Towards a unified theory of mesons and baryons

Abstract

In this review we report on advances in topological soliton models of the nucleon. In chapter I we construct an effective lagrangian of QCD with the low mass mesons ($π,ρ,A_1$ and the scalar meson $ε$) generalising the Skyrme model. The vector meson fields are introduced as massive gauge fields in the linear sigma model and we look for topological soliton solutions of the model. The results for the nucleon-nucleon interaction show that the scalar degrees of freedom give rise to attractive intermediate range forces. This is in sharp contrast to models incorporating vector degrees of freedom where only repulsive forces are found. In chapter II we evaluate the leading correction to the classical Skyrmion mass. The main ultraviolet divergence is cancelled by well known chiral counterterms. The low energy behaviour of the phase shifts which are large and positive dominates the result. As a consequence, the correction is found to be negative and rather large, of the order of 1 GeV for the original Skyrme model. We then show that the situation improves if one introduces higher chiral orders in the effective lagrangian. The problem of the stability of topological solitons when vector fields enter the chiral