Massless positivity in graviton exchange

We formulate Positivity Bounds for scattering amplitudes including exchange of massless particles. generalize the standard construction through dispersion relations to include presence a branch cut along real axis in complex plane Maldestam variable $s$. In general, validity these bounds require cancellation divergences forward limit amplitude, proportional $t^{-1}$ and $\log(t)$. show that this is possible case gravitons if one assumes Regge behavior amplitude at high energies below Planck scale, as previously suggested literature, concrete UV behaviour uniquely determined by structure IR divergences. thus extend previous results sub-leading logarithmic term, which we be universal. The present here have potential constraining very general models modified gravity EFTs matter coupled gravitation.