Chiral model for nucleon and delta

Abstract

We propose a model of the nucleon and delta based on the idea that strong QCD forces on length scales \ensuremath{\sim}0.2--1 fm result in hidden chiral SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) symmetry and that there is a separation of roles between these forces which are also responsible for binding quarks in hadrons and the forces which produce absolute confinement. This leads us to study a linear \ensuremath{\sigma} model describing the interactions of quarks, \ensuremath{\sigma} mesons, and pions. We have solved this model in the semiclassical (mean-field) approximation for the hedgehog baryon state. We refer to this solution as a chiral soliton. In the semiclassical approximation the hedgehog state is a linear combination of N and \ensuremath{\Delta}. We project this state onto states of good spin and isospin to calculate matrix elements of various operators in these states. Our results are in reasonable agreement with the observed properties of the nucleon. The mesonic contributions to ${g}_{A}$ and \ensuremath{\sigma}(\ensuremath{\pi}N) are about two to three times too large, suggesting the need for quantum corrections.