Bootstrap and the physical values of $\pi N$ resonance parameters

TL;DR

This paper develops a formalism for strong interaction scattering theory, applying it to pion-nucleon scattering, testing sum rules, estimating coupling constants, and showing good agreement with experimental data, supporting the scheme's validity.

Contribution

It introduces a practical application of the formalism to pion-nucleon scattering, including sum rule tests and parameter estimations, demonstrating the approach's effectiveness.

Findings

Sum rules are numerically satisfied within the model.

Tensor and vector $NN ho$ coupling constants are estimated.

Low energy coefficients agree with experimental data.

Abstract

This is the 6th paper in the series developing the formalism to manage the effective scattering theory of strong interactions. Relying on the theoretical scheme suggested in our previous publications we concentrate here on the practical aspect and apply our technique to the elastic pion-nucleon scattering amplitude. We test numerically the pion-nucleon spectrum sum rules that follow from the tree level bootstrap constraints. We show how these constraints can be used to estimate the tensor and vector $NN\rho$ coupling constants. At last, we demonstrate that the tree-level low energy expansion coefficients computed in the framework of our approach show nice agreement with known experimental data. These results allow us to claim that the extended perturbation scheme is quite reasonable from the computational point of view.