The recently observed diphoton excess at the LHC may suggest the existence of a singlet (pseudo-) scalar particle with a mass of 750GeV which couples to gluons and photons.
Assuming that the couplings to gluons and photons originate from loops of fermions and/or scalars charged under the Standard Model gauge groups, we show that there is a model-independent upper bound on the cross section of diphoton events as a function of the cutoff scale and masses of the fermions and scalars in the loop.
Such a bound comes from the fact that the contribution of each particle to the diphoton event amplitude is proportional to its contribution to the one-loop beta functions of the gauge couplings.
We also investigate the perturbativity of running Yukawa couplings in models with fermion loops, and show the upper bounds on the cross section of diphoton events for explicit models.