The study of the forward scattering amplitude V(k, λ)V(k′λ′) → V(k, λ)V(k′, λ′) of real massless gauge bosons V, e.g. photons or gluons, leads to a sumrule that can be used to investigate beyond the Standard Model signals at LHC in the γγ channel. The sum-rule only relies on general properties such as analyticity, unitarity and crossing. We use the now buried “750 GeV diphoton resonance” as a case of study to exemplify the constraints that the forward sum-rule requires to any new physics candidate. In the case of a large γγ or gg partial width, of the order of 10 GeV in our 750 GeV analysis, one finds that an infinite tower of states with spin JR = 2 and higher must be ultimately incorporated to the beyond Standard Model theory in order to fulfill the sumrule. We expect these techniques may be useful in next diphoton searches at LHC and future colliders.