Anna Tokareva (Imperial C.), Reconstruction of the UV graviton scattering amplitude from IR singularities.

Wednesday 29 Jun 2022, 11:00 → 12:30 Europe/Stockholm

Scattering amplitudes mediated by graviton exchange display IR singularities in the forward limit. This obstructs standard application of positivity bounds based on twice subtracted dispersion relations. Such divergences can be cancelled only if the UV limit of the scattering amplitude behaves in a specific way, which implies a very non-trivial connection between the UV and IR behaviours of the amplitude. We show that this relation can be expressed in terms of an integral transform, obtaining analytic results when $t \log{s}\rightarrow 0$. Carefully applying this limit to dispersion relations, we find that infinite arc integrals, which are usually taken to vanish, can give a non-trivial contribution in the presence of gravity. This implies that gravitational positivity bounds cannot be trusted unless the size of this contribution is estimated in some way, which implies assumptions on the UV completion of gravitational interactions.