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

Abstract

Excited states of the nucleon were predicted by Wentzel [1] 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 [2] 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 [3] in 1955. This connection was confirmed by Wentzel in 1975 on occasion of his decoration with the Max-Planck-Medal of the German Physical Society. On the other hand there has been the development of the particle physics leading to the concept of the quark model by Gell-Mann and Zweig. Attempts to incorporate the excited nucleon states of Wentzel, Pauli & Dancoff and Fermi into the quark model show that this would require to introduce a new degree of freedom to which the name "colour" has been given and which is not needed in the case of the excited nucleon states of Wentzel and Pauli & Dancoff. Moreover it has been stated by Thomas Walcher [4] that simple observables of the hadrons as mass, spin and magnetic moment cannot be derived from the quantum colour dynamics (QCD) and the same is true for the nuclear forces. Thus genuine field theoretical methods of strong coupling had to be developed in order to be able to derive the pion-nucleon resonance scattering from a model of pion field. In the following contribution a completion of the method of Wentzel and Pauli & Dancoff is sketched following a work of the author [6] 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.