The S-matrix bootstrap with neural optimizers I: zero double discontinuity

TL;DR

This paper introduces a machine learning-based method using neural networks to explore nonperturbative scattering amplitudes, specifically for identical scalar particles, achieving consistent bounds and characterization of the amplitude space.

Contribution

It presents a novel neural network approach integrated with the S-matrix bootstrap to analyze scattering amplitudes with zero double discontinuity, providing new bounds and insights.

Findings

Neural networks effectively parameterize scattering amplitudes.

Derived bounds on low-energy Taylor coefficients.

Neural network results agree with traditional bootstrap methods.

Abstract

In this work, we develop machine learning techniques to study nonperturbative scattering amplitudes. We focus on the two-to-two scattering amplitude of identical scalar particles, setting the double discontinuity to zero as a simplifying assumption. Neural networks provide an efficient parameterization for scattering amplitudes, offering a flexible toolkit to describe their fine nonperturbative structure. Combined with the bootstrap approach based on the dispersive representation of the amplitude and machine learning's gradient descent algorithms, they offer a new method to explore the space of consistent S-matrices. We derive bounds on the values of the first two low-energy Taylor coefficients of the amplitude and characterize the resulting amplitudes that populate the allowed region. Crucially, we parallel our neural network analysis with the standard S-matrix bootstrap, both primal and dual, and observe perfect agreement across all approaches.