On (Scalar QED) Gravitational Positivity Bounds

TL;DR

This paper investigates positivity bounds in gravitational theories, analyzing tree-level and one-loop amplitudes, and finds that the bounds are influenced by the Regge tower, affecting the EFT cutoff scale.

Contribution

It introduces a detailed analysis of gravitational positivity bounds at tree and one-loop levels, incorporating Reggeized amplitudes and their implications for EFT constraints.

Findings

Negativity in higher-derivative coefficients is constrained by gravitational positivity bounds.

One-loop Regge amplitudes contribute finite terms to the bounds, affecting the EFT cutoff.

Positivity bounds do not necessarily impose a small cutoff scale, aligning with sum rule analyses.

Abstract

We study positivity bounds in the presence of gravity. We first review the gravitational positivity bound at the tree-level, where it is known that a certain amount of negativity is allowed for the coefficients of higher-derivative operators. The size of these potentially negative contributions is estimated for several tree-level, Reggeized gravitational amplitudes which are unitary at high energies and feature the t-channel pole characteristic of graviton exchange. We also argue for the form of the one-loop Regge amplitude assuming that the branch cut structure associated with the exchange of the graviton and higher-spin particles is reflected. We demonstrate how the one-loop Regge amplitude appears by summing over Feynman diagrams. For our one-loop amplitude proposal, the positivity bounds generically receive a finite contribution from the Regge tower and do not lead to a parametrically small bound on the cut-off scale of the low-energy EFT, consistent with recent studies based on sum rules of the amplitude.