A broad 750 GeV diphoton resonance? Not alone

The hint for a possible resonance in the diphoton channel with mass of 750~GeV disappeared in the data presented at ICHEP'16 by ATLAS and CMS. However, the diphoton final state remains as one of the golden channels for new physics discoveries at the TeV scale in the LHC experiments. This motivates us to analyze model-independently the implications of an O(TeV) bump in the $\gamma\gamma$ final state. By means of forward sum-rules for $\gamma\gamma$ scattering, we show that a spin-0 resonance with mass of the order of the TeV and a sizable $\gamma\gamma$ partial width -of the order of a few GeV- must be accompanied by higher spin resonances with $J_R\geq 2$ with similar properties, as expected in strongly coupled extensions of the Standard Model or, alternatively, in higher dimensional deconstructed duals. Furthermore, independently of whether the putative O(TeV) candidate is a scalar or a tensor, the large contribution to the forward sum-rules in the referred scenario implies the presence of states in the spectrum with $J_R\geq 2$, these high spin particles being a manifestation of new extra-dimensions or composite states of a new strong sector.