The Diphoton Excess, Low Energy Theorem and the 331 Model

We interpret the diphoton anomaly as a heavy scalar $H_3$ in the so-called 331 model. The scalar is responsible for breaking the $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ gauge symmetry down to the standard model electroweak gauge group. It mainly couples to the standard model gluons and photons through quantum loops involving heavy quarks and leptons. Those quarks and leptons, in together with the SM quarks and leptons, form the fundamental representation of the 331 model. We use low energy theorem to calculate effective coupling of $H_3gg$, $H_3\gamma\gamma$, $H_3ZZ$, $H_3WW$ and $H_3Z\gamma$. The analytical results can be applied to new physics models satisfying the low energy theorem. We show that the heavy quark and lepton contribution cannot produce enough diphoton pairs. It is crucial to include the contribution of charged scalars to explain the diphoton excess. The extra neutral $Z^\prime$ boson could also explain the 2 TeV diboson excess observed at the LHC Run-I.