  We argue that lattice calculations of the $\eta'$ mass in QCD with $N_c=2$
colors performed at non-zero baryon chemical potential can be used to study the
mechanism responsible for the mass of the $\eta'$. QCD with two colors is an
ideal laboratory because it exhibits confinement, chiral symmetry breaking and
a would-be $U(1)_A$ Goldstone boson at all densities. Since the instanton
density and the confinement scale vary with density in a very different way,
instantons are clearly distinguishable from other possible mechanisms. There is
an instanton prediction for the $\eta'$ mass at large density that can be
compared to lattice results. The density dependence of the instanton
contribution is a simple consequence of the integer topological charge carried
by the instanton. We also argue that $N_c=3$ color QCD at finite isospin
density can be used in order to study the origin of OZI-violation in the scalar
sector.
