Bounds on scattering of neutral Goldstones

TL;DR

This paper derives universal bounds on low-energy parameters of neutral Goldstone bosons' scattering amplitudes, reconstructs extremal amplitudes, and explores their non-perturbative Regge behavior, advancing the $S$-matrix bootstrap methods.

Contribution

It establishes new universal bounds on Wilson coefficients for Goldstone bosons and reconstructs the corresponding extremal scattering amplitudes.

Findings

Derived bounds on Wilson coefficients of EFT for Goldstone bosons.

Reconstructed crossing-symmetric, unitary amplitudes saturating the bounds.

Discovered non-perturbative Regge trajectories from complex spin continuation.

Abstract

We study the space of $2\to 2$ scattering amplitudes of neutral Goldstone bosons in four space-time dimensions. We establish universal bounds on the first two non-universal Wilson coefficients of the low energy Effective Field Theory (EFT) for such particles. We reconstruct the analytic, crossing-symmetric, and unitary amplitudes saturating our bounds, and we study their physical content. We uncover non-perturbative Regge trajectories by continuing our numerical amplitudes to complex spins. We then explore the consequence of additional constraints arising when we impose the knowledge about the EFT up to the cut-off scale. In the process, we improve on some aspects of the numerical $S$-matrix bootstrap technology for massless particles.