  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.
