The IR-Side of Positivity Bounds

TL;DR

This paper investigates how infrared loop effects influence positivity bounds in effective field theories, revealing singularities that weaken certain bounds and proposing new dispersive bounds that are unaffected by these singularities.

Contribution

It identifies IR singularities affecting positivity bounds and introduces a new analytic approach to dispersive bounds that bypasses these singularities.

Findings

Infrared singularities weaken crossing symmetry bounds.

A new dispersive bound approach is insensitive to IR singularities.

Loop contributions are explicitly computed and shown not to affect impact parameter bounds.

Abstract

We show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally we show that the singularity do not affect the bounds based on smearing in impact parameter.