  We present the first prediction for the mass distribution function of
Galactic free-floating planets (FFPs) that aims to accurately include the
relative contributions of multiple formation pathways and stellar populations.
We derive our predicted distribution from dedicated simulations of planet
birth, growth, migration, and ejection around circumbinary systems and extend
these results to also include the contributions from single and wide binary
systems. Our resulting FFP mass distribution shows several distinct features,
including a strong peak at $\sim 8 M_{\oplus}$ arising from the transition
between pebble and gas accretion regimes and a trough at $\sim 1 M_{\oplus}$
due to the shift in the dominant ejection process from planet-planet scattering
to ejection through interactions with stars in circumbinary systems. We find
that interactions with the central binary in close circumbinary systems are
likely the dominant progenitor for FFPs more massive than Earth, leading to a
steep power-law dependence in mass that agrees well with existing observations.
In contrast, we find planet-planet scattering events in single and wide binary
systems likely produce the majority of planets at Mars mass and below,
resulting in a shallower power-law dependence. Our results suggest that
existing extrapolations into the sub-terrestrial mass range may significantly
overestimate the true FFP abundance. The features we predict in the mass
distribution of FFPs will be detectable by upcoming space-based microlensing
surveys and, if observed, will provide key insight into the origins of FFPs and
the environments in which they form.
