  Free-floating (or rogue) planets are planets that are liberated (or ejected)
from their host systems. Although simulations predict their existence in
substantial numbers, direct observational evidence for free-floating planets
with masses below ~5 MJup is still lacking. Several cycle-1 observing programs
with JWST aim to hunt for them in four different star-forming clusters. These
surveys are designed to be sensitive to masses of 1-15 MJup (assuming a
hot-start formation), which corresponds to spectral types of early L to late T
for the ages of these clusters. If the existing simulations are not wide off
the mark, we show here that the planned programs are likely to find up to 10-20
giant rogue planets in moderate density clusters like NGC1333 or IC348, and
several dozen to ~100 in high-density regions like NGC2024 and the Orion Nebula
Cluster. These numbers correspond to 1-5% of the total cluster population; they
could be substantially higher if stars form multiple giant planets at birth. In
contrast, the number of free-floating brown dwarfs, formed from core collapse
("like stars") is expected to be significantly lower, only about 0.25% of the
number of stars, or 1-7 for the clusters considered here. Below 10 MJup that
number drops further by an order of magnitude. We also show that the planned
surveys are not at risk of being significantly contaminated by field brown
dwarfs in the foreground or background, after spectroscopic confirmation. Taken
together, our results imply that if a population of L and T dwarfs were to be
found in these JWST surveys, it is expected to be predominantly made up of
rogue planets.
