String loops and gravitational positivity bounds: imprint of light particles at high energies

Abstract

We study loop corrections to positivity bounds on effective field theories in the context of $2\to 2$ scattering in gravitational theories, in the presence of light particles. It has been observed that certain negative contributions at low energies are enhanced by inverse powers of a small mass $m$ and are nontrivial to cancel against other low-energy contributions. These originate from near the forward limit of diagrams involving graviton exchange. We observe that scattering in this kinematics domain remains infrared-sensitive even at high center-of-mass energy. By considering a string-inspired model in which high-energy loops can be calculated using unitarity and Regge behavior of tree amplitudes, we uncover a natural mechanism through which $1/m$-enhanced terms perfectly cancel between low and high energy contributions. This concretely explains possible positivity violations in the presence of gravity from the high-energy viewpoint.

Comments: 27 pages + 4 appendices, 14 figures; v2 matches the accepted version in JHEP