Selection rules for the S-Matrix bootstrap

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