Diphoton excess and running couplings

The recently observed diphoton excess at the LHC may suggest the existence of a singlet (pseudo-)scalar particle with a mass of 750 GeV 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 σ(pp→S→γγ)σ(pp→S→γγ) as a function of the cutoff scale Λ 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 β   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 σ(pp→S→γγ)σ(pp→S→γγ) for explicit models.