Sum-rule constraints on possible diphoton resonances at LHC

The study of the forward scattering amplitude $V(k,\lambda) V(k'\lambda')\to V(k,\lambda) V(k',\lambda')$ of real massless gauge bosons $V$, e.g. photons or gluons, leads to a sum-rule that can be used to investigate beyond the Standard Model signals at LHC in the $\gamma\gamma$ 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 $\gamma\gamma$ 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 $J_R=2$ and higher must be ultimately incorporated to the beyond Standard Model theory in order to fulfill the sum-rule. We expect these techniques may be useful in next diphoton searches at LHC and future colliders.