  Depending on the stellar densities, protoplanetary discs in stellar clusters
undergo background heating, disc truncation-driven by stellar encounter, and
photo-evaporation. Disc truncation leads to reduced characteristic sizes and
disc masses that eventually halts gas giant planet formation. We investigate
how disc truncation impacts planet formation via pebble-based core accretion
paradigm, where pebble sizes were derived from the full grain-size distribution
within the disc lifetimes. We make the best-case assumption of one embryo and
one stellar encounter per disc. Using planet population syntheses techniques,
we find that disc truncation shifts the disc mass distributions to the lower
margins. This consequently lowered the gas giant occurrence rates. Despite the
reduced gas giant formation rates in clustered discs, the encounter models
mostly show as in the isolated field; the cold Jupiters are more frequent than
the hot Jupiters, consistent with observation. Moreover, the ratio of hot to
cold Jupiters depend on the periastron distribution of the perturbers with
linear distribution in periastron ratio showing enhanced hot to cold Jupiters
ratio in comparison to the remaining models. Our results are valid in the
best-case scenario corresponding to our assumptions of: only one disc encounter
with a perturber, ambient background heating and less rampant
photo-evaporation. It is not known exactly of how much gas giant planet
formation would be affected should disc encounter, background heating and
photo-evaporation act in a concert. Thus, our study will hopefully serve as
motivation for quantitative investigations of the detailed impact of stellar
cluster environments on planet formations.
