Gluonic interactions in the soliton bag model

Abstract

Gluonic effects are included to lowest order in calculations using the soliton bag model. The N-Δ splitting is calculated in the one-gluon-exchange approximation, using a gluon propagator which is confined by the σ field. The string constant is obtained, in the Abelian approximation, from a self-consistent calculation for a cylindrical system of σ and gluon fields. These results are used to fix the strong coupling constant ${\alpha }_s$. We obtain values for ${\alpha }_s$ which are ∼2, similar to those in the MIT bag model. Constraints are placed on both the model parameters and the dependence of the dielectric function on the σ field.