  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 $t^{-1}$ 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, as previously suggested in
the literature, and that the concrete UV behaviour of the amplitude is uniquely
determined by the structure of IR divergences. We thus extend previous results
by including a sub-leading logarithmic term, which we show to be universal. The
bounds that we present here have the potential of constraining very general
models of modified gravity and EFTs of matter coupled to gravitation.
