  We generalize known results for heavy quarkonium in a thermal bath to the
case of a finite baryonic density, and provide a number of formulas for the
energy shift and decay width that hold at weak coupling for sufficiently large
temperature and/or chemical potential. We find that a non-vanishing decay width
requires a temperature larger than the typical binding energy, no matter how
large the chemical potential is. This implies that at zero temperature the
dissociation mechanism of heavy quarkonium is due entirely to screening, unlike
in the finite temperature case. We use several effective theories in order to
sort out the contributions of the relevant energy and momentum scales. In
particular, we consider contributions of the so called quasi-static magnetic
modes. The generalization to the case of a finite isospin/strangeness chemical
potential is trivial. We discuss possible applications to the SIS and NICA
conditions, and compare with available lattice results.
