguments.