Selection rules for the S-Matrix bootstrap

TL;DR

This paper explores the space of allowed S-matrices in pion scattering using a numerical bootstrap approach, identifying regions consistent with experimental data and connecting classical models like Lovelace-Shapiro.

Contribution

It applies the numerical S-matrix bootstrap to pion scattering, revealing correlations between Regge trajectories and scattering quantities, and links classical string models to the allowed S-matrix space.

Findings

Identified regions with S-matrices matching low-energy scattering data.

Found linearity in Regge trajectories correlates with reduced scattering and entanglement.

Connected Lovelace-Shapiro model line with allowed S-matrix regions.

Abstract

We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. We also study the line of minimum averaged total cross section in the Adler zeros' plane. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.