Towards the phase diagram of cold and dense heavy QCD

The thermodynamics of QCD with sufficiently heavy dynamical quarks can be described by a three-dimensional Polyakov loop effective theory, obtained after a truncated character and hopping expansion. We investigate the resulting phase diagram for low temperatures by mean field methods. Taking into account chemical potentials for both baryon number and isospin, we obtain clear signals for a liquid-gas type transition to baryon matter at ${\mu }_I=0$ and a Bose-Einstein condensation transition at ${\mu }_B=0$, as well as for their connection when both chemical potentials are non-zero.