  We discuss a possibility to explain the LHC diphoton excesses at $750$GeV by
the new scalar $X$ that couples to the gauge bosons through the loop of new
massive particles with Standard Model charges. We assume that the new particles
decay into the Standard Model particles at the tree level. We systematically
examine the models that preserve the vacuum stability and the perturbativity up
to the Planck scale. When we take scalars for the new particles, we find that
only a few diquark and dilepton models can explain the observed diphoton cross
section without conflicting the experimental mass bounds. When we take
vector-like fermions for the new particles, we find rather different situations
depending on whether their couplings to $X$ are scalar or pseudoscalar type. In
the former case, a few models are allowed if we introduce only one species of
fermions. The more fermions we introduce, the more models are allowed. In the
later case, the most of the models are allowed because of the large coupling
between $X$ and photon. It is interesting that the allowed mass regions of the
scalar particles might be reached by the next lepton colliders.
