The EFT-Hedron

TL;DR

This paper uncovers a geometric structure called the EFThedron that encodes causality and unitarity constraints on low-energy effective field theories, providing new inequalities for scattering amplitudes.

Contribution

It introduces the EFThedron, a novel geometric framework that captures the constraints on EFT operators from fundamental principles, extending the positive geometry concept.

Findings

EFThedron encodes EFT constraints as geometric inequalities.

Derived new bounds for photon and graviton scattering amplitudes.

Revealed a hidden positive structure in EFT constraints.

Abstract

We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden "totally positive" structure strikingly similar to the positive geometries associated with grassmannians and amplituhedra. This forces the infinite tower of higher-dimension operators to lie inside a new geometry we call the "EFThedron". We initiate a systematic investigation of the boundary structure of the EFThedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory. We illustrate the EFThedron geometry and constraints in a wide variety of examples, including new consistency conditions on the scattering amplitudes of photons and gravitons in the real world.