The Phases of the Scalar S-Matrix Island

TL;DR

This paper refines non-perturbative bounds on scalar scattering amplitudes, revealing a phase structure of the boundary related to different UV mechanisms for gapped scalars.

Contribution

It uncovers a classification of boundary phases in the S-matrix bootstrap, linking asymptotic behavior to UV physics and resonance structures.

Findings

Boundaries exhibit universal behavior along edges.

Distinct phases correspond to different UV mechanisms.

Asymptotic Regge behavior characterizes boundary phases.

Abstract

The two-to-two four-dimensional scattering amplitude of identical scalars obeys rigorous two-sided non-perturbative bounds derived via the modern numerical S-matrix bootstrap. These bounds carve out an allowed region with a rich boundary structure, featuring edges and vertices. In this work we further tighten this region and uncover the physics of its boundary by analyzing the asymptotic Regge behavior of the amplitude and the spectrum of resonances and virtual states. We find that the S-matrices along a given edge exhibit universal behavior, sharply contrasting with that on other edges. This reveals a classification of the boundary into distinct phases, corresponding to different UV mechanisms by which a gapped scalar arises.