Models of the LHC diphoton excesses valid up to the Planck scale

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 vectorlike 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 latter case, 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.