  Fermi gases in strongly coupled regimes, such as the unitary limit, are
inherently challenging for many-body methods. Although much progress has been
made with purely analytic methods, quantitative results require ab initio
numerical approaches, such as Monte Carlo (MC) calculations. However,
mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations
due to the infamous sign problem. It was recently pointed out that the sign
problem, for finite spin imbalance, can be circumvented by resorting to
imaginary polarizations and analytic continuation. Large parts of the phase
diagram spanned by temperature and polarization then become accessible to MC
calculations. We propose to apply a similar strategy to the mass-imbalanced
case, which opens up the possibility to study the associated phase diagram with
MC calculations. In particular, our analysis suggests that a detection of a
(tri-)critical point in this phase diagram is possible. We also discuss
calculations in the zero-temperature limit with our approach.
