Massless Positivity in Graviton Exchange

TL;DR

This paper develops positivity bounds for scattering amplitudes involving massless particles like gravitons, accounting for IR divergences and Regge behavior, with implications for constraining modified gravity theories.

Contribution

It extends positivity bounds to include massless particle exchange, incorporating IR divergences and Regge behavior, and identifies universal sub-leading logarithmic terms.

Findings

Positivity bounds can be formulated with massless exchanges.

IR divergences determine the UV behavior of amplitudes.

Universal sub-leading logarithmic terms are identified.

Abstract

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.