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We report the discoveries of low-mass free-floating planet (FFP) candidatesfrom the analysis of 2006-2014 MOA-II Galactic bulge survey data. In thisdataset, we found 6,111 microlensing candidates and identified a statisticalsample consisting of 3,535 high quality single lens events with Einstein radiuscrossing times in the range $0.057 < t_{\rm E}/{\rm days} < 757$, including 13events that show clear finite source effects with angular Einstein radii of$0.90<\theta_{\rm E}/{\rm \mu as} <332.54$. Two of the 12 events with $t_{\rmE} < 1$ day have significant finite source effects, and one event, MOA-9y-5919,with $t_{\rm E}=0.057\pm 0.016$ days and $\theta_{\rm E}= 0.90 \pm 0.14$$\mu$as, is the second terrestrial mass FFP candidate to date. A Bayesiananalysis indicates a lens mass of $0.75^{+1.23}_{-0.46}$ $M_\oplus$ for thisevent. The low detection efficiency for short duration events implies a largepopulation of low-mass FFPs. The microlensing detection efficiency for low-massplanet events depends on both the Einstein radius crossing times and theangular Einstein radii, so we have used image-level simulations to determinethe detection efficiency dependence on both $t_{\rm E}$ and $\theta_{\rm E}$.This allows us to use a Galactic model to simulate the $t_{\rm E}$ and$\theta_{\rm E}$ distribution of events produced by the known stellarpopulations and models of the FFP distribution that are fit to the data.Methods like this will be needed for the more precise FFP demographicsdeterminations from Nancy Grace Roman Space Telescope data.

Terrestrial and Neptune mass free-floating planet candidates from the MOA-II 9-year Galactic Bulge survey