Reconstructing $S$-matrix Phases with Machine Learning

TL;DR

This paper demonstrates that machine learning can accurately reconstruct $S$-matrix phases from their modulus, providing insights into unitarity constraints and revealing new phase-ambiguous solutions.

Contribution

The study introduces machine learning methods to reconstruct $S$-matrix phases from modulus data and uncovers novel phase-ambiguous solutions beyond previous limits.

Findings

Machine learning accurately reconstructs phases when they exist.

Loss function correlates with unitarity consistency.

Discovery of new phase-ambiguous solutions beyond known bounds.

Abstract

An important element of the $S$-matrix bootstrap program is the relationship between the modulus of an $S$-matrix element and its phase. Unitarity relates them by an integral equation. Even in the simplest case of elastic scattering, this integral equation cannot be solved analytically and numerical approaches are required. We apply modern machine learning techniques to studying the unitarity constraint. We find that for a given modulus, when a phase exists it can generally be reconstructed to good accuracy with machine learning. Moreover, the loss of the reconstruction algorithm provides a good proxy for whether a given modulus can be consistent with unitarity at all. In addition, we study the question of whether multiple phases can be consistent with a single modulus, finding novel phase-ambiguous solutions. In particular, we find a new phase-ambiguous solution which pushes the known limit on such solutions significantly beyond the previous bound.