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 here is a model-independent upper bound on the cross section $\sigma (pp\to S\to \gamma \gamma )$ as a function of the cutoff scale $\mathrm{\Lambda }$ 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 $\sigma (pp\to S\to \gamma \gamma )$ for explicit models.