Selection rules for the S-Matrix bootstrap

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 Sand 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. Copyright A. Bose et al.

Automated summary

In this study, the allowed space of S-matrices on the Adler zeros' plane is examined using a numerical S-matrix bootstrap program for pion scattering. The study focuses on two physical quantities, the averaged total scattering cross-section, and the averaged entanglement power. The emerging linearity in the leading Regge trajectory is found to be correlated with a reduction in these quantities, and two potentially viable regions with decent agreement with low energy scattering lengths are identified.