Massless positivity

We formulate Positivity Bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable s. In general, validity of these bounds require the cancellation of divergences in the forward limit of the amplitude, proportional to 1/t and log(t). We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale. The bounds that we present have the potential of constraining very general models of modified gravity and EFTs of matter coupled to gravitation.