Pion-Field Theoretical Description of the Delta^{++}(1236)-Resonance without QCD

TL;DR

This paper develops a meson field theory approach to describe the Delta++(1236) resonance without relying on QCD, using strong-coupling methods to reproduce pion-nucleon scattering results.

Contribution

It introduces a nonlinear transformation method to analyze pion-nucleon resonance scattering within a strong-coupling meson field theory, extending previous models.

Findings

Successfully reproduces lowest pion-nucleon resonance scattering data

Uses same parameters as those for nucleon-nucleon potential

Provides a framework for future extended studies

Abstract

Excited states of the nucleon were predicted by Wentzel already in 1940. Wentzel showed that such kind of states can be derived from models of meson field theory if they are treated above a certain coupling strength. In particular for a pseudo-scalar meson field theory such kind of states were derived by Pauli and Dancoff in 1942 with equal amount of spin and isospin. They can be understood as arising from excitation of the pionic cloud of the nucleon by which the main part of nuclear forces also is coming out. The excitation of these states also is the mechanism by which the pion-nucleon resonance scattering is originated which firstly was experimentally discovered by Fermi in 1955. In the following contribution a completion of the method of Wentzel and Pauli & Dancoff is sketched following a work of the author and treating the pion-nucleon resonance scattering. By means of a canonical and nonlinear transformation of variables the original meson field is split into a free meson part and a self field part of the nucleon. The transformation is defined such that the interaction between the compound nucleon system thus arising and the free mesons vanish in the case of infinitely strong coupling. The solution of this field splitting problem is presented and the problem of calculating the pion-nucleon resonance scattering from this strong-coupling theory is treated on this basis. Numerical results obtained from such a calculation are discussed. For the sake of simplicity the symmetric pseudoscalar fixed-and-extended-source meson field theory is used and found that the lowest pion-nucleon resonance scattering is quite well reproduced with essentially the same parameters necessary to reproduce the nucleon-nucleon-potential. The present investigation will serve to guide more extended considerations in this direction.